Steel Column Design
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India Pavilion at World Expo 2010, Shangai, China
Steel Column Design
STEEL COLUMN DESIGN OF SHOP AREA PLATE GIRDER MEMBER PROPERTY: FLANGE PLATE SIZE:
y tw x
WIDTH B: D
WEB PLATE SIZE:
300 mm
THICKNESS tf:
tf
WIDTH:
D:
334 mm
THICKNESS tw:
8 mm
8 mm
350 mm
B
MEMBER PLATE GIRDER
a cm2
Ixx cm4
I yy cm4
74.72 tf mm 8.00
16522.22 tw mm 8.00
3601.43 d1 mm 334.00
Z xx cm3
Z yy cm3
rxx
ryy
weight g
cm cm kg/m 944.13 240.10 14.87 6.94 58.66 D SECTION DETAILS mm 350.00 PLATE GIRDER WITH 334 x 8 Web plates and 300 x 8 Flange plates
1
India Pavilion at World Expo 2010, Shangai, China
Steel Column Design
STEEL BEAM /COLUMN DESIGN (AS PER IS-800 - 1984) MATERIAL PROPERTIES : Modulus of elasticity of steel Yield stress of steel
= 200000 = 308
MPa MPa
= 350 = 60 = 10
kN kN-m kN-m
= 3.60 = 3.60
m m
= P = 7472.00
mm2
= = = = = =
1.65E+08 3.60E+07 9.44E+06 2.40E+06 148.7 69 4 69.4
mm 4 mm 3 mm 3 mm mm mm
= = = = = =
58.66 8.00 8.00 350.00 334.00 300.00
Kg / m mm mm mm mm mm
LOADS : Axial force (P) Bending moment @ major axis (Mx) Bending moment @ minor axis (My) GEOMETRY : Eff. Length @ x-axis (leffx) Eff. Length @ y-axis (leffy) SECTION PROPERTIES : Section details Area of section (Ax) Moment of inertia @ major axis (Ixx) Moment of inertia @ minor axis (Iyy) Moduli of section @ major axis (Zxx) Moduli of section @ minor axis (Zyy) Radius of gyration @ major axis (rxx) Radius of gyration @ minor axis (ryy) Weight of section Thickness of flange (t f ot T) Thickness of web (tw) Overall depth (D) Clear depth of web (d1) Width of Flange (B)
BOX="B",PLATE_G= 4
SUMMARY OF DESIGN : TYPE OF STRESSES Axial compression stress Bending stress @ major axis Bending stress @ minor axis Ratio of combined stresses
ACTUAL STRESS
PERMISSIBLE STRESS
CHECK
46.85 MPa 6.36 MPa 5.00 MPa 0.35
153.53 MPa 184.54 Mpa 204.00 MPa 1.00
SAFE SAFE SAFE SAFE
India Pavilion at World Expo 2010, Shangai, China
CALCULATION OF ACTUAL STRESSES : Actual compressive stress (σac,cal)
Steel Column Design
= P / Ax
Actual bending stress @ major axis (σbcx,cal)
= 350000 / 7472 = 46.841542 MPa = Mx / Zxx
Actual bending stress @ minor axis (σbcy,cal)
= 60000000 / 9441269 = 6.36 MPa = My / Zyy = 10000000 / 2400951 = 4.17 MPa
CALCULATION OF PERMISSIBLE STRESSES : AXIAL STRESSES : Slenderness ratio in major direction (λx)
Slenderness ratio in minor direction (λy)
= lx / rxx = 3600 / 148.71 = 24.21 = lY / ryy
j dir. ((f ccx ) Elastic critical stress in major
= 3600 / 69.43 = 51.85 = 51.85 = λperm. < 180 2 2 = π ∗ Ε / λx
Elastic critical stress in minor dir. (f ccy )
= π2 ∗ 200000 / 586.11 = 3367.88 MPa 2 2 = π ∗ Ε / λy
Maximum slenderness ratio ( λmax )
Minimum elastic critical stress ( f cc ) Permissible axial stress (σac )
= π2 ∗ 200000 / 2688.86 = 734.11 MPa = 734.11 MPa 0.6 * fcc * fy = 1.4 1.4 1/1.4 [(fcc) + (fy) ] 0.6 * 734.12 * 308 [(734.12)^1.4 + (308)^1.4 ]^1/1.4 = 153.52 MPa (as per clause 5.1.1) = σac,cal σac =
