Please answer in complete solution and draw an fbd.Note: Please use the second picture as guide for the formulas. Thanks° Determine the reactions of the given beam using moment distribution method. w = 25 kN/m, P₁ = 25 kN, and P₂ = 25 KNP2Wping 1.12m8 mI21Numerical answer in 4 decimal places and positive values only:RA =RB =MB =Rc =kN (Downward)kN (Upward)kN-mkN (Upward)B 2m2mс Sign convention - consider clockwise rotation is positive, counterclockwise is negative.MBAMARFixed End Moments (FEM)- moment at the wall or fixed jointMBAMABStiffness Factor - required moment M to rotate the end A of the beam 0₁ = 1 rad.4EI(absolute) K =far end fixed3EIK=far end hingedM1M' = M, far end fixed(relative) K ==, E is constantL'3EIM(relative) K =Carry-Over Moment - the moment induced at the fixed end of a beam by the action of the momentapplied at the other end.4L-, far end hingedBM' = 0, far end hingedDistribution Factor, DF - the distribution factor at a joint of a member is the ratio of the bendingstiffness of the member to the sum of bending stiffness of all the members connected to the joint.кDF=;ΣΚNote: DF = 1, for hinge or roller supportDF = 0, for fixed support

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Engineering

Civil Engineering

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Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

Please answer in complete solution and draw an fbd.
Note: Please use the second picture as guide for the formulas. Thanks°

Determine the reactions of the given beam using moment distribution method. w = 25 kN/m, P₁ = 25 kN, and P₂ = 25 KN
P2
W
ping 1.1
2m
8 m
I
21
Numerical answer in 4 decimal places and positive values only:
RA =
RB =
MB =
Rc =
kN (Downward)
kN (Upward)
kN-m
kN (Upward)
B 2m
2m
с

Sign convention - consider clockwise rotation is positive, counterclockwise is negative.
MBA
MAR
Fixed End Moments (FEM)- moment at the wall or fixed joint
MBA
MAB
Stiffness Factor - required moment M to rotate the end A of the beam 0₁ = 1 rad.
4EI
(absolute) K =
far end fixed
3EI
K=far end hinged
M
1
M' = M, far end fixed
(relative) K ==, E is constant
L'
3EI
M
(relative) K =
Carry-Over Moment - the moment induced at the fixed end of a beam by the action of the moment
applied at the other end.
4L
-, far end hinged
B
M' = 0, far end hinged
Distribution Factor, DF - the distribution factor at a joint of a member is the ratio of the bending
stiffness of the member to the sum of bending stiffness of all the members connected to the joint.
к
DF=;
ΣΚ
Note: DF = 1, for hinge or roller support
DF = 0, for fixed support

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