Civil Engineering (CE) Exam > Civil Engineering (CE) Notes > Structural Analysis > Engesser Theorem & Truss Deflections by Virtual Work Principles - 2
Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 | Structural Analysis - Civil Engineering (CE) PDF Download
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1
Example 6.2
Compute the vertical deflection of joint and horizontal displacement of joint
of the truss shown in Fig. 6.3a due to
b D
a) Applied loading as shown in figure.
b) Increase in temperature of in the top chord BD. Assume
0
25 C
1
C
75000
per a=° , . The cross sectional areas of the
members in square centimeters are shown in parentheses.
2 5
/ 10 00 . 2 mm N E × =
Page 2
Example 6.2
Compute the vertical deflection of joint and horizontal displacement of joint
of the truss shown in Fig. 6.3a due to
b D
a) Applied loading as shown in figure.
b) Increase in temperature of in the top chord BD. Assume
0
25 C
1
C
75000
per a=° , . The cross sectional areas of the
members in square centimeters are shown in parentheses.
2 5
/ 10 00 . 2 mm N E × =
Page 3
Example 6.2
Compute the vertical deflection of joint and horizontal displacement of joint
of the truss shown in Fig. 6.3a due to
b D
a) Applied loading as shown in figure.
b) Increase in temperature of in the top chord BD. Assume
0
25 C
1
C
75000
per a=° , . The cross sectional areas of the
members in square centimeters are shown in parentheses.
2 5
/ 10 00 . 2 mm N E × =
The complete calculations are shown in the following table.
Table 6.3 Computational details for example 6.2
Mem
i
L
i i i
E A L /
i
P
i
v
v
P ) ( d
i
H
v
P ) ( d
i ti
tL a = ?
i i
i i i
v
v
A E
L P P ) ( d
i i
i i i
H
v
A E
L P P ) ( d
ti i
v
v
P ? ) ( d
ti i
H
v
P ? ) ( d
units m (10
-5
)
m/kN
kN kN kN m (10
-3
)
kN.m
(10
-3
)
kN.m
(10
-3
)
kN.m
(10
-3
)
kN.m
aB 5 1.0 -112.5 -0.937 +0.416 0 1.05 -0.47 0 0
ab 3 1.0 +67.5 +0.562 +0.750 0 0.38 0.51 0 0
bc 3 1.0 +67.5 +0.562 +0.750 0 0.38 0.51 0 0
Bc 5 1.0 +37.5 -0.312 -0.416 0 -0.12 -0.16 0 0
BD 6 2.0 -67.5 -0.562 +0.500 0.002 0.76 -0.68 -1.13 1
cD 5 1.0 +37.5 +0.312 +0.416 0 0.12 0.16 0 0
cd 3 1.0 +67.5 +0.187 +0.250 0 0.13 0.17 0 0
de 3 1.0 +67.5 +0.187 +0.250 0 0.13 0.17 0 0
De 5 1.0 -112.5 -0.312 -0.416 0 0.35 0.47 0 0
Bb 4 2.0 +60.0 1 0 0 1.2 0 0 0
Dd 4 2.0 +60.0 0 0 0 0 0 0 0
?
4.38 0.68 -1.13 1
Page 4
Example 6.2
Compute the vertical deflection of joint and horizontal displacement of joint
of the truss shown in Fig. 6.3a due to
b D
a) Applied loading as shown in figure.
b) Increase in temperature of in the top chord BD. Assume
0
25 C
1
C
75000
per a=° , . The cross sectional areas of the
members in square centimeters are shown in parentheses.
2 5
/ 10 00 . 2 mm N E × =
The complete calculations are shown in the following table.
Table 6.3 Computational details for example 6.2
Mem
i
L
i i i
E A L /
i
P
i
v
v
P ) ( d
i
H
v
P ) ( d
i ti
tL a = ?
i i
i i i
v
v
A E
L P P ) ( d
i i
i i i
H
v
A E
L P P ) ( d
ti i
v
v
P ? ) ( d
ti i
H
v
P ? ) ( d
units m (10
-5
)
m/kN
kN kN kN m (10
-3
)
kN.m
(10
-3
)
kN.m
(10
-3
)
kN.m
(10
-3
)
kN.m
aB 5 1.0 -112.5 -0.937 +0.416 0 1.05 -0.47 0 0
ab 3 1.0 +67.5 +0.562 +0.750 0 0.38 0.51 0 0
bc 3 1.0 +67.5 +0.562 +0.750 0 0.38 0.51 0 0
Bc 5 1.0 +37.5 -0.312 -0.416 0 -0.12 -0.16 0 0
BD 6 2.0 -67.5 -0.562 +0.500 0.002 0.76 -0.68 -1.13 1
cD 5 1.0 +37.5 +0.312 +0.416 0 0.12 0.16 0 0
cd 3 1.0 +67.5 +0.187 +0.250 0 0.13 0.17 0 0
de 3 1.0 +67.5 +0.187 +0.250 0 0.13 0.17 0 0
De 5 1.0 -112.5 -0.312 -0.416 0 0.35 0.47 0 0
Bb 4 2.0 +60.0 1 0 0 1.2 0 0 0
Dd 4 2.0 +60.0 0 0 0 0 0 0 0
?
