MECH1230 – SOLID MECHANICSEXAMPLE SHEET 2 – worked solutions

1. Draw the free body diagrams:a. the uniform beam that has a mass of 100kg, centre of gravity at G, and is supported at

smooth surfaces and A, B and C

b. the hand punch, which is pinned at A and bears down on the smooth surface at B

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c. the small lift bridge ADC, having a deck that weighs 400N and centre of gravity at G. The bridge is supported by a pin at C and a lift cable AB.

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2. Find the reactions at the supports and the forces at the joints for the loaded beams below.

a) b)

c) d)

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e) f)

g)Figure 1

Ans.: a) RA= RB=0, MA=M; b) RA= RB=M/L; c) ; d) RAx=54kN, RAy=16kN, RBC=80kN; e) RA=172.5N, RB=393N, RC=455N; f) RAx=192.3N, RAy=180.1N, RB=642N; g) MA=359Nm, RAx=92.3N, RAy=185.9N, RB=449N, RCx=100N, RCy=276N

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Fx=0; RCx = 100N Fy=0; RCy = 276N

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3. Determine the force in members CD, GD and GC of the truss and indicate whether the members are in tension (T) or compression (C).

Ans.: FGD=0, FCD=8kN (T), FGC=7kN (T)

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4. The Howe roof truss supports the vertical loading shown. Determine the force in members KJ, CD, and KD and indicate whether the members are in tension (T) or compression (C).

Ans.: FKJ=5.59kN (C), FCD=7kN (T), FKD=2.83kN (C)

7. For the loaded beams below, determine the equations for the Bending Moment M(x) and Shear Force Q(x) distributions. Apply these equations to sketch the shear force and bending moment diagrams and to determine the location of the maximum bending moment and shear force.

a) b)

b) d)

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P = 800Na = 5mL = 12m

e)

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