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A two span continuous beam ABC is simply supported at A and C and is continuous over support B. Span AB = 6 m, BC = 6m. The beam carries a UDL of 2 t/m over both the spans. EI is constant for the entire beam. The fixed end moment at B in span BA or BC would be
  • a)
    12 t.m
  • b)
    9 t.m
  • c)
    8 t.m
  • d)
    6 t.m
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A two span continuous beam ABC is simply supported at A and C and is c...
Using three moment theorem,

as MA = Mc = 0

or MB = 9 t . m .
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Most Upvoted Answer
A two span continuous beam ABC is simply supported at A and C and is c...
Given data:
Span AB = 6 m
Span BC = 6 m
UDL = 2 t/m
EI = constant

To find: Fixed end moment at B in span BA or BC

Solution:
Let's consider the left side of the beam i.e., span AB to calculate the fixed end moment at B.

Reaction at A = Reaction at C = (UDL x Span)/2 = (2 x 6)/2 = 6 t
Support reaction at B = 2 x UDL x Span = 2 x 2 x 6 = 24 t

Now, consider a section x-x at a distance of 'x' from the support A.
The bending moment at section x-x will be:

Mx = 6x - (2x^2)/2 = 6x - x^2

To find the value of x at point B, we will consider the moment equation at the support B.

ΣM = 0
24 - 6(6) - Mb = 0
Mb = 9 t.m

Therefore, the fixed end moment at B in span BA or BC is 9 t.m (Option B).

Note: The same method can be applied to calculate the fixed end moment at B for span BC by considering the right side of the beam.
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A two span continuous beam ABC is simply supported at A and C and is continuous over support B. Span AB = 6 m, BC = 6m. The beam carries a UDL of 2 t/m over both the spans. EI is constant for the entire beam. The fixed end moment at B in span BA or BC would bea)12 t.mb)9 t.mc)8 t.md)6 t.mCorrect answer is option 'B'. Can you explain this answer?
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