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OTH396: Q1 The force F of magnitude 240 N is to be resolved into two components along lines a-a and b-b as shown in Figure Q1: Civil Engineering Assignment, NUS

OTH396 BTech Engineering Bridging/Preparatory Unit: Civil Engineering

Question 1

The force F of magnitude 240 N is to be resolved into two components along lines a-a and b-b as shown in Figure Q1. Determine by trigonometry the angle α in degrees, knowing that the component F along the line b-b is to be 90 N.

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Question 2
A disabled car is pulled by means of two ropes as shown in Figure Q2. The tension in AB is 2500 N and the angle α is 25°. Knowing that the below resultant of the two forces applied at A is directed along the axis of the car, determine by trigonometry:
a) the tension in rope AC,
b) the magnitude of the resultant of the two forces applied at A

Question 3
The ring shown in Figure Q3 is subjected to two forces, F1 and F2. If the resultant force is 3 kN acting vertically downwards, determine:
a) F1 if θ = 35°
b) F1 if F2 is to be a minimum and
c) θ if F2 is to be a minimum.

Question 4
A collar, which may slide on a vertical rod, is subjected to the three forces as shown in Figure Q4. Determine (a) the value of the angle α for which the resultant of the three forces is horizontal, (b) the corresponding magnitude of the resultant.

Question 5

A 250-kg crate is supported by several rope and pulley arrangements as shown in Figure Q5. Determine for each arrangement the tension in the rope. Neglect the masses of the frictionless pulleys. Take g = 10 m/s2.

Question 6

A 6 kg circular plate of 200 mm radius is supported as shown Figure Q6 by three wires of length L. Knowing that α = 30 o, determine the smallest possible value of the length L in mm, if the tension does not exceed 35 N in any of the wires. (Use g = 10 m/s2).

Question 7
Two loads are applied to a light beam supported by cables attached at B and D as shown in Figure Q 7. Neglecting the weight of the beam, determine the range of values of load Q for which neither cable becomes slack.

Question 8
The lever AB is hinged at C and attached to a control cable at A as shown Figure Q8. If the lever is subjected at B to a 500 N horizontal force, determine (a) the tension in the cable, (b) the reaction at C.

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Question 9
Referring to Figure Q9 below and knowing that θ = 30o
, determine the magnitude of reactions
at B and C.

Question 10*
A basketball scoreboard that weighs 9 kN is to be hung from the roof frame of an indoor stadium using a cable ABC as shown in Figure Q10(a). The ends of the cable are attached to hinges at points A and C. Before the scoreboard is attached at B, the midpoint, cable ABC is slightly slack (i.e. it is longer than 3m). The weight of the scoreboard is to be applied slowly at B until equilibrium is reached. At equilibrium, point B on the cable is at a distance d below the line AC as the cable becomes taut (its length does not change, however). The cable can safely carry a maximum tension of 20 kN. Design limitations require that point B drop not more than 30cm below the horizontal dashed line AC as the scoreboard is attached.

As a consulting engineer, you are asked to design the system. Analyze the given data to see whether you can satisfy the requirements. If requirements are met, specify the precise length of the cable and the value of θ to use. If not, you are required to, design an alternate hanging configuration (shown in Figure Q10(b)) such that all requirements are met.

Question 11*

Your company is asked to design a jib crane (see Figure Q11) to lift truck engines that weigh 6 kN and lower them into crates for shipping. In general, a jib crane consists of a uniform beam (usually a beam of an I-shaped cross section) pinned at one end to a vertical column and supported by a cable or tie rod (a two-force member) at another point along its length. The beam and tie rod are connected to the column in such a way that the beam can rotate about the axis of the column through approximately 180o. The distance a indicates the maximum distance that the chain hoist can travel along the beam, which is up to within 0.3 m from the free end. Because of jars and shocks (dynamic effects) that occur in picking up and moving an engine, as a design requirement, the tie rod must be capable of withstanding a tensile force 2.5 times the static load that an engine places on the crane.

Your supervisor asks you to do a preliminary design of the system (in terms of the length a, b and h) so that the force in the tie rod is minimized. The beam length must not exceed 6.5 m to avoid collision with the surroundings when the crane rotates, yet not shorter than 5.5 m. The beam has a uniformly distributed weight of 0.3 kN/m.

With the above specifications, design the system (i.e. determine appropriate values of a, b and h) so that the tension in the tie rod is minimized, subject to further conditions that h ≤ 4 m. Suggest any further improvement to the jib cranes that might have occurred to you.

Question 12*

Figure Q12 below illustrates a stack of blocks in an equilibrium condition. The block have equal length l and equal out-of-plane thickness. Determine the maximum overhang possible, x, before the stack of blocks falls apart.

You are encouraged to verify your solution by conducting a simple experiment. You can replace the blocks with household items: books, rubber eraser, etc.
Weight of the blocks:
WI = WIII = WIV = w
WII = 2w

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