Question

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The bracket is held to the wal using three A-36 steel bot at BC and D. Each bolt has a diameter of 0.6 in and anstretched length of 2 in. Part A la force of P = 400 lb is placed on the bracket as shown, determine how to the top bracket at bolt D moves away from the wall For the calculation, assume that the bots carry no share the vertical force of 400 lb is supported by the Assume that the wall and bracket are rigid. A greatly exaggerated deformation of the botsis shown in the figure Express your answer to three significant figures and include appropriate units.

Answer 1

Solution:-

Given that

The bracket is held to the wall using three A-36 steel bolts at B, C and D, Each bolt has a diameter of 0.6 in and an unstretched length of 2 in.

FBD of bracket

So FR 2 ܘܙ ܦ܂ cloob Sc c fc 0.51 0.5 2 Axtay

ΣΜ A

FD(3.5) + Fc(1.5) + F(0.5) – 400 x 2 = 0

.........(1)

3.5FD +1.5Fc +0.5FR = 800

from figure (2)

с др 3.5 1.5

$\delta_D=2.333\delta_C$

$\frac{F_DL}{AE}=\frac{2.333F_CL}{AE}$

$F_D=2.333F_C$ ...........(2)

similarly

5В с 0,5 1.5

$\delta_B=0.333\delta_C$

$\frac{F_BL}{AE}=0.333\frac{F_CL}{AE}$

$F_B=0.333F_C$ ...........(3)

Substitute (2) and (3) in (1)

$3.5(2.333F_C)+1.5F_C+0.5(0.333F_C)=800$

$8.1655F_C+1.5F_C+0.1665F_C=800$

$9.832F_C=800$

$F_D=2.333F_C$

$F_D=189.8289$

$F_B=0.333F_C$

$F_B=27.0951$

$\delta_D=\frac{F_DL}{AE}$

$\delta_D=\frac{189.8289*2}{\frac{\pi}{4}(0.6)^2\times 29\times 10^6}$

$\delta_D=\frac{379.6578}{4698\times 10^5}$

$\delta_D=8.081264367 \times10^{-7}$ in

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