OTH396: Determine the maximum weight of the uniform bar ADB that can be supported in the position: Civil Engineering Entrance Examination, Assignment, NUS, Singapore

Question 1

The cable ABCD supports vertical loads PB and PC applied at B and C, respectively, as shown in Figure Q1. Obtain an expression for the ratio P P B C in terms of, , θθθ AB BC CD and determine the

(a) ratio P P B C for which the segment BC will be horizontal,
(b) maximum tension in the cable, if 45o θ CD = and P P B C = = 600 N.

Question 2
Determine the maximum weight of the uniform bar ADB that can be supported in the position shown in Figure Q2 given that the allowable tensile and compressive forces of the horizontal member CD attached to the mid point of the bar are 25 kN and 20 kN, respectively. The mass of member CD is negligible

Question 3
Figure Q3 shows a 4 m long rigid horizontal bar DEF, suspended at its two ends and its center by vertical rods, pinned to the bar and to the anchoring points A, B and C. The three vertical rods are made of different elastic materials, but all  of them have the same cross-sectional area of 15 mm2.

The lengths of the rods and their respective Young’s moduli are indicated in the figure. A 90 kN downward-acting load is applied 1 m from F.

(a) Identify the unknown forces and determine whether the system is determinate or indeterminate.

(b) Sketch how the system deforms after the 90 kN load is applied. How are the deflections of the points D, E and F in the bar (where it is pinned to the vertical rods) related?

(c) Calculate the reactions at the anchoring points of the vertical rods.
Neglect the self-weight of the bar.