I have provided a text book solution fo the following question please work the question in the same format as the solution provided in a step by step manner. Castigliano's Second Theorem - TrussDetermine the vertical displacement of joint B. AE is constant. Use the principle of virtual work.E-1.5 m|B1.5 m2m8 kN MemberABBCBDCDADDEAB。n (kN)0010-1.250.751 kN. AB, = "Σ΄=nNLAEN (kN)-6-644.75 kN. mAE010- 101244.75 kN².mAEL (m)1.51.522.52.51.5nNL (kN².m)000031.2513.5Σ 44.75Ans

Answered: Castigliano's Second Theorem - Truss…

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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I have provided a text book solution fo the following question please work the question in the same format as the solution provided in a step by step manner.

Castigliano's Second Theorem - Truss
Determine the vertical displacement of joint B. AE is constant. Use the principle of virtual work.
E
-1.5 m
|B
1.5 m
2m
8 kN

Member
AB
BC
BD
CD
AD
DE
AB。
n (kN)
0
0
1
0
-1.25
0.75
1 kN. AB, = "
Σ΄
=
nNL
AE
N (kN)
-6
-6
44.75 kN. m
AE
0
10
- 10
12
44.75 kN².m
AE
L (m)
1.5
1.5
2
2.5
2.5
1.5
nNL (kN².m)
0
0
0
0
31.25
13.5
Σ 44.75
Ans

Expert Solution

Step 1: Virtual work method

The virtual work method can be calculated using the below equation,

$1. increment equals sum for blank of fraction numerator n N L over denominator A E end fraction H e r e comma space 1 space equals space E x t e r n a l space v i r t u a l space u n i t space l o a d space a c t i n g space i n space t r u s s space i n space t h e space d i r e c t i o n space o f space d i s p l a c e m e n t space left parenthesis increment right parenthesis increment space equals space E x t e r n a l space j o i n t space d i s p l a c e m e n t space c a u s e d space b y space r e a l space l o a d n space equals space I n t e r n a l space v i r t u a l space m e m b e r space f o r c e s space c a u s e d space b y space e x t e r n a l space v i r t u a l space l o a d N space equals space M e m b e r space f o r c e space c a u s e d space b y space r e a l space l o a d L space equals space L e n g t h space o f space m e m b e r A space equals space C r o s s minus s e c t i o n a l space a r e a E space equals space M o d u l u s space o f space e l a s t i c i t y$

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