Determine Maximum Magnitude P for Shear Stress of Beam

[Chibus]

Homework Statement

Question 3: The beam is supported by a pin at A and a short link BC, as shown in Figure 3.0. Determine the maximum magnitude P of the loads the beam will support if the average shear stress in each pin is not to exceed 80 MPa. The diameter for each of the pins is 18 mm.

http://img13.imageshack.us/img13/7517/chibusq3.jpg

Homework Equations

The Attempt at a Solution

http://img5.imageshack.us/img5/1824/chibus1.jpg
http://img13.imageshack.us/img13/9589/chibus2.jpg

I just wanted to get an idea if I'm way off. Really I don't know how to proceed past finding the required shear force in the pins to shear them.

PS: Sorry for my horrible english and writing skills.

 

[PhanthomJay]

Hello, Chibus, welcome to PF! You are making an error in assuming that there is a support reaction B_y at joint B. There is no external support there. B_y is just the vertical component of the force in the link. Don't add it in twice. Otherwise, your method looks OK, and you should be able to solve for P when you eliminate that extra term. Also, be sure to check that the pin at A does not control the design.

 

[Mene]

Dear student,

Thank you for your question. Based on your attempt at a solution, it seems that you are on the right track. To determine the maximum magnitude P for shear stress of the beam, we need to consider the maximum shear stress that each pin can withstand and ensure that the average shear stress in each pin does not exceed 80 MPa.

To do this, we can use the formula for shear stress in a circular cross-section, which is:

τ = (4/π) * (F/A)

Where τ is the shear stress, F is the applied force, and A is the cross-sectional area.

In this case, we can calculate the cross-sectional area of each pin using the given diameter of 18 mm. Once we have the cross-sectional area, we can then determine the maximum force that each pin can withstand without exceeding 80 MPa. This will give us the maximum magnitude P for the shear stress of the beam.

I hope this helps. If you have any further questions, please feel free to ask. Keep up the good work!

Best regards,