انشاءات معدنية

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April 2020
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 ‫א‬‫א‬‫א‬ ã¹]
 ‫א‬

٢١١

  

 ٢١١

 ‫א‬

 ‫א‬

 

 W،،‫א‬‫א‬،‫א‬



‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬ ‫א‬  ،‫א‬   ‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬        ،‫א‬ ‫א‬‫א‬   ‫א‬  ‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬   ‫א‬    ،   ‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬      ‫א‬  ‫א‬   ،‫א‬     K‫א‬‫א‬،‫א‬‫א‬  ‫א‬ ?   ?  ?  ‫א‬ ? ‫א‬‫א‬    K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ،‫א‬،‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬     W    ‫א‬ ‫א‬  ‫א‬    ‫א‬  K‫א‬



 ‫א‬‫א‬‫א‬‫א‬













  

 ٢١١

 ‫א‬

 ‫א‬

 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬KKK ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬، ،‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬   ‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬ ‫א‬،‫א‬‫א‬،‫א‬‫א‬‫א‬ ‫א‬‫א‬ ‫א‬  ‫א‬‫א‬‫א‬

 K‫א‬‫א‬

‫א‬ ‫א‬  ‫א‬

 W‫א‬K‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬ •



‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬ K‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •

‫א‬ ‫א‬‫א‬‫א‬   ‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬  ‫א‬‫א‬ ‫א‬    ‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬ ã¹]
‫א‬

‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬

١

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬   W‫א‬‫א‬  W‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬ •



K٪100‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬   W‫א‬‫א‬  K٨

  W‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬ • 

 W‫א‬‫א‬  K‫א‬‫א‬

-١-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

‫א‬‫א‬‫א‬  .١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬ ‫א‬   ‫א‬ ‫א‬  ‫א‬   ‫א‬     ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬

‫א‬  ‫א‬ ‫א‬  ‫א‬  ‫א‬  ‫א‬  ‫א‬   ‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬  K‫• א‬



K‫א‬‫א‬‫• א‬ K‫• א‬

K‫א‬‫א‬ •

K‫א‬KKK‫א‬‫• א‬ Areas of using steel in structures

‫א‬‫ א‬‫ א‬‫ א‬ .2  W‫א‬‫א‬‫א‬ 

Bridges ‫ א‬.١٫٢

‫א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬Trusses

‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K

-٢-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

‫א‬‫ א‬.2.٢

 W١٫١‫א‬ 

‫א‬،1.1‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ Skyscrapers‫א‬‫א‬

 K‫א‬

Cranes ‫ א‬.3.2

  ‫א‬ ‫א‬ ‫א‬  ‫א‬  ‫א‬ ‫א‬   ‫א‬ 

‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬       ‫א‬ ‫א‬  ‫א‬ ‫א‬  ‫א‬ ‫א‬ ‫א‬ ‫א‬‫א‬

 K

-٣-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

 Halls‫ א‬.4.2 

 :٢٫١‫א‬ 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K(2.1‫א‬F‫א‬‫א‬‫א‬

 Tunnels ‫ א‬.5.2

 ‫א‬    K‫א‬‫א‬   ‫א‬ ‫א‬  ‫א‬  

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 

 Power Transmission Towers‫א‬‫א‬‫א‬.6.2

 K‫א‬‫א‬‫א‬‫א‬

-٤-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

Tanks‫א‬‫ א‬.7.2

  ‫א‬‫א‬   ‫א‬ ‫א‬  ‫א‬ ‫א‬‫א‬   ‫א‬ 

 K‫א‬‫א‬‫א‬‫א‬ 



Pipe line‫א‬ .8.2

‫א‬‫א‬‫א‬‫א‬‫א‬  K 

 Piles and Sheet Piles

‫א‬‫א‬‫א‬‫א‬‫ א‬.9.2

‫א‬‫א‬‫א‬‫א‬screw piles ‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬Cofferdams‫א‬‫א‬‫א‬‫א‬sheet piles ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬ 

 ‫א‬‫א‬‫א‬‫ א‬.10.2  K‫א‬‫א‬‫א‬‫א‬‫א‬ 

Structural Analysis and Design ‫א‬‫א‬‫א‬.٣ ‫א‬K‫א‬ ‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬ ‫א‬K‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬K ‫א‬‫א‬‫א‬

 W‫א‬‫א‬

 KGeneral Layout of Structures ‫א‬‫א‬‫• א‬

‫א‬‫א‬‫א‬ • K

K‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬EF‫א‬ • -٥-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫• א‬ K‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫• א‬ K‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫• א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 

SI UNITS ‫א‬‫א‬‫ א‬.٤ ، ‫א‬‫א‬‫א‬‫א‬ ،EKilogram, KgFEF‫א‬‫א‬،EMeter, mFEF‫א‬W‫א‬

1.1‫א‬K‫א‬ENewton, NFEF،(Seconds, S) EF‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬٢{١‫א‬،  ‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬ 

 ‫א‬‫א‬‫א‬‫ א‬:١٫١ ‫א‬ E٢F‫א‬

 ‫א‬

Square meter (m2)

Area

 ‫א‬‫א‬

2

Meter per Second squared (m/s )

 EF‫א‬‫א‬‫א‬ 2

Kilogram-meter per second squared (Kg-m/s )=Newton (N)

 ‫א‬Z‫א‬

Newton per squared meter (N/m2) = Pascal

‫א‬

Acceleration

 ‫א‬

 Force

 ‫א‬ Stress

 -٦-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬:٢٫١ ‫א‬ ‫א‬‫א‬‫א‬  1 in.

‫א‬‫א‬‫א‬

= 25.400 mm = 0.25400 m = 645.16 mm2 = 6.451600 x 10- 4 m2

  1 in2.

= 304.800 mm = 0.304800 m

 1 ft.

 Z4.44822 N

 1 lb.

= 4448.222N = 4.448222 KN

 1 Kip

1 PSI (Pounds per square inch)

 L 1 PSF (pounds per square foot)

 L

1 KSI (Kips per square inch)

 L



=6.894757 Kn/m2=0.006895 Mn/m2=0.006895 N/mm2 = 47.880 N/m2 = 0.047800 Kn/m2 = 6.894757 Mn/m2= 6.894757 MPa

Steel structures characteristics ‫א‬‫א‬‫א‬ .٥  W‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬ •

‫א‬‫א‬  ‫א‬‫• א‬ K‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫• א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫• א‬ ‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬ •

 ‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬

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 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬Ductility‫• א‬ K‫א‬

‫א‬‫א‬Elastic Limit‫א‬ • K‫א‬‫א‬‫א‬

K‫• א‬  ‫א‬‫א‬‫א‬‫א‬ .٦  W‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬ • ‫א‬‫א‬‫א‬‫א‬

 K

٥٠٠‫א‬‫א‬ • ‫א‬‫א‬١٢٠٠  K‫א‬‫א‬‫א‬٣‫א‬

  ‫א‬‫א‬ .٧ ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ 0.3%0.1%‫א‬‫א‬‫א‬

Fu‫א‬‫א‬‫א‬‫א‬

 K٢L37(Fu)‫א‬‫א‬‫א‬‫א‬37‫א‬ 

 W‫א‬‫א‬‫א‬

 Wrought Iron E‫א‬WF‫א‬‫• א‬

0.1% ‫א‬

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 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

 Pig IronE‫א‬F • ‫א‬‫א‬‫א‬٪4٪2‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬  Cast IronE‫א‬F‫א‬ •



 K‫א‬‫א‬4%2%‫א‬  Steel‫א‬‫• א‬



 K2%‫א‬‫א‬ 

  .٨ ‫א‬ ‫א‬‫א‬‫א‬

Web Plate‫א‬‫א‬‫א‬Gusset Plate  W KE٣٫١‫א‬FK‫א‬‫א‬‫א‬‫א‬‫א‬WWeb ‫• א‬



K‫א‬‫א‬‫א‬: Flange ‫• א‬

K‫א‬‫א‬‫א‬WGusset Plate‫א‬ • KAngle‫א‬‫א‬WLeg ‫• א‬

K‫א‬WPitch‫• א‬

K‫א‬‫א‬‫א‬WClearance‫• א‬ K‫א‬PlateWFiller‫• א‬



-٩-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬



 ٢١١

 ‫א‬

 ‫א‬

 



 ‫א‬‫א‬‫א‬:٣٫١‫א‬ AISC‫א‬‫א‬‫א‬‫א‬

10‫א‬W 10 x 49 ‫א‬‫א‬ ‫א‬‫א‬‫א‬E73.1F49E25.4F  K‫א‬

EWide Flange BeamF‫א‬‫א‬‫א‬‫• א‬



( ٤٫١ ‫)ا‬MEMiscellaneousFWEWideF 





 Wide flange Beam ‫א‬‫א‬:٤٫١‫א‬

-١٠-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

American Standard Beam ‫א‬‫א‬‫• א‬

(٥٫١ ‫ )א‬S (Standard) 





 American Standard Beam ‫א‬‫א‬‫א‬:٥٫١‫א‬ 

‫א‬‫א‬‫א‬‫א‬‫• א‬

American Standard Channel and Miscellaneous Channel  MC  ‫א‬‫א‬‫ א‬C (American Standard Channel)   

.(٦٫١ ‫ )א‬‫א‬‫( א‬Miscellaneous Channel)

 ‫א‬‫א‬‫א‬‫א‬‫א‬:٦٫١‫א‬

 American Standard Channel and Miscellaneous Channel

-١١-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

Angles ‫א‬‫א‬ • .( ٧٫١ ‫ )א‬L  

 Angles L Shapes(LF‫א‬‫א‬:٧٫١‫א‬

  Structural Tees T‫א‬‫א‬‫• א‬





.( 8.1 ‫( )א‬ST, WT, MT)  

Structural Tees

T ‫א‬‫א‬‫א‬:٨٫١‫א‬

-١٢-





 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

Plates and bars ‫א‬‫א‬‫• א‬

.( ٩٫١ ‫ )א‬BAR ‫ و‬PL    

  Plates and Bars

‫א‬:٩٫١‫א‬

Pipes and Structural Tubing

‫א‬‫א‬‫א‬‫• א‬



،‫א‬‫א‬ TS  .( ١٠٫١ ‫ )א‬ 

 Pipe and Structural Tubing ‫א‬:١٠٫١‫א‬

-١٣-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

Built up Sections  •

 .( 11.1 ‫)א‬‫א‬‫א‬

 ‫א‬‫א‬:١١٫١‫א‬ Structural Sections ‫א‬‫ א‬.٩ ‫א‬Rolled Steel Sections‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬١٢٫١‫א‬  Standard I-Beam ‫א‬‫א‬ EA



Channel‫א‬ EB

Tee Section

-١٤-

T EC



 ‫א‬‫א‬ ‫א‬‫א‬‫א‬



 ٢١١

 ‫א‬

 ‫א‬

 

‫א‬‫א‬:١٢٫١‫א‬ 

Plates

‫א‬‫• א‬

 K(13.1‫א‬F 

Plate

‫ﻟﻮح‬

  :١٣٫١‫א‬

-١٥-

  

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

Angles‫א‬‫• א‬

‫א‬‫א‬‫א‬‫א‬

 K(15.1 ‫א‬ 14.1‫א‬F 

60 60

6

   ‫א‬‫א‬:١٤٫١‫א‬ 



60



7 80

 

 ‫א‬‫א‬ :١٥٫١‫א‬ Channels





(‫א‬‫ )א‬‫• א‬

 K(١٦٫١‫א‬F40080‫א‬‫א‬ 



  ‫א‬ :١٦٫١‫א‬

-١٦-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

 Standard I Beam I‫א‬‫• א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬60080‫א‬‫א‬

 .( ١٧٫١‫א‬F‫א‬‫א‬‫א‬



 

