3-Panel Truss with Flexible Cables Used as Diagonals | CE Board Problem in Structural Engineering and Construction

Date of Exam

May 2016

Subject

Situation
Flexible cables BE and CD are used to brace the truss shown below.

1. Determine the load W to cause a compression force of 8.9 kN to member BD.

A. 7.80 kN	C. 26.70 kN
B. 35.64 kN	D. 13.35 kN

2. Which cable is in tension and what is the tensile reaction?

A. BE = 12.58 kN	C. BE = 6.29 kN
B. CD = 6.29 kN	D. CD = 12.58 kN

3. If W = 20 kN, what will be the tensile reaction of member CE?

A. 6.67 kN	C. 0
B. 13.33 kN	D. 10 kN

Answer Key

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Part 1: [ D ]
Part 2: [ C ]
Part 3: [ A ]

Solution

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$\Sigma M_F = 0$

$12R_A = 4W$

$R_A = W/3$

Part 1 (F_BD = 8.9 kN):

$\Sigma M_E = 0$

$8(\frac{1}{3}W) = 4F_{BD}$

$\frac{8}{3}W = 4(8.9)$

$W = 13.35 ~ \text{kN}$ Answer: [ D ]

Part 2:

$\Sigma F_V = 0$

$F_{BE}\sin 45^\circ = \frac{1}{3}W$

$F_{BE}\sin 45^\circ = \frac{1}{3}(13.35)$

$F_{BE} = 6.29 ~ \text{kN}$ Answer: [ C ]

Part 3 (W = 20 kN):

$\Sigma M_B = 0$

$4F_{CE} = 4(\frac{1}{3}W)$

$4F_{CE} = \frac{4}{3}(20)$

$F_{CE} = 6.67 ~ \text{kN}$ Answer: [ A ]