some useful formula regarding beams and different cases of loads and support conditions.
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TUTORIAL: MOMENT DISTRIBUTION METHOD – BEAM WITHOUT SETTLEMENT Problem 1
Determine the moments at B and C , then draw the moment diagram for the beam.Assume C is a fixed support. EI is constant. Draw the shear and bending moment diagram for the beam. Answers: MAB = 0 kNm MBA = 24 kNm MBC = -24 kNm MCB = 6 kNm
Problem 2
Determine the reactions at the t he supports and then draw the moment diagram. Assume A is fixed. EI is constant.
Answers: MAB = 10.4 kNm MBA = 20.7 kNm MBC = -20.7 kNm MCB = 7.5 kNm MCD = -7.5 kNm MDC = 0 kNm
Problem 3
Determine the moments at B and C , then draw the moment diagram for the beam. Assume the supports at B and C are rollers and A is a pin. EI is constant. Answers: MAB = 0 Nm MBA = 650. 01 Nm MBC = -650.01 Nm MCB = 2400 Nm MCD = -2400 Nm MDC = 0 Nm
TUTORIAL: MOMENT DISTRIBUTION METHOD – BEAM WITH SETTLEMENT Problem 1
A continuous beam ABCD with three spans is shown in Figure Q4. A uniformly distributed load of magnitude 75 kN/m is acting on member BC and a point load of 250 kN is acting at point E. By using the Moment-Distribution Method, a) b) c) d)
Compute the stiffness factor of the beam. Determine the member end moments for the beam. Determine the vertical forces at support A, B, C and D. If support C is temporarily settled by 25 mm, calculate the new value of end moments for section BC of the beam. Take E = 70 GPa, I = 400 x 10 6 mm4.