M.Sc. Acceptance Exam
(September 2019)
Structural Analysis and Mechanics (45 minutes)
2 m. 2 m. 2 m.
(1)- Draw the B.M.D (Bending Moment Diagram) for the Frame shown in Figure (reactions are given).
3t 3t
3 t/m
5t
1 t/m
2 t/m
7t
3t
6 m.
38 t.m.
2 m. 2 m. 2 m.
Figure for Problem 2
9t
(2)- Find the Reactions for the problem shown in Figure (2).
(3)- Draw the Normal Stresses distribution for the Section shown in Figure (3), when subjected to
the following straining actions: N= - 150. tons (compression), Mx = 12. t.m. (tension in first
quadrant) ,and My = 1. t.m. (tension in first quadrant). (A=2400. cm2, Ix=1280000. cm4
Iy=180000. cm4)
(4)- Draw the vertical and horizontal Shear Stresses distribution for the section shown in Figure (4),
when subjected to shear force Qy = 20. Tons Qx = 8. Tons.
(5)- Determine analytically the magnitude and direction of the principal normal stresses and the
principal shear stresses in the shown infinitesimal element in the Figure (5).
500Kg/cm²
Y
80 cm
150Kg/cm²
X
400Kg/cm²
400Kg/cm²
150Kg/cm²
30 cm
500Kg/cm²
Figure for Problems (3)&(4)
Figure for Problem (5)
(6)- For the shown structures in Figure 6 determine if the structure Stable or Unstable? Determinate
or Indeterminate?
(7)- "Without calculation" Sketch the deformed shape for the shown beams shown in Figure 7.
M t.m
(6a)
(7a)
L
L
M t.m
(6b)
(7b)
L
(7c)
(6c)
W t/m
0.75L
Figure for Problem (6)
Figure for Problem (7)
(8)- Calculate the reactions for the shown indeterminate beam
(EI=20,000 t.m2) using the consistent deformation method in Figure (8).
Figure for Problem (8)
Sep. 2019
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0.25L
5 t.m
10 t/m
5m