- Draw the beam free body diagram with support reactions and loads.
- Replace the uniform distributed load (if any) with the equivalent point load.
- If the loading (UDL) diagram is rectangle, the equivalent point load is W = wL, and its point of application is L/2 (mid point of the figure)
- If the loading (UVL) diagram is triangle, the equivalent point load is W = wL/2, and its point of application is L/3 as shown in the figure
- Solve ΣFx = 0 (sum of all horizontal forces) for finding the horizontal reaction (if any)
- Solve ΣMA = 0 (sum of moments about support A) or Solve ΣMB = 0 (sum of moments about support B) This will give you the unknown reactions.
- Check if ΣFy = 0 (sum of all vertical forces) is satisfied.
∑ MA = 0
Apply the second equilibrium equation is:
∑ Fy = 0
RA + RB - 12 - 12 = 0
RA + RB = 24 -----(2)
Substitute the RB in the above equation
RA = 24 - RB = 24 - 14 = 10 KN ans
The equivalent point load P1 = 3 x 5.5 =16.5 KN
Along direction x, there is no imposed force applied to the structure. There is only the one unknown at support C, reaction Rcx in longitudinal axis, this reaction will always be zero.
∑ Fx = 0
Rcx = 0 ---- (1)
∑ MA = 0
- 8 x Rcy + P1x2.75 + P1 x6.75 = 0 ------(1)
- 8 x Rcy + 16.5 x2.75 + 18.75 x6.75 = 0
Rcy = 21.492 KN
Apply the second equilibrium equation is: ∑ Fy = 0
RA + Rcy - 16.5 - 18.75 = 0
RA + Rcy = 35.25 -----(2)
Substitute the Rcy in the above equation
RA = 35.25- Rcy = 35.25 - 21.492 = 13.758KN
∑ MA = 0
∑ MA = {WL/2 }2L/3 - RB L ----(2)
RB = WL/3
and RA = WL/6 (Form eq 1)
Assignment :
Q 1. Determine the support reactions of a simply supported beam loaded with a UDL of 7.7kN/m as shown in fig.
Q 2. Determine the support reactions of a simply supported beam, is loaded with a udl and several concentrated loads as shown in fig.
Q 3. Determine the support reactions of a simply supported beam, with a point load and udl as shown in fig.
1.Ra=1475.295kN/m, Rb=372.705kN/m
ReplyDelete2.R1=1840kg/m, R2=560kg/m
3.R1=950kh/m, R2=650kh/m
4.R1=200N/m, R2=600N/m
1.Ra=1475.3KN,Rb=372.71
ReplyDelete2.R1=1840Kg/m,R2=560Kg/m
3.R1=948.99Kg/m,R2=950Kg/m
4.R1=200N/m,R2=600N/m