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Variation Question

A wooden beam 3in, wide and 5in. deep and 11 feet long holds 2690lb.What load would a beam 2in wide, 7in deep and 13 feet long support

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It is not as easy to give an answer because the dimensions are not in direct proportion to the resistance.
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1 Answer

Hello Stevie, 
 
Let's assume that the original wood beam is simply-supported and capable of holding 2690lb evenly distributed along its length.  This 2690lb includes the weight of the wood.  The shear and tensile strength of the wood can be estimated using the following procedure:
 
1. Draw the shear and bending moment diagrams for the simply-supported original beam with distributed load.  Find the maximum average shear force and maximum bending moment.
 
2. Using the maximum average shear force V, compute the maximum shear stress (VQ/It).  The maximum shear stress in the cross-section occurs at its centroid.
 
3. Using the maximum bending moment M, compute the maximum tensile stress (My/I).  The maximum tensile stress in the cross-section occurs at the fibers furthest from the centroid.
 
Given the maximum shear and tensile stresses of the wood, you can use a similar procedure (working backwards) to find the load-capacity of the 2"x7"x13' beam.
 
If you have specific questions about how to draw shear and moment diagrams, compute first and second moments of inertia (Q, I), or the procedure, feel free to contact me.  I am available for online tutoring.
 
Emma