Ratio of axial compression
SAFE
= 46.84 153.52 = 0.305
India Pavilion at World Expo 2010, Shangai, China
Steel Column Design
BENDING STRESS : FOR PLATE I-SECTION ONLY 5 2 26.5 * 10 / ( l / ryy) Y = = = X
C1 C2 C1/C2 K1 K2 fcbx
(as per clause 6.2.4)
26.5 * 10^5 / ( 51.86 )^2 985.55 MPa 2
[1+ 1/20 * { (l/ryy)*(T/D) } ]
=
Y*
= = = = = = = =
985.55 *
[1+ 1/20 * { ( 51.86)*(8 / 350) }^2 ] 1019.57 MPa Distance Between NA and Top Extreme Fiber Distance Between NA and Bottom Extreme Fiber 1 For ψ = 1.0 1.0 For ω = 0.5 0.0 K1 * ( X + K2 * Y ) * C1/C2
= 1 * ( 1019.58 + 0 * 985.55 ) * 1 = 1019.57 ( If T/t < 2.0 and d 1/t < 1344 / sqrt(fy), f cbx = 1.2 * fcbx & If T/t > 2.0 or d 1/t > 1344 / sqrt(fy) , f cbx = fcbx ) T/t d1/t 1344 / sqrt(fy) fcbx
= =
1 41.75
=
76.58 1.2 *1019.57
= =
σbcx
σbcy
=
1223.484 0.66 x fcbx x fy
=
46.85 153.53
= =
0.31 0.35
(as per clause 6.2.4.1)
[(fcbx)1.4 + (fy)1.4 ] 1/1.4
=
0.66 x 1223.49 x 308 [(1223.49)^1.4 + (308)^1.4 ]^1/1.4
= =
184.54 203.28
=
(as per table 6.3) (as per table 6.4) (as per clause 6.2.4)
MPa
MPa MPa
CHECK FOR COMBINED STRESSES : Cmx = 0.85 Cmy σac,cal = σac
(as per clause 6.2.4)
(as per clause 6.2.5)
(as per 7.1.3) (as per 7.1.3)
0.85
σbcx,cal x Cmx 1 - σac,cal x σbcx 0.6 x fccx
σbcy,cal x Cmy 1 - σac,cal x σbcy 0.6 x fccy
6.36 x 0.85 1 - 46.85 x 184.6 0.6 x 3367.9 0.03 <
4.2 x 0.85 1 - 46.85 x 203.28 0.6 x 734.2 0.02 1.00 SAFE
Steel Column Design
STEEL COLUMN DESIGN OF SHOP AREA PLATE GIRDER MEMBER PROPERTY: FLANGE PLATE SIZE:
y tw x
WIDTH B: D
WEB PLATE SIZE:
300 mm
THICKNESS tf:
tf
WIDTH:
D:
334 mm
THICKNESS tw:
8 mm
8 mm
350 mm
B
MEMBER PLATE GIRDER
a cm2
Ixx cm4
I yy cm4
74.72 tf mm 8.00
16522.22 tw mm 8.00
3601.43 d1 mm 334.00
Z xx cm3
Z yy cm3
rxx
ryy
weight g
cm cm kg/m 944.13 240.10 14.87 6.94 58.66 D SECTION DETAILS mm 350.00 PLATE GIRDER WITH 334 x 8 Web plates and 300 x 8 Flange plates
1
India Pavilion at World Expo 2010, Shangai, China
Steel Column Design
STEEL BEAM /COLUMN DESIGN (AS PER IS-800 - 1984) MATERIAL PROPERTIES : Modulus of elasticity of steel Yield stress of steel
= 200000 = 308
MPa MPa
= 350 = 60 = 10
kN kN-m kN-m
= 3.60 = 3.60
m m
= P = 7472.00
mm2
= = = = = =
1.65E+08 3.60E+07 9.44E+06 2.40E+06 148.7 69 4 69.4
mm 4 mm 3 mm 3 mm mm mm
= = = = = =
58.66 8.00 8.00 350.00 334.00 300.00
Kg / m mm mm mm mm mm
LOADS : Axial force (P) Bending moment @ major axis (Mx) Bending moment @ minor axis (My) GEOMETRY : Eff. Length @ x-axis (leffx) Eff. Length @ y-axis (leffy) SECTION PROPERTIES : Section details Area of section (Ax) Moment of inertia @ major axis (Ixx) Moment of inertia @ minor axis (Iyy) Moduli of section @ major axis (Zxx) Moduli of section @ minor axis (Zyy) Radius of gyration @ major axis (rxx) Radius of gyration @ minor axis (ryy) Weight of section Thickness of flange (t f ot T) Thickness of web (tw) Overall depth (D) Clear depth of web (d1) Width of Flange (B)
