DEVELOP THE FOLLOWING CASTIGLIANO THEOREM EXERCISE STEP BY STEP, PLACING THE MISSING STEPS 9-39. Solve Prob. 9-38 using Castigliano's theorem.The moment function is shown in Fig. a. HereWOLM =4-x-=Wo3L³. ThusWOLXOM dx4Ac =- [~ (~~) - ² / (+-+-+M= 2OPEIJOWOL4120EIWo-x³3LΕΙOM 1aP=2.x.dxAlso, set P = 0, then£+M=£x+ w/² x - W₁² x ³WoWOLWoJRPWo(a)Bاد½/22 wol€ +W

To find the deflection at point C using Castigliano's theorem.

9-39. Solve Prob. 9-38 using Castigliano's theorem. M 1 The moment function is shown in Fig. a. Here = -x. Also, set P= 0, then WOL M = 4 Ac ・I²M(² = WO 3L WOL4 120EI x³. Thus aM dx OP EI ↓ JP WO X ( ( + - ++) (+) 4 3L Jo ΕΙ = 2 dx + WOL M = £ x +w+ ²x - Wo x ³ 3 3² V Wo 1/1/22 P Wo رمان (a) B 31/12 £+ N WOL

9-39. Solve Prob. 9-38 using Castigliano's theorem. M 1 The moment function is shown in Fig. a. Here = -x. Also, set P= 0, then WOL M = 4 Ac ・I²M(² = WO 3L WOL4 120EI x³. Thus aM dx OP EI ↓ JP WO X ( ( + - ++) (+) 4 3L Jo ΕΙ = 2 dx + WOL M = £ x +w+ ²x - Wo x ³ 3 3² V Wo 1/1/22 P Wo رمان (a) B 31/12 £+ N WOL

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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Concept explainers

Slope and Deflection

The slope in a deflected beam is described as an angle in radians made by the tangent of the section with the original axis of the beam. The deflection at any point on the axis of the beam is defined as the lateral displacement of the point before and after loading.

Question

DEVELOP THE FOLLOWING CASTIGLIANO THEOREM EXERCISE STEP BY STEP, PLACING THE MISSING STEPS

9-39. Solve Prob. 9-38 using Castigliano's theorem.
The moment function is shown in Fig. a. Here
WOL
M =
4
-x-
=
Wo
3L
³. Thus
WOL
X
OM dx
4
Ac =
- [~ (~~) - ² / (+-+-+
M
= 2
OPEI
JO
WOL4
120EI
Wo
-x³
3L
ΕΙ
OM 1
aP
=
2.x.
dx
Also, set P = 0, then
£+
M=£x+ w/² x - W₁² x ³
Wo
WOL
Wo
JR
P
Wo
(a)
B
اد
½/22 wol
€ +W

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Step 1: Given:

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Step 2: Apply a dummy force at point C and find the reactions:

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Step 3: Apply the Castigliano's theorem to find the deflection at the point C:

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