Useful Formulas - Displacements

Reactions

l2 l

2

Moments/Forces Required to Generate Unit Displacements

System B

System A

abl abl/2 abl/2 al(b1 + b2)/2 abl/2

abl/2 abl/3 abl/6 al(b1 + 2b2)/6 abl(1+αααα)/6

bl(a1 + a2)/2 bl(a1 + 2a2)/6 bl(2a1 + a2)/6 l(2a1b1 + a1b2 +

a2b1 + 2a2b2)/ 6

bl[(1+β)a1 +

(1+αααα)a2]/6

abl/2 abl(1 + αααα)/6 abl(1 + β)/6 al[(1+β)b1 +

(1+αααα)b2]/6

abl/3

2abl/3 abl/3 abl/3 al(b1 + b2)/3 abl(1 + αααα

β)/3

abl/3 abl/4 abl/12 al(b1+3b2)/12 abl(1 +αααα +

αααα2)/12

2abl/3 5abl/12 abl/4 al(3b1 +

5b2)/12

abl(1 - β -

β2)/12