A force is acting at the top of a building frame as shown. The supporting columns are of equal height and are fixed at the base. The modulus of elasticity E is the same for each column. Assuming the top plate is rigid and
What is the shear distributed to the first column?
Since the columns are rigid, the force is distributed to the columns in proportion to their rigidities (or stiffnesses). The composite stiffness is the sum of the individual column stiffnesses.
Substitute for K1, K2 and K3. Then simplify.
It is given that E1= E2 =E3 and h1=h2=h3. Therefore,
Substitute Eq. 2 into Eq. 1 and solve.