: ١٧٫١‫ א‬‫א‬‫א‬I Standard I Beam

 Broad (Wide) Flange I Beam ‫א‬‫• א‬



١٨٫١‫א‬1000‫א‬‫א‬‫א‬

 K‫א‬ 



 ‫א‬‫א‬W١٨٫١‫א‬

E‫א‬F A :depth •

E‫א‬FB: Web thickness • E‫א‬FC: flange width •

-١٧-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

 K( 19.1‫א‬F Z ‫א‬‫א‬‫א‬     Z‫א‬W١٩٫١‫א‬



Cold Formed Sections‫א‬‫א‬‫• א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

KE٢٠٫١‫א‬F‫א‬‫א‬‫א‬



  

‫א‬‫א‬‫ א‬: ٢٠٫١‫א‬  ‫א‬‫א‬‫א‬.١٠ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ ‫א‬K‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬K‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬K

 ‫א‬W‫א‬‫א‬‫א‬

Elastic ‫א‬،proportional Limit ‫א‬،Yield Point E ‫א‬F

‫א‬‫א‬K‫א‬‫א‬‫א‬Limit

-١٨-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

‫ أو ﻗﺼ ﻔﺔ‬Ductile  ‫א‬‫א‬‫א‬‫א‬K ‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ .Brittle

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬ASTM‫א‬‫א‬‫א‬‫א‬K ‫א‬‫א‬ ‫א‬ 10   ‫א‬ (  1.28 )  0.505  ‫א‬

Mild Steel ‫א‬‫א‬‫א‬‫א‬.‫ﻗﻄﺮهﺎ‬ ‫א‬‫א‬‫א‬   ‫א‬‫א‬  K21.1‫א‬  K‫א‬

‫א‬‫א‬P‫א‬ 0‫א‬

 ‫א‬،‫א‬‫א‬ σ P EProportional LimitF‫א‬K‫א‬

‫א‬KE  ‫א‬‫א‬F ‫א‬

‫א‬ E‫א‬K ‫א‬‫א‬E‫א‬F‫א‬‫א‬‫א‬ .

σ e ‫א‬ P‫א‬

Residual F(Permanent DeformationF‫א‬ ‫א‬ 

‫א‬،‫א‬‫א‬EPK ‫א‬EDeformation  KE



 ‫א‬‫א‬‫א‬W21.1‫א‬ -١٩-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

‫א‬‫א‬‫א‬‫א‬YY1‫א‬‫א‬‫א‬



‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬ ‫א‬K E ‫א‬‫א‬1510‫א‬F‫א‬

‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬،‫א‬ U‫א‬

Strain Hardening‫א‬  ‫א‬‫א‬

‫א‬‫א‬ U‫א‬ . σ u .R Elastic

Ultimate Strength

‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫ א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬ Range W‫א‬‫א‬

.Plastic Range

‫א‬ 

Elasticity ‫ א‬-‫أ‬

‫א‬‫א‬‫א‬‫א‬

 W،‫א‬‫א‬‫א‬‫א‬‫א‬  E‫א‬F/E‫א‬F= ‫א‬  E‫א‬‫א‬F‫א‬/E‫א‬F= ‫א‬

Young‘s Modulus of Elasticity ‫א‬ -‫ب‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬200000 Mpa‫א‬‫א‬‫א‬210000 Mpa200000 Mpa

‫א‬‫א‬‫א‬  ‫א‬‫א‬ ‫א‬K‫א‬

‫א‬‫א‬‫א‬K‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬L‫א‬P.S.I‫א‬‫א‬‫א‬2LN/m2  W‫א‬E‫א‬‫א‬ -٢٠-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 



 E=F e

 W  ‫א‬J E  ‫א‬J F

 ‫א‬J e

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 

 e= ∆L L

 W ‫א‬‫א‬‫א‬‫א‬‫ א‬- ∆L ‫א‬‫ א‬-L



 W

 E= F = FL ∆L L

∆L Poisson’s ratio

‫א‬ -‫ﺟـ‬

‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬K ‫א‬‫א‬Transverse‫א‬

‫א‬Longitudinal Strain‫א‬‫א‬Lateral Strain‫א‬‫א‬

 K0.26 Plasticity ‫ א‬- ‫د‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K ‫א‬‫א‬‫א‬‫א‬‫א‬ 

-٢١-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

 ‫א‬ -‫هـ‬ ‫א‬‫א‬‫א‬‫א‬‫א‬

   (37) ‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬2L37 ‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬KE52F‫א‬‫א‬44‫א‬  

 

 W‫א‬ (Cast Iron)

7.2 t/m3

 7.7 t/m3 7.8 t/m3

(wrought Steel)

(Steel Rolled or cast)







‫א‬J 

 EE‫א‬F‫א‬‫א‬J 

EF‫א‬‫א‬J 

 K‫א‬‫א‬‫א‬ASTM‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 

ASTM ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬: 3.1 ‫א‬  ‫א‬

E2LF

F‫א‬ EL

‫א‬  ‫א‬

E2LF

 ‫א‬‫א‬  ELF

3999J 5515

Tensile Stress (K.S.I) 58-80

4137 4344 4620 4826

60 63 67 70

2758  2895 3172 3447

40 42 46 50

4344 4620 4826 4344 4620 4826

63 67 70 63 67 70

 2895 3172 3447  2895 3172 3447

42 46  50 42 46 50

2483

-٢٢-

Minimum Yield Stress (K.S.I) 36

  ‫א‬ A36  A441   A242  A588

 ‫א‬‫א‬‫א‬ ã¹]
‫א‬ ‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬

٢

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

 W‫א‬‫א‬  K‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬ 

 W‫א‬‫א‬  W‫א‬‫א‬‫א‬ 

‫א‬‫א‬‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬‫• א‬ ‫א‬‫א‬‫א‬‫א‬ •

‫א‬‫א‬‫א‬ •



 W‫א‬‫א‬‫א‬ K٪100‫א‬‫א‬‫א‬   W‫א‬‫א‬

 K 21 

 W‫א‬‫א‬

K‫א‬‫א‬‫א‬ • K‫א‬ • K‫א‬‫א‬ •

  W‫א‬‫א‬  K‫א‬‫א‬ -٢٣-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

 ‫א‬‫א‬‫א‬‫א‬   K١ ‫א‬ ‫א‬‫א‬‫א‬ K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫ א‬‫א‬  ‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   Loads‫א‬٢K  ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬K‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬ 

Dead Loads

‫א‬‫ א‬.1.2

‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬KKKK،،‫א‬،‫א‬،‫א‬‫א‬‫א‬E‫א‬F‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 

Live Loads ‫א‬‫ א‬.2.2

‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬K ‫א‬ ‫א‬‫א‬ECranesF‫א‬،‫א‬‫א‬EMoving LoadsF‫א‬

K‫א‬KKK، ،  ‫א‬EMovable LoadsF ،  ‫א‬‫א‬، ‫א‬، ‫א‬، ‫א‬، ‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬

-٢٤-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

 Snow and Ice Loads ‫א‬‫א‬ .3.2 ‫א‬   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K L 23.94ELF 0.5PSI ‫א‬E 2.54F

‫א‬   ‫א‬‫א‬‫א‬

E L F40  10‫א‬‫א‬K  

‫א‬E‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬K  ‫א‬

‫א‬‫א‬، ‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬

45E L F10‫א‬K ‫א‬‫א‬‫א‬

‫א‬‫א‬ ‫א‬‫א‬K ‫א‬E L F40

KE L F40   ‫א‬ ‫א‬‫א‬ K  

 K‫א‬‫א‬‫א‬ 

Traffic Loads for Bridges

  ‫א‬ .4.2

‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬ 

Impact Loads ‫א‬ .5.2

‫א‬‫א‬K  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

. ‫א‬‫א‬   

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K 

Lateral Loads () ‫א‬‫ א‬.6.2

 K‫א‬‫א‬W‫א‬‫א‬ 

-٢٥-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

Wind Loads ‫א‬ -‫أ‬

‫א‬‫א‬‫א‬;‫א‬‫א‬; ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬K ‫א‬; ‫א‬   ‫א‬‫א‬،  q = C. V 2 

 W‫א‬

 W

 E2LF‫א‬J q ‫א‬‫א‬‫א‬(Shape CoefficientF‫א‬J C  K‫א‬

 ELF‫א‬J V

‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬  W‫א‬

‫א‬20‫א‬‫א‬‫א‬2L75 •

‫א‬100J 20 ‫א‬‫א‬‫א‬2L100 •

 ‫א‬100‫א‬‫א‬‫א‬2L120 •



Earthquake Loading‫א‬–

‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬K ‫א‬‫א‬‫א‬  ‫א‬ K ‫א‬EStiffnessF EMassF‫א‬

‫א‬W ،(١{٢‫א‬F‫א‬‫א‬ ‫א‬

K  ‫א‬‫א‬‫א‬‫א‬‫א‬K ‫א‬ K ‫א‬‫א‬E‫א‬F‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 

-٢٦-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

 

‫א‬

  

‫א‬



  

 ‫א‬:١٫٢‫א‬ ‫א‬‫א‬،‫א‬‫א‬  ‫א‬

‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬ ‫א‬‫א‬

‫א‬‫א‬ ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬EF

 W‫א‬‫א‬ V  V = Z. I. K. C. S. W

 W  ‫א‬‫א‬-Z

 ‫א‬J I

 ‫א‬J K  ‫א‬‫א‬J C

 ‫א‬‫א‬J S

 ‫א‬-W

-٢٧-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

 ‫א‬،‫א‬،‫א‬٣K  W‫א‬‫א‬‫א‬

‫أو‬‫א‬‫א‬،   ‫א‬‫א‬،‫א‬‫א‬‫א‬‫ א‬-‫أ‬

‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬

  ‫א‬‫א‬،EWorking StressF‫א‬‫א‬EAllowable StressF‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬

(Hook's LawF‫א‬ ،‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬K ‫א‬

‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬  K‫א‬‫א‬‫א‬‫א‬ 

‫א‬  ‫א‬‫א‬‫א‬‫ א‬J   K ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬

Load and resistance F‫א‬‫א‬ELoad factor designF‫א‬

 K(Limit States DesignF‫א‬‫א‬،Efactor design  ‫א‬‫א‬‫א‬‫א‬‫א‬  American Institute of Steel Construction, AISC‫א‬‫א‬‫א‬K W‫א‬‫א‬‫א‬‫א‬‫א‬ ‫ م‬1.4 • (‫ )س أو ث أو ط‬0.5 + ‫ ح‬1.6 + ‫ م‬1.2 • ( ‫ ر‬0.8 ‫ ح أو‬0.5) + (‫ )س أو ث أو ط‬1.6 + ‫ م‬1.2 • (‫ )س أو ث أو ط‬0.5 + ‫ ح‬0.5 + ‫ ر‬1.3 + ‫م‬1.2 • ( ‫ ث‬0.2 ‫ ح أو‬0.5) + ‫ ز‬1.5 + ‫ م‬1.2 • ( ‫ ز‬1.5 ‫ ر أو‬1.3) - ‫ م‬0.9 • -٢٨-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

W .‫א‬‫א‬‫א‬‫א‬‫א‬‫م ـ א‬ .‫א‬‫א‬‫א‬‫א‬‫א‬‫ح ـ א‬ .‫א‬‫س ـ א‬  K‫א‬ .‫א‬ ‫ز ـ‬  K‫א‬  ‫א‬‫א‬4K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬K  K‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬ K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K(٢٫٢‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬



( ‫)ب‬



(‫)أ‬

 EFEFW٢٫٢‫א‬ ‫א‬‫א‬E F‫א‬

  ،EM=P.eF‫א‬‫א‬‫א‬‫א‬‫א‬(P/AF‫א‬‫א‬

  EM/ZF‫א‬‫א‬‫א‬‫א‬‫א‬e  K(٣٫٢‫א‬F‫א‬Z -٢٩-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬



 ٢١١

 ‫א‬

 ‫א‬

 

