Course Title: Strength of Materials

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Course Title: Strength of Materials


(CVE 202)

Course Lecturer: Engr. F. M. Alayaki

Civil Engineering Department,

College of Engineering,

University of Agriculture Abeokuta,

Nigeria

Course
Unit: 2

Contact Time: 2 Hours

Laboratory Time: 1 Hour



Course Content


Direct Stress:
Hooke’s experiment. Axially
loaded bar, Tensile and compressive stresses.
Strain; tensile and compressive strains. Stress
-
stain curves for ductile and brittle materials.
Modulus of elasticity. Mechanical properties
of materials; elastic limits, proportional limit,
yield points, ultimate strength. Modulus of
toughness. Percentage reduction in areas.
Percentage elongation.



Principal stress:
Definition, deductions from
Mohr’s circle. Mohr’s circle method of
determining stress and strain. Working stress,
proof stress, Poisson’s ratio, modulus of
rigidity. Factors of safety. Lateral stresses and
strains. Bars of varying cross sections
compound bars under stress and strain.
Temperature stresses.



Torsion:

effects of torsion. Twisting moment.
Polar second moments of area.
Torsional

shearing stresses and strain. Modulus of
elasticity in shear. Angle of twist. Rupture
.


Shearing force and bending
moments
:

Simply
supported beam. Loading forces and
moments in beams. Shear and moment
equations. Shear force and bending moment
diagrams.



Typical Questions

1. The following data were recorded during a tensile steel test:


Diameter of bar = 20mm


Distance between gauge points = 200mm


Elongation due to load of 50KN = 0.18


Load at yield point = 79KN


Failing or ultimate load = 127KN

Calculate in N/mm
2

the stress at yield point, (b) the ultimate stress, (c) the modulus of elasticity of the
steel

2.

( a )

Define the following terms:


Component of Forces


Resultant


Equilibrant


Moment of Forces


Centroid of a Body


( b ) i

Define the terms shear force and bending moment.


ii

What do you understand by the term ‘point of contraflexure’?









( c ) Using simple sketches show the following types of beams


Simply supported beam with a point load.


Simply supported beam with Uniformly Distributed Load (UDL).




3. Three separate members of steel, copper and brass are of identical
dimensions and are equally loaded. Young’s
moduli

for the materials are:
steel, 210,000N/mm
2
; copper, 100,000N/mm
2
; brass, 95,000N/mm
2
. If the
steel member stretches 0.13mm, calculate the amount of elongation in
the copper and brass members.



4. (a) Define the terms shear force and bending moment.

(b)

What do you understand by the term ‘point of
contraflexure
’?

(c)

Using simple sketches show the following types of beams



Simply supported beam with a point load.



Simply supported beam with Uniformly Distributed Load (UDL).



Overhanging beam with UDL.



Cantilever beam with point load at its end.



Simply supported beam with uniformly varying load.





5. A cantilever beam AB 1.5m long is loaded with a UDL of 2 KN/m and a point
load of 3KN as shown in fig. 1. Draw the shear force and bending moment
diagram for the cantilever beam. Indicate the positions and values of the
following.


Point of zero shear force.


Maximum shear force.


Maximum bending moment.



6 (a) Derive from first principle the formula for the moment of inertia of a

rectangular section.


(b) Determine the moment of inertia
Ixx

of the section shown in fig. 2.



7. Define stress, strain, and elasticity. Derive a relation between stress and

strain of an elastic body.



8. Two wires, one of steel and the other of copper, are of the same length and
are subjected to the same tension. If the diameter of the copper wire is
2mm, find the diameter of the steel wire, if they are elongated by the
same amount. Take E for steel as 200 x 10
3
N/mm
2

and that for copper as
100 x 10
3

N/mm
2
.

















3 KN














2KN/m
















A





B





0.25m 1.00m 0.25m














Fig. 1











24mm























24mm










300mm













































Fig. 2


200mm