CN114 Mechanics of Materials
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School of Environment & Technology
Semester 2 Examinations 2009-2010
CN114
MECHANICS OF MATERIALS
Instructions to Candidates:
Time allowed: TWO hours
Answer ALL FOUR questions
Questions carry different marks as indicated below.
Question 1: 12 marks
Question 2: 40 marks
Question 3: 18 marks
Question 4: 30 marks
A formulae catalogue is provided.
June 2010, 2 hours
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CN114 Mechanics of Materials
Question 1
A T bracket carrying a vertical force F= 250 kN is bolted to the flange of a column as
indicated in Figure 1. Assuming that the resistance of the connection is controlled by
the shear strength of the bolts, find the required bolt diameter if the allowable shear
stress in each bolt is  w  240 MPa . List any additional assumptions you made to
solve this question.
(12 marks)
Figure 1. Simple bolted connection
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CN114 Mechanics of Materials
Question 2
The symmetric section of Figure 2a consists of 20 x 2.5 cm flanges and a 0.75 x 50
cm web. If the yield stress of the steel is f y  400 MPa :
a)
Find the yield moment M Y of the section if bending occurs about the X-X axis.
Give your result both in Nmm and in kNm.
(9 marks)
b)
Find the yield moment M Y of the section if bending occurs about the Y-Y axis.
Give your result both in Nmm and in kNm.
(8 marks)
c)
Use first principles to find the plastic moment M p of the section if bending
occurs about the X-X axis. Give your result both in Nmm and in kNm.
(17 marks)
d)
If the beam is loaded as indicated in Figure 2b ( bending occurs about the XX axis):
i)
Do you expect tensile or compressive normal stress in the upper fibres
of the section?. Give reasons to your answer.
(2 marks)
ii)
Estimate the maximum shear stress in the beam.
(4 marks)
Figure 2b. Cantilever beam
under UDL
Figure 2a. I section
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CN114 Mechanics of Materials
Question 3
Figure 3a shows a symmetric box section constructed from recycled plates and
channel profiles. The cross section is used in a 4.5 m long column with pinned ends.
The geometric properties of each channel are given in Figure 3b. The modulus of
elasticity of steel is E  2x108 kN/m 2 . Assume that the column buckles in a nonsway
fashion about the X-X axis of the cross section.
a)
Find the moment of inertia about the X-X axis of the cross section of Figure 3a.
Give your result in both mm4 and m4.
(10 marks)
b)
What is the elastic buckling load Pcrx about the X-X axis of the cross section?
(3 marks)
c)
If the cross section is made of steel with yield stress equal to f y  250 MPa .
Do you expect the column to buckle elastically or inelastically? Give reasons
to your answer.
(5 marks)
I x  21,940 cm 4 ; A  82.1 cm 2
Figure 3a. built-up box section
Figure 3b. Channel
properties
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CN114 Mechanics of Materials
Question 4
The cable structure of Figure 4 is made of steel with modulus of elasticity
E  200 000 N/ mm 2 . The cross sectional area of each cable member is
A  314.2 mm 2 .
(a)
Assume elastic behaviour to evaluate in each member:
(i)
the axial force in N
(14 marks)
(ii)
the normal stress in N/mm2
(4 marks)
(iii)
the normal strain
(4 marks)
(iv)
the elongation in mm
(6 marks)
(b)
If the yield strength of steel is f y  275 MPa indicate if the assumption made
to solve part (a) is correct or not. Give reasons to your answer.
(2 marks)
Figure 4. Simple cable structure
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