 ‫א‬W٣٫٢‫א‬ 

 W‫א‬‫א‬‫א‬‫א‬  f = P + Mc A

I

 K‫א‬‫א‬‫א‬‫א‬‫א‬ 

fa fb + ≤1 Fa F b

 W‫א‬  P A + Mc I ≤ 1 Fa

F b

 W  K‫א‬‫א‬‫א‬J Fa  K‫א‬‫א‬J Fb  K‫א‬‫א‬J f a  K‫א‬J f b    -٣٠-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

 Tension Members‫א‬.5 ‫א‬F‫א‬‫א‬EF‫א‬‫א‬

 KE٥{٢‫א‬K٢4  

 ‫א‬W٤٫٢‫א‬ 

 ‫א‬W٥٫٢‫א‬

•

 ‫א‬‫א‬

A L‫א‬ ‫א‬‫א‬  K٦{٢‫א‬ 

E,A

 

P P

L e

 W٦٫٢‫א‬

-٣١-

   

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

P  ‫א‬ e  ‫א‬‫א‬‫א‬

  ‫א‬‫א‬‫א‬ ( f = P ) f  ‫א‬ ( ε = e )  ‫א‬ ‫א‬ A

L

 W‫א‬‫א‬   e = PL EA

 W

 Young's Modulus of Elasticity ‫א‬‫א‬ -E 

Yield Stress‫א‬‫א‬‫א‬‫א‬  KYield Load ‫א‬ 

 Py = A.Fy

 W  ‫א‬-A  ‫א‬J Fy

 ‫א‬J Py 

‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬،(Strain HardeningF‫א‬ 

Pu = A. Fu





 W  Ultimate Load ‫א‬‫ א‬- Pu

Ultimate Tensile Stress of the Steel ‫א‬‫א‬ -Fu



-٣٢-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

P‫א‬ENecks downF‫א‬‫א‬‫א‬  KEFractureF‫א‬ 

 ‫א‬‫א‬‫א‬‫א‬‫א‬  WEAnetF 

 σ t = N ≤ σe A net 

 W‫א‬ 

 A net = N ≤ σ e σt  W  (Tension StressF2L‫א‬W

σt

 ETension LoadF‫א‬EFW

N

 ENet AreaF‫א‬‫א‬W Anet σe (Elastic Stress Limit) ‫ ﺣﺪ إﺟﻬﺎد اﻟﻤﺮوﻧﺔ‬:

‫א‬‫א‬‫א‬‫א‬Rivet Holes‫א‬  K‫א‬ A net = A Gross - ∑ d.e

: ‫ﺣﻴﺚ إن‬ (Gross Area) ‫א‬‫ א‬:

(Diameter of the Rivet) ‫א‬ :

(Thickness of the member) ‫א‬ : -٣٣-

A Gross d

e

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

 Compression Members‫א‬.٦ ‫א‬‫א‬EF‫א‬‫א‬  KE٧{٢ ‫א‬F‫א‬

  ‫א‬W٧٫٢‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬ (Slenderness RatioF‫א‬‫א‬EBucklingF‫א‬ E ‫א‬‫א‬FL‫א‬‫א‬‫א‬  KE٨{٢‫א‬FERadius of gyrationFr‫א‬



  ‫א‬‫א‬W٨٫٢‫א‬ 

Elastic Buckling‫א‬‫• א‬

‫א‬‫א‬‫א‬‫א‬

 K(٩{٢‫א‬F‫א‬‫א‬‫א‬‫א‬‫ א‬ (Slenderness RatioF -٣٤-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 



P

P

  ‫א‬‫א‬W٩٫٢‫א‬ 

‫א‬‫א‬‫א‬‫א‬  W  Euler Formula  •



‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬

 WCrippling Load‫א‬K

 P=

π2 E I L2

 W  ‫א‬W  I

 ‫א‬‫א‬W  L

 I = A.r 2 W

 W‫א‬‫א‬‫א‬‫א‬

-٣٥-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

 P=

π2 E A r2 L2



2 P =f = π E A c (L/r) 2

 W Crippling Stress ‫א‬‫ א‬:

 Slenderness Ratio ‫א‬W ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬

fc L r 

 ،‫א‬‫א‬



2 π E = 2 (L/r) 2

F y

 2 2π E L  = r F y









W

، Cc  L/r 

 Cc =

2 2π E F y

 126.1 A36   Cc  ‫א‬،‫א‬ Cc    K107.6E50 K.S.IF

‫א‬،‫א‬‫א‬‫א‬‫א‬ KL/r ≥ C c  ‫א‬‫א‬،

 K‫א‬‫א‬‫א‬‫א‬ KL/r < Cc ‫א‬

:  Fa  AISC ‫א‬‫א‬‫א‬ -٣٦-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

 InelasticBuckling ‫א‬‫• א‬  ،‫א‬‫א‬‫א‬

Fa =

⎡ 2⎤ ⎢1 − (KL/r) ⎥ F ⎥ y ⎢ 2C c2 ⎥⎦ ⎢⎣

Fs

Factor of Safety ‫א‬FsW

 W‫א‬‫א‬ 

3

3 (K.L /r) (K.L/r)  F.S = 5 + 8 Cc

3

8 C3c



 ‫א‬‫א‬ (KL/r) =Cc،Fs = 1.67(KL/r) = 0  

Fs = 23/12 = 1.92

Elastic Buckling ‫א‬‫• א‬



Euler Equation ‫א‬‫א‬  Fa =

 F.S = 5 + 3

 W‫א‬‫א‬‫א‬‫א‬‫א‬ π2 E

(L/r) 2 . Fs

3 (K.L /r) (K.L/r)3 8 Cc 8 C3c

 W‫א‬

L/r‫א‬Slenderness ratio ‫א‬ • ‫א‬،‫א‬‫א‬‫א‬ C c  W‫א‬

،(KL/r) <Cc‫• א‬ -٣٧-



 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

 Effective length factor ‫א‬‫א‬KF،(KL/r) ≥ Cc‫• א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬



 FPb ‫א‬‫א‬‫א‬‫א‬ 

  K14 ft.‫א‬W 12 x 72‫א‬‫א‬‫א‬‫א‬‫א‬

:

 KA36‫א‬K‫א‬‫א‬‫א‬ :‫א‬

radii F‫א‬‫א‬‫א‬،‫א‬AISC‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬،Eof gyration

Fy = 36000 P.S.I،E = 29000 K.S.I،ry= 5.31 in. ،rx= 5.31 in. ،A = 21.1 in.



 W‫א‬‫א‬ C c    Cc =

2 2π E F y

2 2 π 2900

=

36

= 126.1

  (KL/r)= 55.3 =

1 (14) 12 ،‫א‬ 3.04

  W‫א‬‫א‬Fs‫א‬ 

(55.3)3 3 (K.L /r) (K.L/r)3 5 3 (55.3) = + − = 1.82  F.S = 5 + 3

8 Cc

8 C3c

3

 -٣٨-

8 (126.1) 8 (126.1)3



 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

 W‫א‬‫א‬ 



2 ⎤ ⎡ ⎡ 2⎤ (55.3) (KL/r) ⎢1 − ⎥F ⎥.36000 y ⎢1 − 2 2 ⎢ ⎥ 2C c ⎦ ⎢ 2 . (126.1) ⎥⎦ Fa = ⎣ =⎣ = 17900 P.S.I  F s



1.82

   W‫א‬‫א‬‫א‬‫א‬‫א‬ P = Fa . A = 17900 . (21.1) = 377000 Kips

 KEAISCF‫א‬‫א‬‫א‬‫א‬‫א‬  KEAISCF‫א‬‫א‬‫א‬‫א‬‫א‬W١{٢‫א‬ 

-٣٩-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 





 Bending Moments ‫א‬٧K ‫א‬ ‫א‬W‫א‬‫א‬ AB‫א‬‫א‬‫א‬K ‫א‬  ‫א‬‫א‬

‫א‬‫א‬ KE١٠٫٢‫א‬FCD ‫א‬‫א‬‫א‬‫א‬E١٠٫٢‫א‬FKE١٠٫٢‫א‬F

 ‫א‬‫א‬‫א‬‫א‬‫א‬

-٤٠-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

  K‫א‬CDAB‫א‬WEF١٠٫٢‫א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬،‫א‬

K  ‫א‬‫א‬‫א‬‫א‬‫א‬

  ‫א‬‫א‬ ‫א‬‫א‬  ،

،NS‫א‬Neutral Surface ‫א‬‫א‬‫א‬K‫א‬  KNeutral Axis‫א‬‫א‬‫א‬‫א‬‫א‬ 



 ‫א‬‫א‬‫א‬‫א‬WEF١٠٫٢‫א‬

 CDAB‫א‬WEF١٠٫٢‫א‬ -٤١-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

‫א‬ ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬

‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬  ‫א‬‫א‬  K‫א‬‫א‬

 W  ENeutral SurfaceF‫א‬‫א‬-R  K‫א‬‫א‬‫א‬-L

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬-Y

 K‫א‬‫א‬Y‫א‬‫א‬E‫א‬F‫א‬J  ε 

 ‫א‬‫א‬‫א‬  R = R+Y L L+εL R (L + ε L) = L(R + Y)





R L+RεL= R L+LY

 RεL= LY

  

Y W R  f ε = W E

  ε = 

-٤٢-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

 W  ‫א‬J f

 ‫א‬-E EY f Y  f = ، = R E R  ‫א‬K  ‫א‬،‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬K ‫א‬‫א‬‫א‬ ‫א‬‫א‬  ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬  ‫א‬ •  W‫א‬‫א‬‫א‬

 M= f I Y

 W

 E I = ∑ Y 2 dA F‫א‬ -I

 ‫א‬-A  ‫א‬-M

 ‫א‬J f

‫א‬‫א‬‫א‬‫א‬‫א‬  M = f I W‫א‬،Y=CC C  M ‫א‬‫א‬‫א‬ f ‫א‬‫א‬ R b f

 M R = b I W‫א‬‫א‬‫א‬ C  Section Modulus ‫א‬ I ‫א‬ C  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

f I  M = b ‫؛‬ f b = M C ‫؛‬ I = M C I C f b

-٤٣-



 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

: ١  ‫א‬W 16 x 36  ‫א‬‫א‬

KA36 ‫א‬ f = 0.6 f ‫א‬‫א‬‫א‬١١٫٢ Y b 1000 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬lb/ft  1000 lb/ft

  

28 in

   

 W١١{٢‫א‬ 



I = 56.5 in 3 W 16 x 36 C   f = 0.6 F Z0.6 (36000) = 22000 P.S.I Y b M = f . S = 22000 x 56.5 = 1240000 in-lb b M = 103 000 ft-lb



1000 + 36 = 1036 lb/ft

:‫א‬‫א‬

 W‫א‬‫א‬‫א‬ W L2 1036 . (28) 2 M= = = 102000 ft-lb 8 8

 K‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬  -٤٤-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

M 102000 x 12 = 21700 P.S.I f = = b S 56.5

‫א‬21700 P.S.I ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K22000 P.S.I

Bending members about two axes‫א‬‫א‬.8

K ‫א‬‫א‬‫א‬

‫א‬‫א‬ ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬K١٢{٢‫א‬  K١٣{٢‫א‬‫א‬ 





 W١٢{٢‫א‬

‫א‬W١٣{٢‫א‬

-٤٥-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬  W‫א‬‫א‬‫א‬ 

f =



M C M x Cx Y Y ± I Ix Y

 W

X-X‫א‬‫א‬‫א‬‫א‬J M x X-X‫א‬‫א‬J  I x X-X‫א‬f‫א‬X-X‫א‬‫א‬J C

X

Y-Y‫א‬‫א‬‫א‬‫א‬J M

Y Y-Y‫א‬‫א‬J  I Y  Y-Y‫א‬f‫א‬Y-Y‫א‬‫א‬J C Y ‫א‬‫א‬ K‫א‬‫א‬ K١٤٫٢‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬

