posted by deel on .
The stiffness S of a rectangular beam is proportional to its width (w) times the cube of its depth/height (h). find the dimensions (i.e.: w and h) of stiffest beam that can be cut from a log which has a circular cross-section with diameter of 12-in.
You would use the relation of the circular cross-section of (w/2)²+(h/2)²=(12/2)² to relate h and w.
After multiplying by 4 on both sides and rearranging, we have w=√(12²-h²).
Now the stiffness has been defined as
S=k(w)(h³) where k is a constant.
If you substitute w from above then S is now a function of h only.
Can you take it from here?
sorry, I'm still confused how to get the function of h. please help me to complete the assignment. thank you
You need to use the relation
w=√12²-h²) to eliminate w from the function S.
S(h)=k w h³
=k √12²-h²) h³
To find the maximum/minimum stiffness, you will proceed normally to equate
S'(h) = 0
to solve for h.
yes i understand now, thanks for your help