Find all the internal forces of the truss. 60 k-U₁L₁(4)-2 at 20 ft = 40 ft(3)10 ft10 ft

Answered: Find all the internal forces of the…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

Find all the internal forces of the truss.

60 k-
U₁
L₁
(4)
-2 at 20 ft = 40 ft
(3)
10 ft
10 ft

Expert Solution

Step 1

Objective: To determine the internal forces in all members of the truss.

Following is the free body diagram of the truss:

NOTE: The joints have been labelled for easier reference.

$\sum M (A) = 0 [C C W +]$

$\to R_{C} \times \frac{1}{\sqrt{1^{2} + 2^{2}}} \times 10 f t + R_{C} \times \frac{2}{\sqrt{1^{2} + 2^{2}}} \times 40 f t - 60 k i p s \times 20 f t = 0$

$\to R_{C} \times \frac{90}{\sqrt{5}} = 1200 k i p s$

$\Rightarrow R_{C} = 1200 \times \frac{\sqrt{5}}{90} k i p s = \frac{40 \sqrt{5}}{3} k i p s$

$\sum F_{x} = 0 [R I G H T +]$

$\to 60 k i p s - A_{x} - R_{C} \times \frac{1}{\sqrt{5}} = 0$

$\to 60 k i p s - A_{x} - \frac{40 \sqrt{5}}{3} k i p s \times \frac{1}{\sqrt{5}} = 0$

$\Rightarrow A_{x} = (60 - \frac{40}{3}) k i p s = \frac{140}{3} k i p s$

$\sum F_{y} = 0 [U P +]$

$\to A_{y} + R_{C} \times \frac{2}{\sqrt{5}} = 0$

$\to A_{y} + \frac{40 \sqrt{5}}{3} k i p s \times \frac{2}{\sqrt{5}} = 0$

$\Rightarrow A_{y} = \frac{80}{3} k i p s$

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