‫א‬‫א‬،‫א‬‫א‬‫א‬

 K‫א‬ETorsionF‫א‬ETwistingF 

‫א‬‫א‬‫א‬‫א‬ WY ( Load ComponentF‫א‬ ‫א‬‫א‬ WX ‫א‬‫א‬K ‫א‬ ‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬K W ‫א‬EFlexural StressF‫א‬‫א‬‫א‬ X ‫א‬،Y-Y‫א‬‫א‬‫א‬E‫א‬F‫א‬  W‫א‬‫א‬‫א‬K I ‫א‬ Y  f=

M

C M C X X± Y Y I I /2 X Y -٤٦-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

 I ‫א‬‫א‬،‫א‬‫א‬   ‫א‬‫א‬ C

C C  KE Y  X F I

Y

I

X

‫א‬‫א‬W١٤{٢‫א‬ 

: 

‫א‬K EGirdersF14‫א‬‫א‬W 8 x 18 ‫א‬

K‫א‬‫א‬15‫א‬‫א‬‫א‬K‫א‬‫א‬300 lb/ft ‫א‬

‫א‬F f = 23800 P.S.I  ‫א‬‫א‬ ‫א‬‫א‬ b  KE١٦٫٢١٥٫٢ : ‫א‬

X-X‫א‬‫א‬‫א‬‫א‬‫א‬

 KY-Y

290 lb/ftZ15300Z WX  77.6 lb/ftZ15300Z WY  W‫א‬‫א‬‫א‬،X-X‫א‬‫א‬ -٤٧-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

WX L2 290 x 14 2  MX = = = 7110 ft - lb 8 8 



 W١٥{٢‫א‬ 

 W‫א‬‫א‬‫א‬،Y-Y‫א‬‫א‬ WY L2 77.6 x 14 2  MY = = = 1900 ft - lb 8 8 ‫א‬  ‫א‬‫א‬‫א‬ ‫א‬‫א‬

M M 7110 (12) 1900 (12)  f = X+ Y = + b SX SY 15.2 1.52 

2

f = 20613 P.S.I < 23800 P.S.I b

-٤٨-



 W‫א‬

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

EA‫א‬F‫א‬‫א‬‫א‬‫א‬  K‫א‬ 



 KEGirdersFW١٦{٢‫א‬ 

 ‫א‬‫א‬‫א‬٩K ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬،‫א‬ ‫א‬ ‫א‬‫א‬  f =± P ± Mc I A

 W‫א‬‫א‬  W  ‫א‬‫א‬–P

 ‫א‬

J A

 ‫א‬-M

 ‫א‬ J I

 ‫א‬f‫א‬‫א‬‫א‬J c 

 -٤٩-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

P M

M

 

 P

 ‫א‬W17.2‫א‬  ‫א‬‫א‬‫א‬١٠ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬  W‫א‬‫א‬‫א‬

P Mx MY  f = ± A ± Z ± Z ≤1 x Y





 ‫א‬‫א‬‫א‬‫א‬‫א‬  f Tot. 

 W‫א‬‫א‬‫א‬

 f = f a + f bx + f by < f Tot.

-٥٠-



 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

 W

 E P = F‫א‬‫א‬J f a A X‫א‬‫א‬J f bx Y‫א‬‫א‬J f by 

 Shear Stress Members‫א‬‫א‬‫א‬١١K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ K ‫א‬

K‫א‬‫א‬‫א‬‫א‬ ‫א‬K‫א‬‫א‬

‫א‬‫א‬K ‫א‬‫א‬EF١٨٫٢ ‫א‬  ‫א‬‫א‬ . 2-21-1‫א‬‫א‬  Kdx‫א‬‫א‬ 

 ‫א‬‫א‬WEF١٨{٢‫א‬ 

2-2 1-1‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬  ‫א‬‫א‬KEF١٨٫٢‫א‬

 Kdx‫א‬‫א‬

-٥١-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 



 ‫א‬WEF١٨{٢‫א‬ ‫א‬‫א‬M2M1‫א‬‫א‬2-21-1‫א‬

 KEF١٨{٢‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬EF١٨‫א‬ M1  M2  ‫א‬‫א‬ C 2  C1  b.dx‫א‬H‫א‬‫א‬  C 2 - C1 = H = v (b) dx 

 W‫א‬‫א‬‫א‬

 W‫א‬



 C 2 - C1 =

M 2 - M1 ∑ y dA I

-٥٢-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

 W‫א‬‫א‬‫א‬‫א‬‫א‬ 

 V = dM dx

 W‫א‬‫א‬‫א‬‫א‬‫א‬ ∑ y dA ‫א‬  fv =

V.Q b.I

 W

٢b١٩٫٢‫א‬‫א‬  

WNA،٣،٢،١‫א‬‫א‬Q‫א‬‫א‬

 ‫א‬‫א‬ :١٩٫٢ ‫א‬ Q1 = 2(1) .3.5 = 7 in.3 Q2 = 2(2) .3 = 12 in.3 Q3 = 2(3) .2.5 = 15 in.3 QNA = 2(4) .2 = 16 in.3

‫א‬٨٥{٥in.٤Ebh3L١٢F‫א‬‫א‬

‫א‬‫א‬‫א‬٥٠kipsV‫א‬ v = V . Q ‫א‬ I.b

‫א‬‫א‬‫א‬ ‫א‬  ‫א‬K١٩‫א‬  W‫א‬‫א‬ 

-٥٣-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

 v = V.Q = V(b) (h/2) (h/4) b (bh 3/12)

b.I

 W،‫א‬‫א‬ bh = A ‫א‬ 

 v = V.Q = V(b) (h/2) (h/4) b (bh 3/12)

b.I

  ‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬ 3/2  K‫א‬‫א‬

AW‫א‬V‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬ 

 Fv = V

Aw



   ‫א‬‫א‬Fv‫א‬‫א‬‫א‬‫א‬‫א‬  

EFy= 36 k.s.iFA36‫א‬‫א‬K‫א‬Fy٠{٤Fy  K٠{٤ Fy= 14.4 k.s.i‫א‬‫א‬

-٥٤-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 

   Fv‫א‬‫א‬‫א‬،S 10 x 25.4‫א‬

 KA36١٤٥٠٠p.s.i 

 W‫א‬

F Z١٤٥٠٠p.s.i، V = Fv . A w 

  v

S 10 x 25.4‫א‬ AISC ‫א‬‫א‬‫א‬  W‫א‬10 (0.311) = 3.11 in.2 

V = 14500 (3.11) = 45100 lb.

  ‫א‬‫א‬‫א‬ .12 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 f Tot.

 W‫א‬‫א‬‫א‬‫א‬‫א‬ P V.Q Mx ±  f =± ± A b.I Zx   ‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬

 f = f a + f bx + f v < f Tot.

 W

 E P = F‫א‬‫א‬J f a A X‫א‬‫א‬J f bx (

V.Q =) b.I

‫א‬J f v

‫א‬20.2

 K‫א‬‫א‬ 

-٥٥-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬

 



q P

P 

0.8 m



V



V

 K‫א‬W٢٠٫٢‫א‬ 

-٥٦-





 ‫א‬‫א‬‫א‬ ã¹]
‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬

٣

 ‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 W‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬ 

 W‫א‬‫א‬  W‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬ 

K٪١٠٠‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬

 W‫א‬‫א‬  K١٠  W‫א‬‫א‬ K‫א‬‫א‬ 

 W‫א‬‫א‬  K‫א‬‫א‬  

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 ‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 .١ ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬EF  W‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬

 Riveted Connections ‫א‬‫א‬J 

 Bolted Connections

 Welded Connections  Pin Connections

‫א‬‫א‬‫א‬J  



‫א‬‫א‬J  ‫א‬‫א‬J 

 Rivets‫א‬K٢ ‫א‬Mild Steel،E‫א‬F‫א‬‫א‬‫א‬  KEShankF‫א‬EHeadF‫א‬

‫א‬E F‫א‬‫א‬

،‫א‬K ‫א‬‫א‬‫א‬K  ‫א‬‫א‬‫א‬ ‫א‬E F،Button HeadEFW  ‫א‬ ‫א‬١{٣‫א‬K K ‫א‬  K‫א‬‫א‬         

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 ‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

Button head

Countersunk head

Truss head

Flat head

Pan head

‫א‬‫א‬W١٫٣ ‫اﻟﺸﻜﻞ‬ Types of Riveted Joints ‫א‬‫א‬‫א‬.1.2

 , Lap JointE‫א‬‫א‬F‫א‬W‫א‬‫א‬ . Butt JointE‫א‬‫א‬F 

Lap Joint

(‫א‬‫ )א‬‫א‬ (‫أ‬

‫א‬ ‫א‬ ‫א‬       ‫א‬  ‫א‬  ‫א‬ ‫א‬

Single   ‫א‬  ‫א‬   ‫א‬ ‫א‬  ‫א‬ ‫א‬    ‫א‬ ‫א‬

 ‫א‬   ‫א‬‫א‬  ‫א‬  riveted lap joint ‫א‬K‫א‬ Double riveted lap joint‫א‬

 KPitch‫א‬ 

Butt Joint E‫א‬‫א‬F‫א‬ ( ‫ب‬

‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬ 

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 ‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 ‫א‬‫( א‬‫א‬) ‫א‬‫א‬ .٢٫٢    ‫א‬‫א‬‫א‬E‫א‬F‫א‬‫א‬EF،،

K‫א‬ Punching ‫א‬‫א‬K‫א‬

 DrillingE‫א‬F‫א‬ ‫א‬‫א‬ ‫א‬

 KAISC‫א‬‫א‬‫א‬‫א‬‫א‬KDriller‫א‬ 

(STD)  Standard Hole ‫א‬‫أ – א‬ 





 EOVSFOversized Hole‫א‬‫א‬‫א‬–





- ٦٠ -

 ‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 ESSLF Short Slotted Hole‫א‬‫א‬J  





(LSL)  Long Slotted Hole ‫א‬‫د – א‬

 (NSL) ‫א‬‫א‬‫א‬‫א‬J ‫هـ‬  Short or Long Slotted Hole Normal to Load Direction



 

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 ‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

Bolts in Tension ‫א‬ .٣٫٢

‫א‬ ‫א‬‫א‬  (‫א‬) ‫א‬‫א‬

‫א‬‫א‬‫א‬E‫א‬‫א‬F‫א‬‫א‬‫א‬ ٢{٣‫א‬KAnet‫א‬‫א‬‫א‬‫א‬ ‫א‬

 K



 W٢{٣‫א‬

   ‫א‬        ‫א‬  ‫א‬  P  ft = t A

 W‫א‬  W

 E2LF‫א‬J f t EF‫א‬‫א‬ J Pt

 E2F‫א‬‫א‬‫א‬J A ‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬  KNet Section ‫א‬‫א‬‫א‬K‫א‬

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 ‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 K٣{٣‫א‬‫א‬‫א‬ •



 ‫א‬‫א‬W٣{٣‫א‬

 W‫א‬‫א‬‫א‬‫א‬  A net = t (W - d)  W  ‫א‬J d ‫א‬J t

‫א‬J W

EF‫א‬‫א‬  • K٤{٣‫א‬not Staggered

 ‫א‬W٤{٣‫א‬ 

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 ‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 W‫א‬‫א‬‫א‬‫א‬ 

 A net = t (W - n . d)

 W 

 ‫א‬‫א‬J n 

‫א‬     ‫א‬     AISC ‫א‬ ‫א‬‫א‬  85% ( A net F‫א‬‫א‬‫א‬‫א‬‫א‬85%‫א‬  15% ‫א‬ ( A φ ) ‫א‬‫א‬ ( A gross F‫א‬‫א‬  W‫א‬‫א‬‫א‬،‫א‬‫א‬ 

