- #1
Dell
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- 0
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, let's say the left one,
since the support A can move(↔) since the lengths of the bars don't 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?
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, let's say the left one,
since the support A can move(↔) since the lengths of the bars don't 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?