# Engineering Mechanics

(Joyce) #1

(^224)  A Textbook of Engineering Mechanics
Example 12.5. A beam AB of span 3m, overhanging on both sides is loaded as shown in Fig. 12.12.
Fig. 12.12.
Determine the reactions at the supports A and B.
Solution. Given: Span (l) = 3 m
Let RA = Reaction at A, and
RB = Reaction at B.
We know that anticlockwise moment due to RB and load* at C about A
=RB × l + (1 × 1.5) = RB × 3 + (1 × 1.5) = 3RB + 1.5 kN ...(i)
= (2 × 2) 1 + (3 × 2) + (1 × 1) 3.5 = 13.5 kN-m ...(ii)
Now equating anticlockwise and clockwise moments given in (i) and (ii),
3 RB + 1.5 = 13.5
or
13.5 – 1.5 12
4kN
B 33
R === Ans.
and RA = 1 + (2 × 2) + 3 + (1 × 1) – 4 = 5 kN Ans.
Example 12.6. A beam AB 5 m long, supported on two in termediate supports 3 m apart,
carries a uniformly distributed load of 0.6 kN/m. The beam also carries two concentrated loads of
3 kN at left hand end A, and 5 kN at the right hand end B as shown in Fig. 12.13.
Fig. 12.13.
Determine the location of the two supports, so that both the reactions are equal.
Solution. Given: Length of the beam AB (L) = 5 m and span (l) = 3 m.
Let RC = Reaction at C,
RD = Reaction at D, and
x = Distance of the support C from the left hand end
We know that total load on the beam
= 3 + (0.6 × 5) + 5 = 11 kN

• The 1 kN load at C, will also cause an anticlockwise moment about A.