Determining X to Find Ultimate Shear Stress in Glued Joint

[williamx11373]

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An inclined member is braced with a glued block, as shown. The ultimate shear stress in the glued joint is 1050 psi. Determine the dimension X at which the glued joint will fail.


I know that


-shearstress= (Pressure x length) dived by (Area x modulus of elasticity)


- At point A there is X forces and Y forces, at point B there is Normal Force.


-Pressure max = (Shearstress X Area)


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so far i know that Force at A in the X direction is 1050x (2x2) = 4200 lbs



other than that I am stuck and i don't know where to start...any help would be appreciated.

 

[anathema]

Thank you for your question. I would like to provide some guidance on how to approach this problem.

Firstly, it is important to understand the concept of shear stress and how it relates to the failure of the glued joint. Shear stress is a type of stress that occurs when two forces act parallel to each other in opposite directions, causing the material to deform or fail. In this case, the glued joint will fail when the shear stress exceeds 1050 psi.

Next, let's examine the forces acting on the inclined member. As you have correctly stated, there is a force in the X direction at point A and a force in the Y direction at point A. At point B, there is a normal force acting perpendicular to the surface.

To determine the dimension X at which the glued joint will fail, we need to find the maximum shear stress acting on the glued joint. This can be calculated by dividing the force in the X direction (4200 lbs) by the area of the glued joint. The area of the glued joint can be calculated by multiplying the length of the glued joint (X) by its width (2 inches).

Now, we have the value for maximum shear stress. We can set this equal to 1050 psi and solve for X. This will give us the dimension at which the glued joint will fail.

I hope this helps you in solving the problem. Remember to always understand the concept and equations involved before attempting to solve a problem. If you have any further questions, please do not hesitate to ask. Keep up the good work in your studies!