=========================preview======================
(civl115)[2006](f)quiz1~PPSpider^solution_10058.pdf
Back to CIVL115 Login to download
======================================================
CIVL 115 Fall 2006 Quiz 1 Solutions by Dr. Hu
Question 1 (50%)
A rectangular plate is supported by three cables AB, AC and AD as shown above. If the tension in cable AC is 54 kN, and the resultant of the forces exerted by the three cables at A is vertical, determine the tension in cables AB and AD.
Solution:
1. Create the unit vectors UAB, UAC, UAD 5. Get components
and
2. Assign numerical value to FAC (tension in AC)
3. Sum of cable forces =
6. Solve 2 equations: FX = 0 and FZ = 0 for 7. Use decimal places to get floating point #.
2 unknowns: {tension in AB and in AD} Answer: FAB = 489.6 kN, FAD = 514.8 kN
y
x
Question 2 (50%)
A fence made with four wooden posts and a steel cable is shown below. The cable is fastened to each post, and anchored to the ground at A and D. The sum of the moments about the z-axis due to the two forces exerted by the cable on posts at B and C is -66 N.m. If the tension in cable BA is TBA = 112 N, determine the magnitude of TCD , i.e. tension in CD.
Solution:
1.
Create unit vectors in B-A and C-D directions
2.
Create r = [0, 1, 0], a vector going straight up, from the rotation axis z (at bottom of post B or C) to top of the post, where cable force is applied. Note that the same r can be used for both posts when doing the cross product Frvv.
3.
Compute total moment =:
4. Equate the z-component of m to -66, solve for the unknown FCD:
Answer: FCD = 27N