Chapter 12 : Support Reactions 235
∴ Reaction at A, (^) RA=+WWW^22 (1. 25 ) =1. 6 Ans.
Let θ = Angle, which the reaction RA makes with the vertical.
∴ (^) 0.8
1.25
W
W
θ= = or θ = 38.6° Ans.
Example 12.14. Fig. 12.29 shows a pin-jointed frame carrying vertical loads of 1 kN each
at the joints B and G and a horizontal load of 4 kN at D.
Fig. 12.29.
Find graphically, or otherwise, the reactions at A and E.
Solution. Given: Span = 8 m
Let RA = Reaction at A, and
RE = Reaction at E.
Since the frame 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 the left hand support (A)
will be the resultant of vertical and horizontal forces, and inclined with the vertical.
Taking moments about A and equating the same,
RE × 8 = (1 × 2) + (1 × 4) + (4 × 4.5) = 24
∴
24
3.0 kN
EE 8
RV== = ( ↑ ) Ans.
Now vertical component of reaction
RA = VA = 3 – 2 = 1 kN (↓)
and horizontal reaction at the left hand support A,
HA = 4 kN (←)
∴ Reaction at A, RA=+=(4)^22 (1) 4.12 kN Ans.
Let θ = Angle, which the reaction at A makes with the vertical
∴
4
tan 4
1
θ= = or θ = 75.9° Ans.