School of Civil and Mechanical Engineering
Structural Dynamics (STEN4006)
Assignment 1
Due: 04 September 2026
[Total 30 Marks]
Q 1. Figure 1 shows a single-story building frame with all the mass lumped at the
level of the rigid girder BC. Neglect the axial and shear deformations of the columns
AB and DC. Take I = 7.6 x 106 mm 4 and E = 200 GPa for the columns and the
bracings, L = 6 m, H = 3.5 m and mass m = 4000 kg. Bracings AC and BD are solid
circular bars of 25 mm diameter.
1 (a). Determine the critical damping constants and damped natural frequencies of
the structure at 2% and 15% of critical damping for vibration in the sidesway.
(8 Marks)
1 (b). If a machine exerting a horizontal force of F(t) = 285 sin 50 t kN is firmly
placed on the girder when it was at rest, find the equations of the subsequent motion
of the girder with 2% and 15% of critical damping.
(14 Marks)
1 (c) Explain the effect of damping on the transient, steady state and total responses
of the structure by plotting 10 cycles of displacement versus time curves of the frame
with 2% and 15% of critical damping under the load of 1(b).
(8 Marks)
m
C
B
H
I
I
A
D
L
FIGURE 1
Dr Prabir Sarker, Civil Engineering, Curtin University, Western Australia.
1