# Exercise4. - University of Nairobi

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30 Οκτ 2013 (πριν από 4 χρόνια και 8 μήνες)

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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

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