1
Prof. Stephen M. Mutuli, Dept. of Mechanical & Manufacturing Engineering,
University of Nairobi (e

mail : mutulis1@gmail.com)
EXERCISE 4
Tutorials
FME 202
–
Solid & Structural Mechanics

Tutorial No. 3
( Deflection of Beams
)
Q1.
Fig Q1 shows a cantilever beam of length
meters fixed at the left

hand end
and supporting a point load of magnitude
Newtons, a clockwise couple of
magnitude
and a di
stributed load varying linearly in magnitude from zero
to
over a span length of
meters.
Derive expressions for the deflection and slope of the beam at the free end in terms of
the indicated parameters
Q2.
Fig Q2 shows a beam of length
meters and simply supported over a span of length
meters and supporting a point load of magnitude
Newtons, an anticlockwise
couple o
f magnitude
and a distributed load varying in magnitude from zero
at the left

hand support to
at the right

hand end.
Fig Q1
Fig Q2
2
Prof. Stephen M. Mutuli, Dept. of Mechanical & Manufacturing Engineering,
University of
Nairobi (e

mail : mutulis1@gmail.com)
(i)
Derive expressions for the deflection and slope at the point in

between the
supports
(ii)
Derive expressions for the slope at the left

hand support and at the right

hand
support
Q3.
Fig Q3 shows a bea
m of length
and simply supported at the ends. The beam
supports a distributed load varying linearly in magnitude from
at the left end to
at the right

hand end.
Derive expressions
for the slope and deflection at the center of the beam
Q4.
Fig Q4 shows a cantilever beam
long and supporting an anti

clockwise couple of
magnitude
and a point load of magnitude
, all applied at the center.
The beam also supports a distributed load varying in magnitude linearly from zero to
over a span of
. Calculate
(i)
the deflection at the free end
(ii)
the slope of the beam
at a point
from the constrained end.
;
Fig Q3
Fig Q4
3
Prof. Stephen M. Mutuli, Dept. of Mechanical & Manufacturing Engineering,
University of Nairobi (e

mail : mutulis1@gmail.com)
Q5.
Fig Q5 shows a simply supported beam
long and carrying an anti

clockwise
couple of magnitude
as well as a distributed load varying in magnitude
from zero to
.
(a)
If
the ratio of the deflection at point A
to that at point B
can be
Expressed as :
, find
(b)
Calculate the magnitude of the deflection at the m
id

point of the beam
;
Q6.
Fig Q6 shows a beam
long and simply supported at its ends. The beam supports
a distributed load varying in magnitude li
nearly from zero to
as well as a
point load of magnitude
and an anti

clockwise couple of magnitude
, all applied at the center
Fig Q5
Fig Q6
4
Prof. Stephen M. Mutuli, Dept. of Mechanical & Manufact
uring Engineering,
University of Nairobi (e

mail : mutulis1@gmail.com)
(a)
Calculate the magnitude of the deflection at the center of the beam
(b)
Calculate the magnitude of the deflection at section
of the beam
;
5
6
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