T  A gross =  A net = T Ftp 0.85 . Ftp K‫א‬‫א‬J Ftp ‫א‬ - T

‫א‬‫ א‬- A net ‫א‬‫ א‬- A gross ‫א‬‫א‬‫א‬‫א‬Efastener PitchF‫א‬  Kg‫א‬‫א‬‫א‬‫א‬‫א‬S  Staggered Rows EF‫א‬‫א‬ •  K٥{٣‫א‬

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

 ‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

  ‫א‬EF‫א‬‫א‬W٥{٣‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬،K‫א‬‫א‬

S2  A net = t (W - n.d + ∑ ) 4g



 W  KE‫א‬‫א‬‫א‬‫א‬‫א‬F‫א‬J S  K‫א‬‫א‬‫א‬‫א‬‫א‬J g  K‫א‬J d 

Gusset F‫א‬‫א‬(SplicesF‫א‬ A net ‫א‬‫א‬  K‫א‬‫א‬٪٨٥Eplates Shear Strength of Rivet

‫א‬‫א‬ .٤٫٢

 W‫א‬‫א‬‫א‬‫א‬ Single Shear‫א‬‫• א‬

 K٦٫٣‫א‬‫א‬‫א‬‫א‬‫א‬ 

- ٦٥ -

 ‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 



  

 W٦٫٣‫א‬

Double Shear ‫א‬‫• א‬

‫א‬ ‫א‬  ‫א‬      ‫א‬ ‫א‬ ‫א‬    

،‫א‬‫א‬‫א‬‫א‬   K٧٫٣‫א‬ 

 W٧٫٣‫א‬  - ٦٦ -

 ‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

  ‫א‬  ‫א‬  ‫א‬       ‫א‬   •    ‫א‬     (Single ShearF ‫א‬   ‫א‬

W‫א‬

Vs = Fv . A

 W

‫א‬ -Vs  ‫א‬‫א‬‫א‬J Fv

2  E π d F‫א‬ J A 4 Double F   ‫א‬        ‫א‬    •

 W‫א‬‫א‬‫א‬EShear Vs = 2. Fv . A W‫א‬‫א‬‫א‬n‫א‬‫א‬ •  Vs = n. Fv . A  W1

 K12‫א‬٨٫٣‫א‬‫א‬‫א‬‫א‬ 



  W٨٫٣‫א‬

 W‫א‬

 ‫א‬‫א‬‫א‬ ‫א‬ Vs = Fv . A

 W‫א‬‫א‬

 35= Vs

2 2  A = π . d = 3.14 x 12 = 113.04 mm 2 ،‫א‬ 4 4 2 113.04W‫א‬‫א‬

 W‫א‬‫א‬

- ٦٧ -

 ‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

Vs 35 x 103 = = 309.62 N/mm 2 Fv = A 113.04  309.62 N/mm 2 W‫א‬‫א‬‫א‬



 W2

  ‫א‬    ‫א‬    ‫א‬  ‫א‬ ‫א‬ 

   15    ‫א‬     K ٩{٣ ‫א‬        N/m 2 210 x 106 ‫א‬‫א‬ 

Vs

Vs

 ‫א‬W٩٫٣‫א‬

 W‫א‬

EDouble ShearF‫א‬‫א‬

 W‫א‬‫א‬‫א‬ Vs = 2. Fv . A  ،‫א‬ 2 2  A = π . d = 3.14 x 15 = 176.625 mm 2 4 4  A = 176.625 x 10- 6 m 2

 W‫א‬‫א‬‫א‬‫א‬  Vs = 2 . Fv . A = 2 x 210 x 106 x 176.625 x 10- 6 = 74182.5 N 

 W

K ¾ in.  A307 ‫א‬‫א‬

 K¾in.‫א‬A325‫א‬‫א‬

- ٦٨ -

 ‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 W‫א‬  ‫א‬ 2

 Av = π d = 4

3.14 (0.75) 2 = 0.4418 in. 2 4



  W‫א‬‫א‬Fv= 10 k.s.iA307‫א‬‫א‬  Vs = Fv . A v = 10 x 0.4418 = 4.42 Kips  A325‫א‬‫א‬‫א‬

π d 2 3.14 (0.75) 2 Av = = = 0.4418 in. 2 W‫א‬ 4 4

‫א‬ ‫א‬        Fv =17k.s.i   A325   ‫א‬ ‫א‬   Vs = 2 Fv . A v = 2 x 17 x 0.4418 = 15.0 Kips 

Bearing

 K‫א‬

E‫א‬‫א‬‫א‬‫א‬F ‫א‬ ‫א‬ ‫ א‬.٥٫٢ stress Failure

F ‫א‬    ‫א‬  ‫א‬ ‫א‬  ‫א‬  ‫א‬  

‫א‬F ‫א‬    ‫א‬ ‫א‬ ‫א‬  ‫א‬   Bearing Stress E‫א‬

‫א‬‫א‬‫א‬‫א‬ Yield Stress ‫א‬ (١٠٫٣  ‫א‬



 ‫א‬‫א‬‫א‬‫א‬W١٠٫٣‫א‬

‫א‬‫א‬ Fp‫א‬ ‫א‬‫א‬

‫א‬ Vb‫א‬‫א‬K‫א‬  K‫א‬‫א‬‫א‬ - ٦٩ -

 ‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 Vb = Fp . A = Fp . d . t  ‫א‬،  19 (A36F‫א‬14‫א‬‫א‬

Fp= 477.11 x 106 N/m2  W‫א‬ Fp

Vb = Fp . A = Fp . d . t = 477.11 x 106 x 0.019 x 0.014 =126911 N

‫א‬   ‫א‬     ‫א‬    ‫א‬ ‫א‬‫א‬  ‫א‬   K‫א‬ Welded Connections ‫ א‬‫ א‬.٣  Welding Process‫א‬ .١٫٣

‫א‬EMolten State )‫א‬‫א‬‫א‬‫א‬‫א‬

Electric F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،

EWeld RodF‫א‬EOxyacetylene FlameF‫א‬‫א‬Earc  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬ Metal Arc Welding ‫א‬‫• א‬



‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬ EFluxF ‫א‬  EShielded ElectrodesF‫א‬‫א‬  ‫א‬W‫א‬‫א‬ ‫א‬K‫א‬‫א‬‫א‬

E‫א‬ F ‫א‬ ‫א‬ ‫א‬  EShield -metal arc weldingF ‫א‬ ‫א‬  W‫א‬١١{٣‫א‬Submerged arc welding

Gas-metal arc welding‫א‬‫א‬‫א‬‫• א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K

 ‫א‬‫א‬ ‫א‬‫א‬   ‫א‬   ‫א‬  ‫א‬    

 K‫א‬‫א‬‫א‬‫א‬‫א‬

- ٧٠ -

 ‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ : ١١٫٣‫א‬

‫א‬‫א‬‫א‬‫א‬: ١٢٫٣‫א‬

 Resistance Welding (‫א‬) ‫א‬‫• א‬

‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬ Advantages of Welding

‫א‬‫א‬ .٢٫٣

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬EGusset PlatesF‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬،‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬،‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬،‫א‬،‫א‬

 K

K‫א‬‫א‬‫א‬‫א‬‫א‬‫• א‬ K‫א‬‫א‬‫א‬ • - ٧١ -

 ‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 ‫א‬          ‫א‬ ‫• א‬ KE‫א‬‫א‬F‫א‬‫א‬

K‫א‬ •  Disadvantages of Welding‫א‬ .٣٫٣  ‫א‬‫א‬ •

‫א‬‫א‬  ‫א‬‫א‬ • K‫א‬

 W‫א‬‫א‬‫א‬  K‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬ •

 Types of Welded Connections‫א‬‫א‬ .4.3  W‫א‬  Butt Joint • Tee Joint  •

Lap Joint‫א‬ •

Corner Joint‫א‬ •

 Edge Joint  • K‫א‬‫א‬EF٣٫١٣ ()١٣٫٣‫א‬

- ٧٢ -

 ‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

BUTT



TEE

LAP

EDGE

CORNER

 ‫א‬‫א‬W()١٣٫٣‫א‬

 W‫א‬‫א‬‫א‬  Flat  •

Vertical  •

Horizontal • Overhead  •

 W‫א‬  Groove Weld EF • Fillet Weld 

Plug Weld Slot Weld 

- ٧٣ -



‫א‬ •

 ‫א‬ •

  •

 ‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

                    ‫א‬‫א‬W()١٣٫٣‫א‬

- ٧٤ -



 ‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 W (١٥٫٣‫א‬FFillet Weld ‫א‬‫א‬‫א‬ 

 ‫א‬‫א‬‫א‬‫א‬W ١٥٫٣‫א‬   - ٧٥ -

 ‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 WE٣٫١٦‫א‬FGroove Weld E‫א‬F‫א‬‫א‬  

  ‫א‬‫א‬‫א‬:١٦٫٣‫א‬ 

Allowable Stresses of Welding

ِ ‫א‬‫א‬‫א‬‫ א‬.٥٫٣

‫א‬      ‫א‬   ‫א‬   ‫א‬ ‫א‬‫א‬ 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ K  W‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬ 

   f t = 0.7 f pt

Butt Weld

 E

‫א‬ •

 W  K‫א‬‫א‬‫א‬‫א‬- f pt ١٧{٣‫א‬ Groove Weld ‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬

- ٧٦ -

 ‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 



  ‫א‬‫א‬‫א‬W١٧{٣‫א‬ 

 ft = P L. Te  W  ‫א‬J P  ‫א‬J L

 ‫א‬‫א‬J Te 

 W‫א‬‫א‬،١٨٫٣‫א‬‫א‬ 



 ‫א‬‫א‬‫א‬W١٨{٣‫א‬  - ٧٧ -

 ‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

 f= P2

L. Te

 ‫א‬ •

Fc = 1.0 f pc



 W

 K‫א‬‫א‬‫א‬‫א‬- f c  ‫א‬ •

q = 0.55 f pt

  



Fillet Weld‫א‬E

0.4 f pt  ‫א‬‫א‬‫א‬ •

  K‫א‬‫א‬‫א‬‫א‬١{٣‫א‬ 

٢

L‫א‬‫א‬

‫א‬

1420

EF‫א‬‫א‬

١٥٧٥

 EF‫א‬

١٠٢٥

E‫א‬F‫א‬   

Pin Connections (‫ )א‬‫א‬‫א‬.٤

٩‫א‬‫א‬K‫א‬‫א‬E‫א‬F‫א‬‫א‬

‫א‬،‫א‬‫א‬ ٣٠٠‫א‬‫א‬

 W‫א‬ - ٧٨ -

 ‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

Forged Steel Pins ‫א‬ J 

 EF‫א‬‫א‬ Undrilled Pins J  

 (Pilot nutF

 K‫א‬‫א‬‫א‬(Driving nutF  Drilled Pins J  ‫א‬K ٢٠‫א‬

 K‫א‬‫א‬ 

Bolted Connections (‫א‬) ‫א‬ ‫ א‬‫ א‬.5 ‫א‬،١٩٫٣‫א‬E‫א‬‫א‬F‫א‬ EThreadsF‫א‬‫א‬K(HeadFEShankF‫א‬

  ‫א‬‫א‬KENutF  K‫א‬‫א‬(WasherF‫א‬ 



- ٧٩ -



 ‫א‬‫א‬

 ٢١١

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

 

‫א‬ ‫א‬ • 

 W‫א‬‫א‬ 

Black Bolts ‫א‬‫א‬ (‫أ‬

‫א‬     A307  EASTMF ‫א‬ ‫א‬‫א‬    ‫א‬‫א‬‫א‬ 60 P.S.I‫א‬

 K4

‫א‬‫א‬ASTM‫א‬‫א‬‫א‬‫א‬A325  ‫א‬E  .120 p.s.iK105 p.s.i

150 ‫א‬‫א‬ASTM‫א‬‫א‬‫א‬A490  ‫א‬E

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬p.s.i

 

