A plane frame shown in the figure (not to scale) has linear elastic springs at node H. The spring constants are kx = ky = 5 × 105 kN/m and kq = 3 × 105 kNm/rad

Q. A plane frame shown in the figure (not to scale) has linear elastic springs at node H. The spring constants are kx = ky = 5 × 10⁵ kN/m and kq = 3 × 10⁵ kNm/rad.

For the externally applied moment of 30 kNm at node F, the rotation (in degrees, round off to 3 decimals) observed in the rotational spring at node H is

 Solution:

Since horizontal reaction at E = Hc = 0

Bending moment at F for member FE = MFE = 0

Member FH behaves like propped cantilever beam   

30 kNm = 3 × 10⁵ kNm/rad × θ

⇒ θ = 1 × 10^-4 radians = 0.0057°