An engineer wants to build a bridge using a 12\" wide and 2\" deep wooden plank
ID: 1828563 • Letter: A
Question
An engineer wants to build a bridge using a 12" wide and 2" deep wooden plank by pushing the long plank from A to B. The wood has unit weight is 40 lb/ft^3, modulus of elasticity is 2000 ksi, Poisson's ratio is 0.2. Wood will fail if the tensile stress exceeds 1300 psi, compressive stress exceeds 1700 psi or shear stress exceeds 100 psi. The first picture shows a 10 feet wide shallow crevice.
Can the plank be pushed from end A to B without failing? If yes, what is the factor of safety?
So I know that L is an unknown and that is what I want to find. Also V is also unknown, and W is also unknown. but V,W are functions of L. But I am not sure wshat to do to so many unknown.
Explanation / Answer
as no tension or compression is used it can only fail by shear.
weight of the plank act at its CG;
net force=66.67lb (weight of the elevated part will only cause shear)
shear stress=66.67/(2*12)=2.88psi
so, it can easily pass from Ato B;
Risk factor=100/2.88=34.7 (i think there is some error in the data)