CVE 411-Structural Analysis II
Page 1
TUTORIAL 2 - SOLUTION
OBAFEMI AWOLOWO UNIVERSITY, ILE-IFE
Harmattan Semester 2019/2020 Session
SOLUTION TO CVE 411 TUTORIAL 2
REVISION OF MOMENT-AREA METHOD
Due Date: Sunday 14 March 2021
1. Determine the vertical deflection at B in Figure 1 by using the moment-area
method.
20 kN
B
A
ΔB
C
2 m
2 m
Figure 1. Beam 1
M/EI
diagram
m
ΔB = moment of M/EI diagram between A and B about B
That is,
Dr. K.T. Oladepo
Department of Civil Engineering, OAU, Ile-Ife
3/20/21
CVE 411-Structural Analysis II
Page 2
TUTORIAL 2 - SOLUTION
2. Determine the vertical deflection at B in Figure 2 by using the moment-area
method.
ᵟbb
A
B
C
2 m
1 kN
2 m
Figure 2. Beam 2
M/EI
diagram
ᵟbb = moment of M/EI diagram between A and B about B
That is,
Dr. K.T. Oladepo
Department of Civil Engineering, OAU, Ile-Ife
3/20/21
CVE 411-Structural Analysis II
Page 3
TUTORIAL 2 - SOLUTION
3. Determine the vertical deflection at B and C in Figure 3 by using the moment-area
method.
30 kN
5 kN/m
A
C
B
4 m
D
2.5 m
2.5 m
Figure 3. Beam 3
5 kN/m
ΔIB
B
A
C
D
4 m
2.5 m
ΔIC
2.5 m
Figure 3a. Beam 3a
M/EI
diagram
)+5
ΔIIB
30 kN
B
A
C
ΔIIC
D
4 m
2.5 m
2.5 m
Figure 3b. Beam 3b
5 m
M/EI
diagram
Dr. K.T. Oladepo
Department of Civil Engineering, OAU, Ile-Ife
3/20/21
CVE 411-Structural Analysis II
Page 4
TUTORIAL 2 - SOLUTION
For Figure 3a,
ΔIB = moment of M/EI diagram between A and B about B
That is,
ΔIC = moment of M/EI diagram between A and C about C
That is,
For Figure 3b,
ΔIIB = moment of M/EI diagram between A and B about B
That is,
ΔIIC = moment of M/EI diagram between A and C about C
That is,
SUMMARY
Dr. K.T. Oladepo
Department of Civil Engineering, OAU, Ile-Ife
3/20/21
CVE 411-Structural Analysis II
Page 5
TUTORIAL 2 - SOLUTION
4. Determine the vertical deflection at B and C in Figure 4 by using the moment-area
method.
ᵟbb
ᵟcb
A
C
D
B
1 kN
4 m
2.5 m
2.5 m
Figure 4. Beam 4
M/EI
diagram
= ⅓ (4) = 4/3 m
ᵟbb = moment of M/EI diagram between A and B about B
That is,
ᵟcb = moment of M/EI diagram between A and C about C
That is,
Dr. K.T. Oladepo
Department of Civil Engineering, OAU, Ile-Ife
3/20/21
CVE 411-Structural Analysis II
Page 6
TUTORIAL 2 - SOLUTION
5. Determine the vertical deflection at B and C in Figure 5 by using the moment-area
method.
ᵟbc
ᵟcc
A
C
D
B
1 kN
4 m
2.5 m
2.5 m
Figure 5. Beam 5
M/EI
diagram
1m
= ⅓ (9) = 3 m
Dr. K.T. Oladepo
Department of Civil Engineering, OAU, Ile-Ife
3/20/21