DEPARTMENT OF CIVIL ENGINEERING
CE2005 STRUCTURAL ANALYSIS I
Tutorial Sheet 1
Solve the following problems by Macaulay’s method
1. Determine the expression for slope and deflection for the simply supported beams subjected to loadings as
shown in figures 1(a) and 1(b).
W
M
a
a
b
b
EI
EI
l
l
Figure 1(a)
Figure 1(b)
2. A beam simply supported over a span of 10 m carries concentrated loads of 40, 20 and 60 kN at 2, 5 and 9m
from the left hand support as shown in Fig. 2. Determine the position and amount of maximum deflection. I
for the section = 695.054 × 106 mm4 and E = 2×105 N/mm2.
200 N
40 kN
20 kN
60 kN
100 N/m
100 Nm
2m
3m
4m
10 m
1m 1m
2m
Figure 2
3m
Figure 3
3. Determine the equation of the deflection curve for the simply supported beam with overhang as shown in
Figure 3. Also find the value of slope and deflection under the 200 kN load.
Solve the following problems by Moment Area method.
4. For the simply supported beam loaded as shown in Fig.4, find the slopes at A and B and the deflection at C.
Take EI = 60000 kN-m2.
5. For the beam loaded as shown in Fig. 5, find the slope at A and deflection at B. Take EI = 50000 kN-m2.
100 kN
90 kN
B
A
2I
4m
C
A
I
2m
4m
Figure 4
B
D
C
2m
2m
Figure 5
M0
6. A simple beam AB is subjected to couples M0 and 2M0 acting
as shown in Fig.6. Determine the angles of rotation θA and θB
at the ends of the beam and the deflection δ at point D.
2M0
B
A
D
L/3
EI
L/3
Figure 6
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E
L/3