Engineering Mechanics

(^234) „„„„„ A Textbook of Engineering Mechanics
Since the structure is supported on rollers at the right hand support (C), therefore the reaction
at this support will be vertical (because of horizontal support). The reaction at the left hand support
(A) will be the resultant of vertical and horizontal forces, and thus will be inclined with the vertical.
Taking moments about A and equating the same,
RC × 4 = (8 × 1.5) + (12 × 2) = 36
∴
36
9.0 kN
4
RVCC== = Ans.
Now vertical component of reaction RA
VA = 12 – 9 = 3 kN
and horizontal reaction at the left hand support A,
HA = 8 kN (←)
∴ Reaction at A, RA=+=(8)^22 (3) 8.54 kN Ans.
Let θ = Angle, which the reaction RA makes with the vertical.
∴ (^) tan^8 2.6667
3
θ= = or θ = 69.4° Ans.
Example 12.13. A truss of 8 m span and 4 m height is loaded as shown in Fig 12.28.
Find the reactions at A and E.
Fig. 12.28.
Solution. Given: Span = 8 m
Let RA = Reaction at A, and
RE = Reaction at C
Since the truss is supported on rollers at the right hand support (E), therefore the reaction at
this support will be vertical (because of horizontal support). The reaction at A will be the resultant of
vertical and horizontal forces, and thus will be inclined with the vertical.
Taking moments about A and equating the same,
RE × 8 = (2W × 2) + (W × 2) = 6W
∴
6
0.75
E 8
W
R ==W Ans.
Now vertical component of reaction RA
= VA = 2W – 0.75 W = 1.25 W
and horizontal reaction at the left hand support A
HA = W (←)