The aluminum plate of thickness t = 3.5 mm. is to be designed so the maximum str

Question

The aluminum plate of thickness t = 3.5 mm. is to be designed so the maximum stress remains below 100 MPa. The hole must have a diameter of b = 25 mm. Determine the allowable plate width a within the nearest 5 mm. if it is to withstand an axial force of P = 25 KN.

I have tried to work on this problem for the past hour, but can't figure out how to get past the point where I have gotten stuck. I have found one equation with two unknowns, K and a, in it, but cannot figure out another equation to relate the two of them. Please help me!

The following picture shows how the object is loaded in relation to the hole as well as the dimensions a,b, and t. This problem deals with stress concentrations around the hole, so don't forget to account for that! The answer should be a = 230 mm.

Explanation / Answer

Average stress = Load / area = 25*10^3 / ((a*3.5)*10^-6) = 25000/(3.5*a) MPa

Maximum stress in a plate with centrally located circular hole is given by 3 times average stress. (Refer page 4 in this document http://www.nptel.iitm.ac.in/courses/Webcourse-contents/IIT Kharagpur/Machine design1/pdf/Module-3_lesson-2.pdf

So, 100 = 3*25000/(3.5*a)

So, a = 214.3 mm

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