Ministry of High Education - CadKad

Ministry of Higher Education Giza Higher Institute for Eng. & Tech. Civil Engineering Department Course Name: Theory of Structures (2) Course Code : CIV 202

Academic Year : 2014?2015

Semester : Second Level : 2nd Time : 3 Hours Date : 7 / 6 / 2015 Examiner: Dr. M. Abdel-Kader

Second Semester Final Examination

- Attempt all questions. - The Exam consists of 4 questions in 2 pages. - Maximum grade is 60 Marks.

Question (1): (15 Marks) For the shown cross-section, determine the following: (a) The location of the centroid. (b) The moments of inertia about the centroidal axes. (c) The direction of the principal axes. (d) The principal moments of inertia.

40 cm 24

40 cm

30 30

Question (2): (15 Marks) (a) A rod of variable cross-section is

subjected to axial loads as shown. Determine the maximum safe value of axial load P.

Given Data: Allowable stress for bronze = 100 MPa Allowable stress for aluminum = 90 MPa Allowable stress for steel = 140 MPa

Bronze Aluminum

Steel

A=200 mm2 A=400 mm2 A=500 mm2

P

P

1.5P

450 kN

1.2 m

50 kN

(b) At the base section (40 cm ? 60 cm) of the shown column, draw the normal stress distribution and calculate the maximum normal stresses. Neglect the column weight.

3m

160 kN

40 cm

y x 60 cm

Question (3) : (15 Marks)

(a) For the shown cantilevered beam of variable circular d = 15 cm

cross-section,

A

200 kN.m

50 kN.m

d = 10 cm

3m

B 2m C

- Draw the twisting moment diagram.

- Determine the maximum shear stress in each part (AB and BC). - Determine the angle of twist at section C. G = 8000 kN/cm2

Tr and TL

J

JG

Please turn over

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Ministry of Higher Education Giza Higher Institute for Eng. & Tech. Civil Engineering Department Course Name: Theory of Structures (2) Course Code : CIV 202

Academic Year : 2014?2015

Semester : Second Level : 2nd Time : 3 Hours Date : 7 / 6 / 2015 Examiner: Dr. M. Abdel-Kader

(b) A bolted butt joint is shown. The diameter of bolts is 2 cm. Q The width and the thickness of the plates are as shown in the figure. Determine the safe load Q that can be applied to the joint, and the efficiency of Q the joint.

Plate of thickness 1.5 cm

3 6 3 3 6 3 cm

The allowable stresses are as follows:

Bolts: Allowable shear stress for bolts, all = 0.96 t/cm2 Plates: Allowable bearing stress for plates,bearing all = 1.5 t/cm2

Allowable tensile stress for plates, t all = 1.4 t/cm2

Q

Splice plates of

thickness 0.8 cm

4 cm 8

Q

8 4

Question (4): (15 Marks) For the shown beam, calculate and draw: (a) The normal stress distribution over the cross-section at b.

(b) The shear stress distribution over the cross-section at a.

100 cm

y

20 cm

50 kN

60.77

25 kN/m

C

x

100 cm

a

b

c

4m

4m

20 cm

20 20 20

Cross-section of the beam

With my best wishes Dr. M. Abdel-Kader

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