Solucionario Mecanica Analitica

PROBLEM 5.67 For the beam and loading shown, determine (a) the magnitude and location of the resultant of the distributed load, (b) the reactions at the beam supports.

SOLUTION

(a)

RI RII R

1 (1100 N/m) (6 m) 2200 N 3 (900 N/m) (6 m) 5400 N RI

RII

2200 5400 7600 N

XR

xR :

X

2.5658 m

MA

(b)

X (7600)

(2200)(1.5) (5400)(3) R

7.60 kN ,

X

2.57 m

0: B (6 m) (7600 N)(2.5658 m) 0 B 3250.0 N B 3.25 kN

Fy

0: A 3250.0 N 7600 N

A

0 4350.0 N

A

4.35 kN

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PROBLEM 5.69 Determine the reactions at the beam supports for the given loading.

SOLUTION RI RII

1 (50 lb/in.)(12 in.) 2 300 lb (50 lb/in.)(20in.) 1000 lb

Fy

0: Ay

300 lb 1000 lb 400 lb 0 A 900 lb

MA

0: M A

(300 lb)(8 in.) (1000 lb)(22 in.)

400 lb 38 in.

0 MA

9200 lb in.

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PROBLEM 5.76 Determine the reactions at the beam supports for the given loading when wO 400 lb/ft.

SOLUTION

1 1 wO (12 ft) (400 lb/ft)(12 ft) 2 2 1 (300 lb/ft)(12 ft) 1800 lb 2

RI RII

MB

C

Fy B

2400 lb

0: (2400 lb)(1 ft) (1800 lb)(3 ft) C (7 ft)

428.57 lb

0

C 429 lb

0: B 428.57 lb 2400 lb 1800 lb 0 3771 lb

B

3770 lb

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PROBLEM 5.78 The beam AB supports two concentrated loads and rests on soil that exerts a linearly distributed upward load as shown. Determine the values of A and B corresponding to equilibrium.

SOLUTION

RI RII MD

For a

1 2 1 2

A (1.8

m) 0.9

A

B (1.8

m) 0.9

B

0: (24 kN)(1.2 a ) (30 kN)(0.3 m) (0.9

0.6 m,

A )(0.6

m)

24(1.2 0.6) (30)(0.3) 0.54 14.4 9 0.54

Fy

0:

A

0

24 kN 30 kN 0.9(10 kN/m) 0.9

a A

B

0

B

0 0 10.00 kN/m 50.0 kN/m

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