Question

using the delfection function given in Eq.(3.3.13a,b) for the beam column shown in figure. 3.5a, formulate the expression for the deflection y for the beam-columns shown in figure 3.5b by the priciple of

superposition. you are suppose to derive it.

P -х ET-constant P- EL-constant L/3 L/3 L/3

Answer 1

Substituting a = 6/3 y = Q/EIK^3 sin 2k.L/3/ sin cl times sin k-x - theta/3EIK^2 times x 0 less than or equal to x less than or equal to L/3 y = -theta sin 2 kL/3/EIk^3 tan KL sin kx + theta sin KL/3/EIK^3 cos kx - theta/3EIK^2 times (l-x) L/3 less than or equal to x les than or equal to L substituting a = 2L/3 ty = Q/EIk^3 sin KL/3/sin KL times sin k.x - theta/3EIK^2 times x 0 less than or equal to x less than or equal to 2L/3 y = -Q sin 2kL/3/EIK^3 tan kL times sin kx + Q sin 2kL/3/EIK^3 cos kx -2 Q/3EIK^2 (L-x)x/3 less than or equal to L substituting: - 0 less than or equal to x less than or equal to L/3: - y = Q times sin kx/EIk^3 times sin KL (sin kx/ RIK^3 times sin Kl (sin 2kL/3 + sin kL/3) -Qx/EIk^2