# Principal of virtual work

1. Mar 14, 2010

### Dell

using the principal of virtual work, find the reactions of the following structure

as far as i know, to solve using virtual work i take the statically determinate structure and release one of the support reactions making it indeterminate (1st degree),

after picking my brain with the geometry i came to the assumption that when the right side drops δ, the left side rises δ, (when i release the "y" reaction on the left side), this gives me

Ay*δ=P*δ
Ay=P (↑)

when i release the middle "y" reaction, i get

By*δ/2=P*δ
By=2P (↓)

since i can use statics to solve these i know that they are correct,

but for the "x" reactions i know (from statics) that Ax=Bx=0
but using virtual work, when i release one of the "x" reactions, lets say the left one,
since the support A can move(↔) since the lengths of the bars dont change, when the support moves to the right, the point at P, must drop, leaving me with

Ax*Δ=P*δ
Ax=P*δ/Δ

havent bothered trying to find the relation of δ-Δ since i know that Ax is meant to be 0.

a) what is the best way to prove that when the left side rises δ, the right side drops δ,
b) what am i doing wrong with my calculations for Ax, Bx?