Prof. Stephen M. Mutuli, Dept. of Mechanical & Manufacturing Engineering,
University of Nairobi (e-mail : mutulis1@gmail.com)
EXERCISE 5
Tutorials
FME 202 – Solid & Structural Mechanics
- Tutorial No. 5
( Eccentric Loading )
0.22a
Q1. X
Y
0.8a
0.22a
0.22a
X
0.8a
0.4a Y
9a
(ii )
Block
of
(i )
Concrete
Fig Q1
Fig Q1(i) shows a clamp gripping a concrete block and thereby generating a load
between the grips of magnitude W. The dimensions of the cross-section at section
X  Y is shown in Fig Q1(ii) and all the dimensions are indicated as functions of ‘ a ’
At section X  Y :
(i)
derive in terms of the indicated parameters, expressions for the maximum tensile
stress and the maximum compressive stress
(ii)
If the limiting stresses of the clamp material are respectively 380 MN / m 2 and
200 MN / m 2 in tension and in compression, and if a  180mm , calculate the
acceptable value of W
Prof. Stephen M. Mutuli, Dept. of Mechanical & Manufacturing Engineering,
University of Nairobi (e-mail : mutulis1@gmail.com)
Q2.
Steel
Frictionle ss
Pulley
Cable
0.8a
2W
0.16a
30 0
2a
0.16a
x
y
0.16a
6a
(i)
0.6a
2a
6W
0.4a
(ii)
Fig Q2
Fig Q2(i) shows a bracket in the form of a cantilever beam with loads of magnitudes
2W and 6W applied eccentrically. The cross-section of the beam is indicated in
FigQ2(ii) and all the dimensions are given as functions of ‘ a ’.
Derive expressions for the maximum tensile stress and the maximum compressive
stress at the fixed end of the beam (section x  y ) in terms of the indicated parameters.
Q3.
4a
6a
2W
45 0
1.6W
4a
28 0
Weld
0.6a
2a
0.2a
0.6a
3a
(i)
2W
Weld
0.2a
(ii)
Fig Q3
Fig Q3(i) shows a beam fixed at the left-hand end and supporting loads of magnitude
2W , 2W and 1.6W applied eccentrically. The cross-section of the beam is indicated in
Fig Q3(ii) and all the dimensions are shown as functions of ‘ a ’.
Prof. Stephen M. Mutuli, Dept. of Mechanical & Manufacturing Engineering,
University of Nairobi (e-mail : mutulis1@gmail.com)
Derive expressions for the maximum tensile stress and maximum compressive stress at
the fixed end of the beam.
4a
Q4
0.8a
W
0.2a
28 0
0.2a
Weld
3.6a
0.8a
Weld
0.2a
0.6a
(ii)
4a
Fig Q4
20 0
2.8W
6a
(i)
Fig Q4(i) shows a steel bracket fixed at the left-hand end and supporting two loads of
magnitude W and 2.8W applied eccentrically. The cross-section of the beam at the fixed
end is shown in Fig Q4(ii) and all the dimensions are indicated as functions of ‘ a ’.
Show that the expressions for the maximum tensile stress ( max (Tensile )) and
maximum compressive stress ( max (Compressive)) at the fixed end can respectively be
given in terms of the indicated parameters as :
W
W
 max (Tensile ))  79.6326 2 and  max (Compressive))  110.1563 2
a
a
Q5.
Weld
0.2a
x
x
y
0.4a
6a
12 0
y
0.4a
8a
(i)
4W
Fig Q5
(ii)
Prof. Stephen M. Mutuli, Dept. of Mechanical & Manufacturing Engineering,
University of Nairobi (e-mail : mutulis1@gmail.com)
For a bracket indicated in Fig Q5(i) supporting a load of magnitude 4W and having
a trapezoidal cross-section shown in Fig Q5(ii), derive expressions for the maximum
tensile stress and the maximum compressive stress at the fixed end ( section x  y ).
Q6
If for the bracket indicated in Fig 5(i),the
cross section of the horizontal beam is a
semi-circle (Fig Q6) of radius ‘ a ’, derive
expressions for the maximum tensile
stress and the maximum compressive stress
at the fixed end.
a
Fig Q6