BOX="B",PLATE_G= 4
SUMMARY OF DESIGN : TYPE OF STRESSES Axial compression stress Bending stress @ major axis Bending stress @ minor axis Ratio of combined stresses
ACTUAL STRESS
PERMISSIBLE STRESS
CHECK
46.85 MPa 6.36 MPa 5.00 MPa 0.35
153.53 MPa 184.54 Mpa 204.00 MPa 1.00
SAFE SAFE SAFE SAFE
India Pavilion at World Expo 2010, Shangai, China
CALCULATION OF ACTUAL STRESSES : Actual compressive stress (σac,cal)
Steel Column Design
= P / Ax
Actual bending stress @ major axis (σbcx,cal)
= 350000 / 7472 = 46.841542 MPa = Mx / Zxx
Actual bending stress @ minor axis (σbcy,cal)
= 60000000 / 9441269 = 6.36 MPa = My / Zyy = 10000000 / 2400951 = 4.17 MPa
CALCULATION OF PERMISSIBLE STRESSES : AXIAL STRESSES : Slenderness ratio in major direction (λx)
Slenderness ratio in minor direction (λy)
= lx / rxx = 3600 / 148.71 = 24.21 = lY / ryy
j dir. ((f ccx ) Elastic critical stress in major
= 3600 / 69.43 = 51.85 = 51.85 = λperm. < 180 2 2 = π ∗ Ε / λx
Elastic critical stress in minor dir. (f ccy )
= π2 ∗ 200000 / 586.11 = 3367.88 MPa 2 2 = π ∗ Ε / λy
Maximum slenderness ratio ( λmax )
Minimum elastic critical stress ( f cc ) Permissible axial stress (σac )
= π2 ∗ 200000 / 2688.86 = 734.11 MPa = 734.11 MPa 0.6 * fcc * fy = 1.4 1.4 1/1.4 [(fcc) + (fy) ] 0.6 * 734.12 * 308 [(734.12)^1.4 + (308)^1.4 ]^1/1.4 = 153.52 MPa (as per clause 5.1.1) = σac,cal σac =
Ratio of axial compression
SAFE
= 46.84 153.52 = 0.305
India Pavilion at World Expo 2010, Shangai, China
Steel Column Design
BENDING STRESS : FOR PLATE I-SECTION ONLY 5 2 26.5 * 10 / ( l / ryy) Y = = = X
C1 C2 C1/C2 K1 K2 fcbx
(as per clause 6.2.4)
26.5 * 10^5 / ( 51.86 )^2 985.55 MPa 2
[1+ 1/20 * { (l/ryy)*(T/D) } ]
=
Y*
= = = = = = = =
985.55 *
[1+ 1/20 * { ( 51.86)*(8 / 350) }^2 ] 1019.57 MPa Distance Between NA and Top Extreme Fiber Distance Between NA and Bottom Extreme Fiber 1 For ψ = 1.0 1.0 For ω = 0.5 0.0 K1 * ( X + K2 * Y ) * C1/C2
= 1 * ( 1019.58 + 0 * 985.55 ) * 1 = 1019.57 ( If T/t < 2.0 and d 1/t < 1344 / sqrt(fy), f cbx = 1.2 * fcbx & If T/t > 2.0 or d 1/t > 1344 / sqrt(fy) , f cbx = fcbx ) T/t d1/t 1344 / sqrt(fy) fcbx
= =
1 41.75
=
76.58 1.2 *1019.57
= =
σbcx
σbcy
=
1223.484 0.66 x fcbx x fy
=
46.85 153.53
= =
0.31 0.35
(as per clause 6.2.4.1)
[(fcbx)1.4 + (fy)1.4 ] 1/1.4
=
0.66 x 1223.49 x 308 [(1223.49)^1.4 + (308)^1.4 ]^1/1.4
= =
184.54 203.28
=
(as per table 6.3) (as per table 6.4) (as per clause 6.2.4)
MPa
MPa MPa
CHECK FOR COMBINED STRESSES : Cmx = 0.85 Cmy σac,cal = σac
(as per clause 6.2.4)
(as per clause 6.2.5)
(as per 7.1.3) (as per 7.1.3)
0.85
σbcx,cal x Cmx 1 - σac,cal x σbcx 0.6 x fccx
σbcy,cal x Cmy 1 - σac,cal x σbcy 0.6 x fccy
6.36 x 0.85 1 - 46.85 x 184.6 0.6 x 3367.9 0.03 <
4.2 x 0.85 1 - 46.85 x 203.28 0.6 x 734.2 0.02 1.00 SAFE
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