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3 kN 30° 0.1 m 0.1 m -0.2 m -0.3 m- 5 kN 4 kN (a)

3 kN 30° 0.1 m 0.1 m -0.2 m -0.3 m- 5 kN 4 kN (a)

Structural Analysis
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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Replace the force and couple system shown  by an
equivalent resultant force and couple moment acting at point O.

3 kN 30° 0.1 m 0.1 m -0.2 m -0.3 m- 5 kN 4 kN (a)
Transcribed Image Text:3 kN 30° 0.1 m 0.1 m -0.2 m -0.3 m- 5 kN 4 kN (a)
Expert Solution
Step 1 Introduction:-

Civil Engineering homework question answer, step 1, image 1

Free body diagram with all representation of values obtained in answer

Step 2 Solution:-
  • Forces Calculations:-

The forces are resolved in x and y components.

∑(FR)x=  ∑ Fx

(FR)x = 3cos 30 + (3/5)*5 = 5.598 kN

∑(FR)y=  ∑ Fy

(FR)y = 3sin30 – (4.5) *5 – 4 = -6.50 kN

Using Pythagorean theorem:-

FR =√(FR)x2 + (FR)y 2

FR=√(5.598)2+(6.50)2

FR = 8.58kN

ϴ = tan-1 ((FR)x  /(FR)y)

ϴ = tan-1 ( 6.50 / 5.598) = 49.3

  • Calculation of moments:-

(MR)O = ∑ Mo

(MR)O= {3 * sin30 *0.2} –{ 3* cos 30*0.1}  +{( 3/5) *5*0.1}-{(4/5) *5*0.5} – ( 4*0.2)

(MR)O = - 2.46kNm

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