Maximum Force Supported by Allowable Shear

[Bracketology]

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

Homework Equations

$\Sigma$F_x=0
$\Sigma$F_y=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=P_failure/(P_actual)
Safety Factor=$\nu$_failure/($\nu$_actual)

The Attempt at a Solution

http://img196.imageshack.us/img196/5855/scan1dl.jpg 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?

 

[PhanthomJay]

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?

 

[Bracketology]

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.

 

[PhanthomJay]

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.

 

[DeeNos]

I would suggest using the equations you have listed to determine the maximum force that can be supported by the structure. First, you can use the equation \SigmaFx=0 to find the horizontal reaction force at point A, which will be equal to the horizontal component of the force P. Then, you can use \SigmaFy=0 to find the vertical reaction force at point A, which will be equal to the vertical component of the force P.

Next, you can use the equation \tauallow=\taufailure/(Safety factor) to determine the maximum allowable shear stress in the steel pin at point C. This will give you the maximum force that can be supported by the pin at C, which you can then compare to the maximum allowable force from the pin's ultimate shear strength.

Similarly, you can use the equation \sigmaallow=\sigmafailure/(Safety Factor) to determine the maximum allowable normal stress in the steel strut AB. This will give you the maximum force that can be supported by the strut, which you can then compare to the maximum allowable force from the strut's yield strength.

Finally, you can use the equation Safety Factor=Pfailure/(Pactual) to determine the maximum force that can be supported by the entire structure, taking into account both the maximum forces from the pin and the strut.

I hope this helps guide you towards finding the maximum force that can be supported by the structure. Remember to always check your units and make sure they are consistent throughout your calculations. Good luck!