# Maximum Force Supported by Allowable Shear

## Homework Statement

The simple pin-connected structure carries a concentrated load P as shown. The rigid bar supported by structure AB and by pin at C. The steel strut Ab has a cross sectional area of .25in2 and a yield strength of 60ksi. The diameter of the steel pin at C is 0.375in and the ultimate shear strength is 54ksi. If a factor of safety of 2.0 is required in both the strut and the pin at C. determine the maximum load P that can be supported by the structure.

http://img707.imageshack.us/img707/21/photowb.jpg [Broken]

## Homework Equations

$\Sigma$Fx=0
$\Sigma$Fy=0
$\sigma$allow=$\sigma$failure/(Safety Factor)
$\tau$allow=$\tau$failure/(Safety factor)
Safety Factor=$\sigma$failure/($\sigma$actual)
Safety Factor=$\tau$failure/($\tau$actual
Safety Factor=Pfailure/(Pactual)
Safety Factor=$\nu$failure/($\nu$actual)

## The Attempt at a Solution

http://img196.imageshack.us/img196/5855/scan1dl.jpg [Broken]

I know the max allowable P at each point, but what I'm having trouble finding is the max P, based on those max loads at the points. How do I finish solving this?

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## Answers and Replies

PhanthomJay
Science Advisor
Homework Helper
Gold Member
Unless you have not clearly drawn the diagram , it appears that the pin at B is not in double shear, so you may have divided by 2 once too often. What are the member lengths and structure dimensions? They are necessary to solve the problem. Which part of the structure controls the design? How would you then go about solving for the force in the pin at B?

Unless you have not clearly drawn the diagram , it appears that the pin at B is not in double shear, so you may have divided by 2 once too often. What are the member lengths and structure dimensions? They are necessary to solve the problem. Which part of the structure controls the design? How would you then go about solving for the force in the pin at B?

Oops, forgot to upload the picture so you can check my work.

Picture uploaded for reference.

The pin in question is pin C. I don't need to know in B do I? As it doesn't ask for pin B, it ask for the bar AB. So I have solved for the shear in pin C, but the stress/strain in bar AB.

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PhanthomJay
Science Advisor
Homework Helper
Gold Member
Oh sorry, I misread the question. Yes, the pin at C is in double shear. So you need to find the shear force acting at C (in terms of P), and the tensile force in AB (in terms of P), to see which controls based on the allowable values. You first must use your equilibrium equations to determine Cx, Cy, and the axial force in AB.