Answered: Determine the Shear force and Bending…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

Determine the Shear force and Bending moment calculations and draw the Shear force and Bending moment diagrams

A
4 kN
2 m
4 kN/m
B
8 kN C
1 m
Figure 6.44
1 m
ալ
D
F
60°
10 kN
1 m
E

Expert Solution

Step 1: Replace the force applied at point F with equivalent force-couple system at point D.

Resolve the force applied at point F into horizontal and vertical components.
a) Horizontal component $F subscript x equals 10 space kN cross times sin 60 degree equals 8.66 space kN$
b) Vertical component $F subscript y equals 10 space kN cross times cos 60 degree equals 5 space kN$

Evaluate the equivalent force couple system at point D.
Equivalent force:

Equivalent force along x-direction at D is
$table row cell D subscript x end cell equals cell F subscript x end cell row blank equals cell 8.66 space kN end cell end table$

Equivalent force along y-direction at D is
$table row cell D subscript y end cell equals cell F subscript y end cell row blank equals cell 5 space kN end cell end table$

Equivalent couple:

Equivalent couple/moment at point D due to force at F is
$M subscript D equals open parentheses F subscript x cross times DF close parentheses$
Here DF is distance between points D and F.
$table row cell M subscript D end cell equals cell open parentheses 8.66 space kN cross times 1 space straight m close parentheses end cell row blank equals cell 8.66 space kN times straight m open parentheses clockwise close parentheses end cell end table$

Represent the beam with modified loading as shown.

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