# Finding max elastic energy of a bow

1. Jun 28, 2013

### spanky489

Hi guys, im trying to find the theoretical maximum elastic energy of a bow with a constant square cross section with its moment of inertia I, made from a homogenous material throughout the whole length so we can say that the Youngs modulus E is also constant. This bow is attached to a string on both ends and to simplify the problem lets say that the forces pulling both ends are always transverse/tangential in reference to the cross section.

This is the first thing im trying to calculate and is also the prerequisite to calculating the maximum initial velocity of the arrow being launched by the bow.

i know that i need to find the yield strength of the material and through Hooke's law solve the force that causes the maximum strain. The problem im facing is that i do not know which theory to apply to this problem. If the deflections werent so big i would use the euler-bernoulli equations but since that wont work here i was thinking of using the von karman strains.

while searching for information i came across this doctors dissertation which could also be useful in my case but im not sure how it fares with von karman strains in this situation.

any help at all will be appreciated.

thanks
spanky