- ٨٠ -

 ‫א‬‫א‬‫א‬ ã¹]
٤

‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ٢١١

 ‫א‬

 ‫א‬

 

 W‫א‬‫א‬  K‫א‬‫א‬،‫א‬‫א‬‫א‬ 

 W‫א‬‫א‬  W‫א‬‫א‬‫א‬ 

K‫א‬‫א‬‫א‬ •

K‫א‬‫א‬ •   W‫א‬‫א‬‫א‬  K٪١٠٠‫א‬‫א‬‫א‬  W‫א‬‫א‬

 K٦ 

 W‫א‬‫א‬

K‫א‬‫א‬ •  K‫א‬‫א‬ •

  W‫א‬‫א‬  K‫א‬‫א‬

-٨١-

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ٢١١

 ‫א‬

 ‫א‬

 

 W.١ K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬

‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬ ‫א‬   ‫א‬‫א‬

 K‫א‬١{٤‫א‬‫א‬  

M



W

W

  

B

B

 P







Pmax

  

 EFEF  ‫א‬‫א‬‫א‬W١{٤‫א‬ 

-٨٢-



 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ٢١١

 ‫א‬

 ‫א‬

 

١{٤‫א‬EF‫א‬KB‫א‬‫א‬‫א‬   W‫א‬‫א‬‫א‬

 P= W B

 W

 K‫א‬‫א‬J W  K‫א‬J B 

 W‫א‬١{٤‫א‬EF‫א‬‫א‬ 

 Pmax = W + M = W + 6 M A

Z

B

B2



 Pmin = W − M = W − 6 M A

Z

B

B2

 W

 E١x BF‫א‬‫א‬-A 2

 ‫א‬-M

 E B F‫א‬J Z 6



‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬،‫א‬‫א‬ ‫א‬‫א‬ ‫א‬  ‫א‬‫א‬K‫א‬  .Broad (Wide) Flange I Beam ‫א‬‫א‬‫א‬‫א‬Standard I Beam

  ‫א‬.٢  W‫א‬ 

-٨٣-

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ٢١١

 ‫א‬

 ‫א‬

 

Single Rolled Steel Sections :  .١٫٢ Broad (Wide) ‫א‬‫א‬‫א‬ Standard I Beam

K‫א‬‫א‬‫א‬‫א‬،Flange I Beam Built up Sections :  .٢٫٢

 W‫א‬‫א‬‫א‬‫א‬  ‫א‬ •

     Lacing Bars‫א‬ •    

 

 ‫א‬‫א‬ •

   

 ‫א‬I‫א‬ •





  -٨٤-

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ٢١١

 ‫א‬

 ‫א‬

 

 Web Plates ‫א‬I‫א‬ • 

  ‫א‬‫א‬ •



    Standard I Beam • 





 ‫א‬ •

    

  •

    

-٨٥-

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ٢١١

 ‫א‬

 ‫א‬

 

 ‫א‬‫א‬‫א‬ •   

    K‫א‬‫א‬Welded Box  •

    



   ‫א‬‫א‬‫א‬.٣  W‫א‬‫א‬‫א‬

 Base Plate without Gusset Plates‫א‬E1  Gusseted base‫א‬(2

 K ‫א‬‫א‬‫א‬

‫א‬‫א‬KEBearingF‫א‬‫א‬

‫א‬KGusseted base‫א‬  KGussets‫א‬‫א‬‫א‬‫א‬‫א‬

-٨٦-

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ٢١١

 ‫א‬

 ‫א‬

 

‫א‬ .1.3 

 



  ‫א‬W2.4‫א‬



،‫א‬ ‫א‬E٢٫٤‫א‬F‫א‬ ‫א‬‫א‬‫א‬ ‫א‬‫א‬ ‫א‬  K  ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ،‫א‬‫א‬

 W‫א‬‫א‬

2  t = 3W (A 2 − B ) 4

F b

 W 

 ‫א‬-t

 ‫א‬‫א‬‫א‬‫א‬-P  ‫א‬‫א‬‫א‬‫ א‬-A ‫א‬‫א‬‫א‬‫ א‬-B

2L1890‫א‬‫א‬‫א‬J Fb   -٨٧-

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ٢١١

 ‫א‬

 ‫א‬

 

 W‫א‬  W  P=

W  ‫ﻣﺴﺎﺣﺔ اﻟﻘﺎﻋﺪة‬

 W‫א‬‫א‬ 



 

2  = PA  2

 ‫א‬ 

WA‫א‬‫א‬‫א‬ 

2  = PB   WB‫א‬‫א‬‫א‬ 2  WA‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

PA 2



1 PB 2

−  MA = m 2 2 

 Poisson`s Ratio‫א‬ 1  m



2 P 2 B  M A = (A − ) 2 m

  M = f.z  2  P (A 2 − B ) = F × 1 × 1 × t 2 b 6 M 2  





 

-٨٨-

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬



  ٢١١

 ‫א‬

 ‫א‬

 

2 t 2 = 3P (A 2 − B ) m F b 

 t=

 t=

3P (A 2 − B2 ) m F b  W،٠٫٢٥‫א‬

3P (A 2 − B2 ) F 4 b 

‫א‬‫א‬‫א‬ ‫א‬

K‫א‬‫א‬‫א‬

‫א‬(cap)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬(column shaft) ‫ اﻟﻌﻤﻮد‬‫א‬‫א‬  W‫א‬‫א‬ 

 t=

9W D 16F D − d b

 W  ‫א‬J t  ‫א‬‫א‬‫א‬J W

 ‫א‬‫א‬‫א‬ -D  ‫א‬‫א‬J F b  ‫א‬‫א‬‫א‬J d ‫א‬‫א‬‫א‬‫א‬‫א‬  K25

 K‫א‬‫א‬1,5‫א‬ -٨٩-

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ٢١١

 ‫א‬

 ‫א‬

 

 Gusset bases‫א‬.٢٫٣

‫א‬،‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬

 K

‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   KE٣{٤‫א‬F 





‫א‬W3.4‫א‬ 

 Design of gusset plates ‫א‬‫א‬‫א‬ .٣٫٣

 KE٤{٤‫א‬F‫א‬‫א‬‫א‬

 W‫א‬



L B−b ) ( 2 2

= 2P =



PL (B − b) 2

 ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬،‫א‬  ‫א‬‫א‬K ‫א‬  ‫א‬‫א‬‫א‬ (Gusset plate) ‫א‬K

W‫א‬  -٩٠-

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ٢١١

 ‫א‬

 ‫א‬

 

 ‫א‬‫א‬‫ א‬:٤٫٤ ‫א‬ P L (B − b) ⎛⎜ B − b ⎞⎟ ⎜ 4 ⎟ 4 ⎝ ⎠  P L2 (B − b)2 16 

  ،‫א‬  ‫א‬

 K١

 Design of Cleat Angle ‫א‬‫א‬‫א‬ .٤٫٣ KBearings‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

1890   ‫א‬‫א‬    ‫א‬‫א‬‫א‬

‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬K2L  K‫א‬‫א‬‫א‬

-٩١-

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ٢١١

 ‫א‬

 ‫א‬

 

Design of Base Plate ‫א‬ .٥٫٣

‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬

  ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬،‫א‬  ‫א‬‫א‬K ‫א‬‫א‬   K‫א‬‫א‬    ‫א‬‫א‬‫א‬‫א‬ .٦٫٣

K  ‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬E

‫א‬‫א‬‫ א‬e‫א‬‫א‬‫א‬bl  KE٥٫٤‫א‬F

 W‫א‬‫א‬‫א‬ 

  = 3 ⎜⎜ l - e ⎟⎟ . b ⎝2 ⎠  p W‫א‬‫א‬   P = 1 . 3 ( l - e).b 2 2  ⎛

⎞

 W

 p =

4P  3 (l - 2.e).b  

‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬K

-٩٢-

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ٢١١

 ‫א‬

 ‫א‬

 



 :٥٫٤ ‫א‬

  K1

70 tonnes‫א‬ISHB 300 x 58.8 Kg/m ‫א‬‫א‬

 K 40 Kg/cm2،Ebearing capacityF 

 W‫א‬  W‫א‬‫א‬‫א‬‫א‬ 

 

‫اﻟﺤﻤﻞ‬ Z(PF‫א‬‫א‬ ‫ﻣﺴﺎﺣﺔ اﻟﻘﺎﻋﺪة‬   2

 1750 = 70000 = W  =‫א‬ 40

P

 

  40x45‫א‬‫א‬ 

  38.9Kg/cm 2 = 70000 W‫א‬‫א‬ 45x40

 7.5 = B = AW -٩٣-

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ٢١١

 ‫א‬

 ‫א‬

 

 W‫א‬‫א‬‫א‬    t =

3P 2 B 2 (A − ) F 4 b

  t=

(7.5) 2 3 x 38.9 ) ((7.5) 2 − 4 1890



 1.614= t

 ١٨=t ‫א‬

20‫א‬‫א‬6 x65x65‫א‬

 K‫א‬ 

 ‫א‬‫א‬K٤  ،،‫א‬‫א‬

‫א‬‫א‬‫א‬ K ‫א‬‫א‬‫א‬   ‫א‬‫א‬‫א‬‫א‬      ‫א‬‫א‬

‫א‬‫א‬K‫א‬  K‫א‬E2.54F1‫א‬Cement Grout

‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬K ‫א‬‫א‬  ‫א‬K ‫א‬Anchor Bolt ‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬  A= P f b -٩٤-

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ٢١١

 ‫א‬

 ‫א‬

 

 W  (Column loadF‫א‬J P

 ‫א‬‫א‬‫א‬J fb ‫א‬ ‫א‬‫א‬



0.95Equivalent Rectangle‫א‬‫א‬K‫א‬‫א‬ ‫א‬‫א‬K ‫א‬0.80‫א‬‫א‬

‫א‬‫א‬‫א‬E ٦٫٤‫א‬F‫א‬ ‫א‬‫א‬Kmn  .AISC‫א‬‫א‬‫א‬ 



 ‫א‬‫א‬W٦٫٤‫א‬ 

‫א‬‫א‬‫א‬‫א‬‫א‬ 2

A = N x BW‫א‬K L6040‫א‬‫א‬

 EF‫א‬J N  EF‫א‬-B  EF‫א‬J P

 EF‫א‬J bf

 Ep.s.i2LF‫א‬‫א‬‫א‬J Fp

 E،2F‫א‬J A

-٩٥-

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ٢١١

 ‫א‬

 ‫א‬

 

( f P = P ) ‫א‬‫א‬‫א‬ -fP N.B

 EF‫א‬J t

‫א‬‫א‬‫א‬ -Fb 

 K‫א‬‫א‬‫א‬BN‫א‬، A = P ‫א‬ F b

‫א‬ ‫א‬‫א‬‫א‬1‫א‬‫א‬

 WEquivalent Rectangle ‫א‬

2 m fP m  M = f P (m) = 2 2





f n2 n  M = f (n) = P P 2 2  WSection ModulusS‫א‬



2  S= M =f . m P 2.F F b b  2  S= M =f . n P 2.F F b b  I/C ‫א‬

 W t 1‫א‬‫א‬‫א‬ P  1 (t )3 t  I= P = P 12 12  

-٩٦-

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ٢١١

 ‫א‬

 ‫א‬

 

t   C = P W‫א‬C 2  W

t3 3 2 P I 12 t P 2 t P  S= = = . = C t P 12 t 6 P 2



2 2 I M t P fP . m  S= = = = C F 6 2F b b



2 2 t f .n I  S= = P = P C 6 2F b



2 2 3. f . n 3.f . m P P   t 2P =  t 2P = F F b b ‫א‬‫א‬‫א‬‫א‬AISC ‫א‬‫א‬‫א‬

 W Fb = Fy Bearing Plates  3. f . m P t = P F y

2 = 3.m

f

P F y

 f

f

 t P = 2 . n P  t P = 2 . m P WAISC ‫א‬‫א‬‫א‬ F F y y   -٩٧-

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ٢١١

 ‫א‬

 ‫א‬

 

 :1  KN)383000 lbW 14 x 90‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬،٧٫٤‫א‬(١٧٠٣٫٥  ‫א‬

 K(٣٤٤٫٧KN/m2F50 p.s.i.  



