Academic Year : 2016-2017
Semester : First
Level : Second
Time : 1½ Hours
Date : 22 / 11 / 2016
Examiner: Dr. M. Abdel-Kader
Ministry of Higher Education
Giza Higher Institute for Eng. & Tech.
Civil Engineering Department
Course Name: Theory of Structures (1)
Course Code : CIV 201
Answer of Mid-Term Exam
34 kN.m
Question (1): (9 Marks)
For the shown structure,
determine the reactions at
the supports A, B and C
and the force in the link
member AE.
28.5 kN
8 kN/m
4 kN/m
B
H
C
E
D
3m
A
4m
4
4
4
3m
28.5 kN
Part DC:
+  M D  0 :
8 kN/m
(8×4)(2) + (28.5)(4) + (½×8×3)(5) – Cy(7) = 0

+  Fy  0 :
D
Cy = 34 kN 
Dx
Dy + Cy – 32 – 28.5 – 12 = 0

Part HD
C
Cx
Dy
4
Dy = 38.5 kN 
4 kN/m
D
B
H
E
Dx
0.6FAE
4
FAE
4m
By
4
–34 – (4×4)(6) – (0.6FAE)(4) + (38.5)(4) = 0  FAE = +10 kN 
+  Fy  0 :
Cy
38.5 kN
34 kN.m
+  M B  0 :
3m
FAE = 10 kN 
–16 – 0.6(10) + By – 38.5 = 0

By = + 60.5 kN

By = 60.5 kN 
– 0.8(10) + Dx = 0

Dx = + 8 kN

Dx = 8 kN 
   Fx  0 :
Part DC:
   Fx  0 : – 8 + Cx = 0 
Cx = + 8 kN  Cx = 8 kN 
8 kN
Part AE:
   Fx  0 :
8 – Ax = 0
 Ax = +8 kN
 Ax = 8 kN 
+  Fy  0 :
6 – Ay = 0
 Ay = +6 kN
 Ay = 6 kN 
E
6 kN
A
Ax
Ay
28.5 kN
34 kN.m
8 kN/m
4 kN/m
B
H
E
C
D
8 kN
3m
8 kN
A
4m
6 kN
4
60.5 kN
4
34 kN
4
3m
Final Reactions
- The force in the link member AE = 10 kN (Tension)
With my best wishes
Dr. M. Abdel-Kader
15 kN
Question (2): (8 Marks)
3
4
8 kN/m
a
9 kN
b
c
32 kN
28 kN
2m
4m
12 kN
8 kN/m
(a)
b
a
9 kN
9 kN c
32 kN
x = 2.5 m
28 kN
2m
(b) Location and value of M max +ve
9
9
+
Zero shear at:  Fy left  0
32 – 12 – 8 x = 0
4m
0 N.F.D (kN)
0
 x = 2.5 m
32
2
M max +ve = 32 (2.5) – 12 (0.5) – 8 (2.5) /2
Or
16
+
= 49 kN.m
4
0 S.F.D (kN)
0
-
Zero shear at:  Fy right  0
2.5 m
8 x – 28 = 0  x = 3.5 m from support b
M max +ve = 28 (3.5) – 8 (3.5)2/2
-28
0 B.M.D (kN.m)
0
= 49 kN.m
+
M max +ve = 49 kN.m at 2.5 m from the support a.
28
40
48 49
Mmax +ve
Question (3): (3 Marks)
F
F
Zero
Parallel reactions
(1) Stable + Determinate.
(2) Unstable.
(3) Unstable.
With my best wishes
Dr. M. Abdel-Kader