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A overhanging beam AB 5m with W1 acting in downward direction at A and 25KN acting in upward direction at B and in BC part at 4m from B ,W2 acting in downward direction and from 2 m from W2 at C , R1 acting in upward direction and its Bending moment diagram 50knm hogging upwards acting till 9 m and 2m sagging moment downwards acting M1
The values of W1, M1, W2 and R1 will be
ANS 10 KN, 10 KNm, 20 KN, 5 KN?
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A overhanging beam AB 5m with W1 acting in downward direction at A and...
Given:
Length of beam AB = 5m
Load W1 acting downward at A
Load W2 acting downward at C, 2m from C
Load R1 acting upward at B
Bending moment diagram: 50kNm hogging upwards till 9m, 2m sagging moment downwards, acting M1

To determine the values of W1, M1, W2, and R1, we can use the concepts of equilibrium and bending moment equations.

1. Equilibrium at point A:
Sum of vertical forces = 0
W1 - R1 = 0
Therefore, R1 = W1

2. Equilibrium at point B:
Sum of vertical forces = 0
R1 - 25kN = 0
Therefore, R1 = 25kN

3. Equilibrium at point C:
Sum of vertical forces = 0
W2 - R1 = 0
Therefore, W2 = R1 = 25kN

4. Bending moment at point B:
The bending moment at point B can be determined by considering the moments of the forces acting on the beam.
For the hogging moment (50kNm) upwards till 9m:
M1 + (25kN * 9m) - (W1 * 5m) = 50kNm
Substituting R1 = W1 and R1 = 25kN:
M1 + (25kN * 9m) - (R1 * 5m) = 50kNm
M1 + 225kNm - (25kN * 5m) = 50kNm
M1 + 225kNm - 125kNm = 50kNm
M1 + 100kNm = 50kNm
Therefore, M1 = 50kNm - 100kNm = -50kNm

5. Bending moment at point C:
For the sagging moment (2m) downwards:
M1 + (25kN * 9m) - (W2 * 4m) - (R1 * 2m) = 0
Substituting the values of M1, W2, and R1:
-50kNm + (25kN * 9m) - (25kN * 4m) - (25kN * 2m) = 0
-50kNm + 225kNm - 100kNm - 50kNm = 0
25kNm - 50kNm = 0
Therefore, the bending moment at point C is 25kNm.

Thus, the values of W1, M1, W2, and R1 are:
W1 = R1 = 25kN (as determined from equilibrium at point A and B)
M1 = -50kNm (as determined from the bending moment equation at point B)
W2 = R1 = 25kN (as determined from equilibrium at point C)
R1 = 25kN (as determined from equilibrium at point B)

ANS: W1 = 10kN, M1 = -10kNm, W2 = 20kN, R1 = 5kN
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A overhanging beam AB 5m with W1 acting in downward direction at A and 25KN acting in upward direction at B and in BC part at 4m from B ,W2 acting in downward direction and from 2 m from W2 at C , R1 acting in upward direction and its Bending moment diagram 50knm hogging upwards acting till 9 m and 2m sagging moment downwards acting M1The values of W1, M1, W2 and R1 will beANS 10 KN, 10 KNm, 20 KN, 5 KN?
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