1. A continuous beam ABCD is constructed of built-up sections whose effective flexural rigidity EI...

Question

1. A continuous beam ABCD is constructed of built-up sections whose effective flexural rigidity EI is constant throughout its length. Bay lengths are AB=1m, BC=5m and CD=4m. The beam is simply at B, C and D, and carries point loads of 20kN and 60kN at A and midway between C and D respectively, and a distributed of 30kN/m over BC. Determine the bending moments and vertical reactions at the supports and sketch the BM and SF diagrams.
2. A continuous beam ABCD is simply supported over three spans AB=1m, BC=2m and CD=2m. The first span carries a central load of 20kN and the third span a uniformly distributed load of 30kN/m. The central span remains unloaded. Calculate the bending moments at B and C and draw the shear force and bending moment diagrams. The supports remain at the same level when the beam is loaded.

Robert · Accepted Answer

1-
The whole beam is continuous and simply supported at B, C and D. 
By Vertical Equilibrium:- 
               RB + RC + RD = 20+60+30*5 =230…………………………………………………………………….(1) 
By applying overall moment equilibrium about point B 
             20*1 – 150*2.5 -60*7 = RC*5 + RD*9………………………………………………………………..(2) 
By applying overall moment equilibrium about point C 
20*6 + 150*2.5- 60*2 - RB * 5 + RD * 4 = 0…………………………………………………………………….(3) 
By solving the above equations  
RB= 85.7 KN 
RC= 130.93 KN 
RD= 13.

1. A continuous beam ABCD is constructed of built-up sections whose effective flexural rigidity EI is constant throughout its length. Bay lengths are AB=1m, BC=5m and CD=4m. The beam is simply at B, C...

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