 W٧٫٤‫א‬

 : ‫א‬

 W‫א‬‫א‬‫א‬ 

 A = P = 383000 = 766 in.2 ( ٠٫٥٠ m2) F P

500

 K‫א‬28 x 28‫א‬ 27.7 in.‫א‬  W‫א‬‫א‬

 f b = P = 383000 = 489 p.s.i. (٣٣٧١٫١٦Kn/m2) N . B (28) 2 

 W‫א‬

d = 14.5 in. (36.8 cm) ; bf = 14 in.(35.5 cm) ; m = 8.2 in.(20.8 cm) ; n = 7.35 in.(18.7 cm) -٩٨-



 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ٢١١

 ‫א‬

 ‫א‬

 

 K‫א‬m m > n   f

489  t = 2 . m P = 2. (8.2). = 1.91 in. (4.85 cm) P 36000 Fy

 W‫א‬‫א‬‫א‬‫א‬‫א‬E٥F٢‫א‬  K٥x٧١x٧١ 

 W2

 250 Kips‫א‬W 12 x 58A36‫א‬‫א‬

‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬KE١١١٢KnF K٨{٤‫א‬ (١٢ Mpa) 1.8 ksi‫א‬  

 W٨٫٤‫א‬

-٩٩-



 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ٢١١

 ‫א‬

 ‫א‬

 

 W‫א‬ 

 ،  ‫א‬J N

 ‫א‬J B  ‫א‬J t

 K‫א‬‫א‬‫א‬-m

 K‫א‬‫א‬‫א‬J n 

 WA‫א‬‫א‬ 

A = P / Fp A = 250 kips / 1.8 ksi 2

2

A = 138.9 in. (0.09 m ) 



 ‫א‬،‫א‬‫א‬،  N = B = 11.8 in.( ٣٠ cm)  Km=n 

 W،‫א‬‫א‬‫א‬‫א‬

 ١٢{١٩in.‫א‬‫א‬J d

 ١٠٫٠١٤in.‫א‬J b 

 K‫א‬m = n 

N = 2m + 0.95 d 2 m = N - 0.95 d = 11.8 - 0.95 x 12.19 2 m = 11.8 - 11.58 = 0.22 in.  m = 0.11 in.  -١٠٠-

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ٢١١

 ‫א‬

 ‫א‬

 

،‫א‬  ‫א‬



 Km‫א‬‫א‬‫א‬m = 1.21 in.‫א‬ 

N = 2m + 0.95 d = 2 x 1.21 + 0.95 x 12.19 N = 2 x 1.21 + 0.95 x 12.19 = 2.42 + 11.58 = 14 in.

 ١٢in. B 

B = 2 n + 0.80 b 2 n = B - 0.80 b = 12 - 0.80 x 10.014 2 n = 3.99 in.

n = 2 in. 250 kips

 Kn



 fP = = 1.49 k.s.i W‫א‬‫א‬ 12 x 14  W‫א‬‫א‬  Fb = 0.75 FY = 0.75 x 36 = 27 k.s.i

 



 W‫א‬،‫א‬‫א‬ 



3. f . n2 3 . f . m2 P P t= = F F b b

 

3 . f . m2 3 x 1.49 x 1.212 P t= = = 0.50 in. F 27 b

 -١٠١-

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬



  ٢١١

 ‫א‬

 ‫א‬

 

3 . f . m2 3 x 1.49 x 2 2 P t= = = 0.81 in . 27 F b



 K‫א‬‫א‬،‫א‬ ‫א‬ t = 0.81 in.

  K٩٫٤‫א‬‫א‬‫א‬‫א‬



 K‫א‬‫א‬‫א‬:٩٫٤‫א‬

    

-١٠٢-

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ٢١١

 ‫א‬

 ‫א‬

 

 W ٢٤٠٠٠lb‫א‬ ‫א‬،A 36‫א‬W 10 x 22

‫א‬‫א‬١٠{٤‫א‬٨ in. ‫א‬  KFP =225 P.S.I ‫א‬ 

 W‫א‬  W‫א‬‫א‬‫א‬‫א‬  A = R = 24000 = 107 in. 2

F 225 P B = 13.5 in. C = 8in.



١٣٫٥ x ٨= ‫א‬  W‫א‬‫א‬

 f P = 24000 = 222 P.S.I 8 x 13.5  ٠٫٧٥in. KAISC‫א‬  Wn١١{٤‫א‬ 



 K‫א‬:١٠٫٤‫א‬ 

 n = B - K = 13.5 - 0.75 = 6.0 in. 2

2

-١٠٣-

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ٢١١

 ‫א‬

 ‫א‬

 

 W‫א‬E١٢٫٤‫א‬F‫א‬‫א‬،١in.‫א‬ 

f . n 2 222 .(6.0) 2  M= b = = 3996 in - lb 2 2



 W‫א‬‫א‬ 

 Fb = 0.75 (36) = 27 K.S.I   S = M = 4.0 = 0.148 in.3 F b

 W‫א‬

27

 W‫א‬‫א‬‫א‬،‫א‬  S=bt



3

12 c

 W

 E C = t F،‫א‬J c 2

 ‫א‬J t  W‫א‬،C 

b t3 b t3 b t2  S= = = t 6 t 6 12 2  Kt،١in. (bF‫א‬‫א‬

 

-١٠٤-

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ٢١١

 ‫א‬

 ‫א‬

 

 K‫א‬:١١٫٤‫א‬  S=t

2

6



⇒ t = 6.S = 6. (0.148)

  t = 0.94 in.، 

8 x 13.5 x 1 in.W‫א‬





 K‫א‬‫א‬W١٢٫٤‫א‬ 

AISC‫א‬‫א‬‫א‬‫א‬t‫א‬  K‫א‬‫א‬t‫א‬‫א‬ -١٠٥-

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ٢١١

 ‫א‬

 ‫א‬

 

3 . f . n2 3 (222). 6 2 b = = 0.94 in.  t= 27000 F b



 W‫א‬‫א‬‫א‬‫א‬‫א‬  

6.S =

3 . f . n2 b F b

 KB‫א‬‫א‬‫א‬‫א‬‫א‬

-١٠٦-

  

 ٢١١

 ‫א‬

 ‫א‬

 

 ‫א‬‫א‬‫א‬

  EW Shape (Wide flange shapes

d

b

t1

t2 mm

Ix 106 mm4

Sx 103 mm3

Iy 106 mm4

Sy 103 mm3

mm

mm

mm

W920 x 446ً

٩٣٣

٤٢٣

٤٢٫٧

٢٤٫٠

٨٤٥٠

١٨١١٠

٥٤١

٢٥٦٠

W920 x 201

٩٠٣

٣٠٤

٢٠٫١

١٥٫٢

٣٢٥٠

٧٢٠٠

٩٣٫٧

٦١٦

W840 x 299ً

855

400

٢٩٫٢

١٨٫٢

٤٧٩٠

١١٢٠٠

٣١٢

٩٠٫٤

W840 x 176ً

835

٢٩٢

١٨٫٨

١٤٫٠

٢٤٦٠

٥٨٩٠

٧٧٫٨

٥٨٫٩

W760 x 257ً

773

381

٢٧٫١

١٦٫٦

٣٤١٠

٨٨٢٠

٢٤٩

٨٧٫١

W690 x 217ً

٦٩٥

٣٥٥

٢٤٫٨

١٥٫٤

٢٣٤٠

٦٧٩٠

١٨٤٫٤

٨١٫٥

W610 x 155

611

324

١٩٫٠

١٢٫٧

١٢٩٠

٤٢٢٠

١٠٧٫٨

٧٣٫٩

W530 x 150

543

312

20.3

١٢٫٧

١٠٠٧

٣٧١٠

١٠٣٫٢

٧٣٫٤

W460 x 158

476

284

23.9

15.0

795

٣٣٤٠

٩١٫٦

٦٧٫٦

W410 x 114

420

261

19.3

11.6

462

2200

57.4

٦٢٫٧

W360 x 551

٤٥٥

٤١٨

٦٧٫٦

٤٢٫٠

٢٢٦٠

٩٩٣٠

٨٢٨

١٠٨

W360 x 39

٣٥٣

١٢٨

١٠٫٧

٦٫٥

١٠٢٫٠

٥٧٨

٣٫٧١

٢٧٫٤

Designation

- ١٠٧ -

  

 ٢١١

 ‫א‬

 ‫א‬

 

EW Shape (Wide flange shapes

d

b

t1

t2 mm

Ix 106 mm4

Sx 103 mm3

Iy 106 mm4

Sy 103 mm3

mm

mm

mm

W310 x 143ً

323

309

22.9

14.0

347

٢١٥٠

١١٢٫٤

728

W310 x 60

303

203

١٣٫١

٧٫٥

١٢٩

٨٥١

١٨٫٣٦

180

W310 x 23.8ً

305

101

6.7

5.6

42.9

281

1.174

23.2

W250 x 167ً

289

265

31.8

19.2

298

2060

98.2

741

W250 x 58ً

252

203

13.5

8.0

87

690

18.73

184.5

W200 x 86ً

222

209

20.6

13.0

94.9

855

31.3

300

W200 x 52

206

204

12.6

7.9

52.9

514

17.73

173.8

W200 x 35.9

201

165

10.2

6.2

34.5

343

7.62

92.4

W150 x 37.1

162

154

11.6

8.1

22.2

274

7.12

92.5

W130 x 28.1

131

128

10.9

6.9

10.91

166.6

3.8

59.4

W130 x 23.8

127

127

9.1

6.1

8.87

139.7

3.13

49.3

W100 x 19.3

106

103

8.8

7.1

4.7

88.7

1.607

31.2

Designation

- ١٠٨ -

  

 ٢١١

 ‫א‬

 ‫א‬

 

ES Shapes (American Standard Shapes

d

b

t1

t2 mm

Ix 106 mm4

Sx 103 mm3

Iy 106 mm4

Sy 103 mm3

mm

mm

mm

S610 x 149ً

610

184

22.1

19.0

995

3260

19.9

216

S610 x 134

610

181

22.1

15.8

937

3070

١٨٫٦٩

٢٠٧

S510 x 141ً

508

183

23.3

20.3

670

2640

20.69

226

S510 x 112ً

508

162

20.1

16.3

533

2100

12.32

172.1

S460 x 104ً

٤٥٧

159

17.6

18.1

385

1685

10.03

126.2

S380 x 74ً

381

١٤٣

15.8

14

202

1060

6.53

91.3

S310 x 74

305

١٣٩

16.8

17.4

127

833

٦٫٥٣

٩٤

S250 x 52

254

126

12.5

15.1

61.5

482

3.48

55.2

S200 x 34

203

106

10.8

١١٫٢

27

266

1.794

33.8

S180 x 30

178

97

10

11.4

17.65

198.3

١٫٣١٩

٢٧٫٢

S130 x 22

127

83

8.3

12.5

6.33

99.7

0.695

16.75

S100 x 14.1

102

70

7.4

8.3

2.83

55.5

0.376

10.74

S 75 x 11.2

76

63

6.6

8.9

1.22

32.1

0.244

٧٫٧٥

Designation

 - ١٠٩ -

  

 ٢١١

 ‫א‬

 ‫א‬

 

