Question 1:
The loaded truss shown in figure 1 is supported by a pin at A and a roller at D and is in equilibrium. All members of the structure are rigid body and their weight is negligible. AM = AO. Lines JB and NX are horizontal. Determine (In all the calculations, the free body diagrams need to be shown)
a) All zero-force members.
b) The reaction forces at the points A and D.
c) Is the truss internally statically determinate?
d) The internal force for members listed in the table (copy and complete the table).
e) By comparing the internal force of members in the table, which one is the closest to the limiting member? (The maximum internal load for tension is 1500 kN; for compression for L < 3.8 m is 1500 kN; and for compression for L >= 3.8 m is 1200 kN)
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Member
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Force (kN)
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Tension (T) Compression (C)
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L (m}
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ZB
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YB
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SU
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SV
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TV
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RT
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RS
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QS
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JL
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JK
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NP
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MP
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HO
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HM
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IO
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MO
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Question 2:
A simple frame is loaded and supported by a pin at A and a roller at B as shown in the Figure 2. The contact at point E between members AFCE and DE is smooth. Mass for all members is negligible. Determine (In all the calculations, the free body diagram must be shown).
a) The reaction forces at the points A, B and D.
b) All the forces acting on the member AFCE.
c) The internal force for member FG.
Question 3:
The two flat blocks are positioned as shown in Fig. 3. The blocks are connected by a solid rod. The solid rod is attached to each block with frictionless pins.
a) If the coefficients of friction between the floor and blocks A and B are 0.3 and 0.4 respectively; find the minimum weight of block A to prevent motion if block B weighs 200 kg
b) Assume block A weighs 400 kg and block B weighs 300 kg. Find the minimum coefficient of friction between the floor and block A to prevent motion, if µ = 0.2 between block B and the floor.
c) Assume the coefficient of friction µ = 0.25 for both blocks and the block A weighs 180 kg. If a rightward force F of 2200 N is applied to the block A, find the maximum weight of block B that can started it moving up the incline.
Free body diagrams must be provided for each case.
Question 4:
Use integration to locate the centre of mass for the uniform density quarter-cone of height h and base radius a shown in Figure 4.
Question 5:
A circus man slide down as shown in figure 5 along a curve defined by a parabola equation Y=0.04X2. The man and sled weighs 100 kg treated as a particle.
a) When the speed of the circus man at XA = 12 m is VA= 6 m/s, calculate the rate of increase of speed of the man and his normal force exerted on the slop.
b) If the speed of the man at A (XA = 5m and YA = 1m) is VA = 9 m/s and the increase of his speed is dVA/dt = 13 m/s2, calculate the magnitude of his acceleration and the slop angle at this point.