EC Shapes (American Standard Channels

d

b

t1

t2 mm

Ix 106 mm4

Sx 103 mm3

Iy 106 mm4

Sy 103 mm3

mm

mm

mm

C389 x 74ً

381

94

16.5

18.2

188.2

883

4.58

62.1

C389 x 60

381

89

16.5

13.2

145.3

763

3.84

55.5

C310 x 45ً

305

80

12.7

13

67.7

442

2.14

34

C250 x 45ً

254

76

11.1

17.1

42.9

338

1.64

27.6

C230 x 30ً

229

67

10.5

11.4

25.4

222

1.01

19.29

C230 x 22ً

229

63

10.5

7.2

21.4

185

0.80

16.69

C200 x 27.9

203

64

9.9

12.4

18.31

180

0.82

16.6

C180 x 22

178

58

9.3

10.6

11.32

127

0.57

12.9

C150 x 19.3

152

54

8.7

11.1

7.24

95.3

0.44

10.67

C130 x 13.4

127

47

8.1

8.3

3.7

58.3

0.26

7.54

C100 x 10.8

102

43

7.5

8.2

1.911

37.5

0.18

5.74

C75 x 8.9

76

40

6.9

9.0

0.862

22.7

0.13

4.47

Designation

- ١١٠ -

  

 ٢١١

 ‫א‬

 ‫א‬

 

Angles (Equal Legs)

Designation

Mass per Meter Kg / m

Area 2

I ٦ ١٠ 4 mm ٣٧

Sٍ ٣ ١٠ 3 mm ٢٥٩

x or y mm

L 203 x 203 x 25.4ً

٧٥٫٩

mm ٩٦٨٠

L 203 x 203 x 19.0

57.9

7360

29

200

٥٧٫٩

L 152 x 152 x 25.4

55.7

7100

14.78

140.4

47.2

L 152 x 152 x 15.9

36

4590

11.74

92.8

43.9

L 127 x 127 x 9.0

35.1

4480

6.53

74.2

38.6

L 127 x 127 x 12.7

24.1

3070

4.7

51.8

36.3

L 102 x 102 x 19.0

27.5

3510

3.19

46

32.3

L 102 x 102 x 6.4

9.8

1252

1.265

17.21

27.7

L 89 x 89 x 12.7

16.5

2100

1.515

24.4

26.9

L 76 x 76 x 12.7

14

1774

0.924

17.53

23.7

L 64 x 64 x 12.7

11.4

1452

0.512

11.86

20.5

L 51 x 51 x 9.5

7

877

0.1994

5.75

16.15

- ١١١ -

٦٠٫٢

  

 ٢١١

 ‫א‬

 ‫א‬

 

Angles (Unequal Legs)

Designation

L 203 x 150 x 25.4ً

Ix ٦ ١٠ 4 mm ٣٣٫٦

S xٍ ٣ ١٠ 3 mm ٢٤٧

L 203 x 150 x 19.0

٢٦٫٤

L 152 x 102 x 19.0

y

٦٧٫٣

Iy ٦ ١٠ 3 mm ١٦٫١٥

Syٍ ٣ ١٠ 3 mm ١٤٦٫٢

٤١٫٩

١٩٢

٦٥٫٠

١٢٫٧

١١٣٫٤

٣٩٫٦

10.2

102.4

52.8

3.61

48.7

27.4

L 152 x 102 x 9.5

5.62

54.4

49.3

2.04

26.2

23.9

L 127 x 76 x 12.7

3.93

47.7

44.5

1.074

18.85

19.0

L 127 x 76 x 6.4

2.13

25.1

42.2

0.599

10.06

16.7

L 102 x 76 x 12.7

2.1

31

33.8

1.007

18.35

21.0

L 102 x 76 x 6.4

1.15

16.36

31.5

0.566

9.82

18.7

L 89 x 76 x 12.7

1.35

23.1

30.5

0.566

12.45

17.9

L 89 x 76 x 9.5

1.06

17.86

29.5

0.454

9.7

١٦٫٨

L 64 x 51 x 9.5

0.38

8.96

21.1

0.214

5.95

14.8

L 64 x 51 x 6.4

0.27

6.24

20.0

0.1548

4.16

13.4

mm

- ١١٢ -

x mm

  

 ٢١١

 ‫א‬

 ‫א‬

 

Round Tubingٌ

Size and Thickness

Mass per Meter

mm

Kg / m

12 x 2

Area

٠٫٤٩

mm ٠٫٦٢٨

I ٦ ١٠ 4 mm ٠٫٠٨٢

Sٍ ٣ ١٠ 3 mm ٠٫١٣٦

16 x 2

0.687

0.879

0.22

0.275

16 x 3

0.956

١٫٢٥٥

٠٫٢٧٣

٠٫٣٤١

20 x 4

1.569

2.01

0.684

0.684

25 x 4

2.06

2.638

1.508

1.206

25 x 5

2.452

3.14

١٫٦٦٠

١٫٣٣٦

30 x 5

٣٫٠٦٥

٣٫٩٢٥

٣٫١٩٢

٢٫١٢٨

42 x 5

٤٫٥٣٦

٥٫٨٠٩

١٠٫١٣

٤٫٨٢٥

50 x 4

٤٫٥١٢

٥٫٧٧٨

١٥٫٤٠٩

٦٫١٦٤

50 x 5

٥٫٥١٧

٧٫٠٦٥

١٨٫١١٨

٧٫٢٤٧

2

- ١١٣ -

  

 ٢١١

 ‫א‬

 ‫א‬

 

Square Tubing

Square Side

Mass per Meter

Thickness

mm ٢٠

Kg / m ٠٫٨٧

mm ١٫٥

١٫١١

١٫٥

١٫١١

١٫٥

١٫٣٤

١٫٥

١٫٧٦

٢٫٠

٢٫٠٧

٢٫٠

١٫٨٠

١٫٥

٢٫٣٩

٢٫٠

٢٫١٢

١٫٥

٣٫٠٢

٢٫٠

٣٫٧٣

٢٫٥

٦٠

٣٫٦٤

٢٫٠

٧٠

٦٫٣٢

٣٫٠

٨٠

٧٫٢٦

٣٫٠

٢٥

٣٠ ٣٥ ٤٠ ٤٥ ٥٠

- ١١٤ -

  

 ٢١١

 ‫א‬

 ‫א‬

 

Rectangular Tubing

Width , W

Mass per Meter

Height, H

Thickness

mm ٢٠

Kg / m ٠٫٦٧

mm ١٠

mm ١٫٥

٢٥

٠٫٨٧

١٥

١٫٥

٠٫٨٧

١٠

١٫٥

١٫١١

٢٠

١٫٥

١٫٤٥

٢٠

٢٫٠

١٫٣٨

٢٠

١٫٥

١٫٧٦

٢٠

٢٫٠

١٫٥٨

٣٠

١٫٥

٢٫٠٧

٣٠

٢٫٠

٢٫٠٦

٢٥

٢٫٠

٢٫٠٧

٢٠

٢٫٠

٢٫٢٥

٢٥

٢٫٠

٢٫٣٩

٣٠

٢٫٠

٣٫٠٢

٤٠

٢٫٠

٣٠

٤٠

٤٥

٥٠

٦٠

- ١١٥ -

 ‫א‬‫א‬ 

 ٢١١

 ‫א‬

 ‫א‬

 

1. Stanley, W. Crawley & Robert, M. Dillon (1993), Steel Buildings, Analysis and Design, 4th Edition, John Wiley & Sons, Inc. 2. Vazirani, V. N. & Ratwani, M. M. (1984), Steel Structures, Analysis. Design and Deatails of Structures, Vol. III, Khanna Publishers, Delhi. 3. Edwin, H. Gaylord, Jr. , Charles, N. Gaylord & James, E. Stallmeyer (1992), Design of Steel Structures, 3rd Edition, McGraw-Hill, Inc. 4. Russell C. Hibbeler (1995), Structural Analysis, 3rd Edition, Prentice Hall International, Inc. 5. Robert Englekirk (1994), Steel Structures, Controlling Behavior Through Design, John Wiley & Sons, Inc.

 K،،‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬،E١٩٨٦FK٦ 

،‫א‬ ‫א‬‫א‬ ‫א‬ ‫א‬  ،‫א‬ ‫א‬  ،E ١٩٨٧ F    K٧  K، 

 K‫א‬W،‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬،E٢٠٠١FK٨

- ١١٦ -

 ‫א‬ 

 ٢١١

 ‫א‬

 ‫א‬

 

 ‫א‬

  

٢

‫א‬‫א‬‫א‬W‫א‬‫א‬

٢

 ‫א‬‫א‬‫א‬‫א‬

٥

 ‫א‬‫א‬‫א‬

٦

 ‫א‬‫א‬‫א‬K٤

٧

 ‫א‬‫א‬‫א‬K٥

٨

 ‫א‬‫א‬‫א‬‫א‬

٨

 ‫א‬‫א‬‫א‬‫א‬K٧

٨

 ‫א‬‫א‬K٨

١٤

 ‫א‬‫א‬K٩

١٨ ٢٤

 ‫א‬‫א‬‫א‬K١٠  ‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬

٢٤

٣١

 ‫א‬،‫א‬،‫א‬K٣  ‫א‬‫א‬K٤

 ‫א‬K٥

٣٤

 ‫א‬K٦

٤٠

 ‫א‬K٧

٤٥

 ‫א‬‫א‬K٨

٤٩

 ‫א‬‫א‬‫א‬K٩

٥٠

 ‫א‬‫א‬‫א‬K١٠

٥١ ٥٥

 K١

 ‫א‬K٢

٢٨ ٢٩

 

 ‫א‬‫א‬‫א‬K١١

 ‫א‬‫א‬‫א‬K١٢ 

 ‫א‬ 

٥٧

 ٢١١

 ‫א‬

 ‫א‬

 

 ‫א‬‫א‬‫א‬‫א‬‫א‬ W‫א‬‫א‬

٥٨ ٥٩ ٦٠ ٦٢ ٦٥ ٦٩ ٧٠ ٧٠ ٧١ ٧٢ ٧٢ ٧٦ ٧٨ ٧٩ ٨٢ ٨٣ ٨٤ ٨٤ ٨٦ ٨٧ ٩٠ ٩٠ ٩١ ٩٢

 

 ‫א‬

 ‫א‬‫א‬‫א‬

١J ٢

 ‫א‬‫א‬E‫א‬F‫א‬‫א‬

٢J ٢

 ‫א‬‫א‬

٤J ٢

 ‫א‬

 ‫א‬‫א‬‫א‬

٣J ٢ ٥J ٢

 ‫א‬‫ א‬.3

 ‫א‬

١J ٣

 ‫א‬‫א‬

٢J ٣

 ‫א‬‫א‬

٤J ٣

 ‫א‬

 ‫א‬‫א‬‫א‬

٣J ٣

٥J ٣

 E‫א‬F‫א‬‫א‬K٤

 E‫א‬F‫א‬‫א‬‫א‬K٥  ‫א‬‫א‬‫א‬‫א‬‫א‬ W‫א‬‫א‬‫א‬

 

K١

 ‫א‬

K٢

 K١{٢

 K٢{٢  ‫א‬‫א‬‫א‬

K٣

 ‫א‬K١{٣  ‫א‬K٢{٣

 ‫א‬‫א‬‫א‬K٣{٣

 ‫א‬‫א‬‫א‬K٤{٣  ‫א‬K٥{٣

 ‫א‬ 

٩٢ ٩٤ ١٠٧ ١١٦

 ٢١١

 ‫א‬

 ‫א‬

 

 ‫א‬‫א‬‫א‬‫א‬K٦{٣  ‫א‬‫א‬

K٤

 ‫א‬  ‫א‬‫א‬

      

      ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬E‫א‬F‫א‬‫א‬ GOTEVOT appreciates the financial support provided by BAE SYSTEMS

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