4.38 0.68 -1.13 1
a) Vertical deflection of joint b
Applying principle of virtual work as applied to an ideal pin jointed truss,
1
11
()
m
vij i i
jj
ji
ii
PPL
Fu
EA
d
d
==
=
??
(1)
For calculating vertical deflection at b , apply a unit virtual load 1
b
F d = . Then the
above equation may be written as,
?
= ×
i i
i i i
v
v v
b
A E
L P P
u
) (
1
d
(2)
1) Due to external loads
? =
=
+
?=
mm
m
KN
KNm
u
b
38 . 4
00438 . 0
1
00438 . 0
2) Due to change in temperature
?
? = ?
ti i
v
v
t
b
P u ) ( ) )( 1 ( d
m
KN
m KN
u
t
b
00113 . 0
1
. 001125 . 0
- =
-
?=
? = mm u
t
b
13 . 1
b) Horizontal displacement of joint ‘D’
1) Due to externally applied loads
?
= ×
i i
i i i
H
v H
b
A E
L P P
u
) (
1
d
? =
=
+
?=
mm
m
KN
KNm
u
H
D
68 . 0
00068 . 0
1
00068 . 0
Page 5
Example 6.2
Compute the vertical deflection of joint and horizontal displacement of joint
of the truss shown in Fig. 6.3a due to
b D
a) Applied loading as shown in figure.
b) Increase in temperature of in the top chord BD. Assume
0
25 C
1
C
75000
per a=° , . The cross sectional areas of the
members in square centimeters are shown in parentheses.
2 5
/ 10 00 . 2 mm N E × =
The complete calculations are shown in the following table.
Table 6.3 Computational details for example 6.2
Mem
i
L
i i i
E A L /
i
P
i
v
v
P ) ( d
i
H
v
P ) ( d
i ti
tL a = ?
i i
i i i
v
v
A E
L P P ) ( d
i i
i i i
H
v
A E
L P P ) ( d
ti i
v
v
P ? ) ( d
ti i
H
v
P ? ) ( d
units m (10
-5
)
m/kN
kN kN kN m (10
-3
)
kN.m
(10
-3
)
kN.m
(10
-3
)
kN.m
(10
-3
)
kN.m
aB 5 1.0 -112.5 -0.937 +0.416 0 1.05 -0.47 0 0
ab 3 1.0 +67.5 +0.562 +0.750 0 0.38 0.51 0 0
bc 3 1.0 +67.5 +0.562 +0.750 0 0.38 0.51 0 0
Bc 5 1.0 +37.5 -0.312 -0.416 0 -0.12 -0.16 0 0
BD 6 2.0 -67.5 -0.562 +0.500 0.002 0.76 -0.68 -1.13 1
cD 5 1.0 +37.5 +0.312 +0.416 0 0.12 0.16 0 0
cd 3 1.0 +67.5 +0.187 +0.250 0 0.13 0.17 0 0
de 3 1.0 +67.5 +0.187 +0.250 0 0.13 0.17 0 0
De 5 1.0 -112.5 -0.312 -0.416 0 0.35 0.47 0 0
Bb 4 2.0 +60.0 1 0 0 1.2 0 0 0
Dd 4 2.0 +60.0 0 0 0 0 0 0 0
?
4.38 0.68 -1.13 1
a) Vertical deflection of joint b
Applying principle of virtual work as applied to an ideal pin jointed truss,
1
11
()
m
vij i i
jj
ji
ii
PPL
Fu
EA
d
d
==
=
??
(1)
For calculating vertical deflection at b , apply a unit virtual load 1
b
F d = . Then the
above equation may be written as,
?
= ×
i i
i i i
v
v v
b
A E
L P P
u
) (
1
d
(2)
1) Due to external loads
? =
=
+
?=
mm
m
KN
KNm
u
b
38 . 4
00438 . 0
1
00438 . 0
2) Due to change in temperature
?
? = ?
ti i
v
v
t
b
P u ) ( ) )( 1 ( d
m
KN
m KN
u
t
b
00113 . 0
1
. 001125 . 0
- =
-
?=
? = mm u
t
b
13 . 1
b) Horizontal displacement of joint ‘D’
1) Due to externally applied loads
?
= ×
i i
i i i
H
v H
b
A E
L P P
u
) (
1
d
? =
=
+
?=
mm
m
KN
KNm
u
H
D
68 . 0
00068 . 0
1
00068 . 0
2) Due to change in temperature
?
? = ?
ti i
H
v
Ht
D
P u ) ( ) )( 1 ( d
m
KN
m KN
u
Ht
D
001 . 0
1
. 001 . 0
= ?=
? = mm u
Ht
D
00 . 1
Summary
In this chapter the Crotti-Engessor’s theorem which is more general than the
Castigliano’s theorem has been introduced. The unit load method is applied
statically determinate structure for calculating deflections when the truss is
subjected to various types of loadings such as: mechanical loading, temperature
loading and fabrication errors.
Read More
|
34 videos|140 docs|31 tests
|
FAQs on Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 - Structural Analysis - Civil Engineering (CE)
| 1. What is Engesser's Theorem? |  |
Engesser's Theorem is a principle in structural engineering that allows the calculation of deflections in trusses using virtual work principles. It provides a method to determine the displacement of individual members in a truss structure under external loads.
| 2. How does Engesser's Theorem work? | |
Engesser's Theorem applies the principle of virtual work, which states that the virtual work done by external forces on a system in equilibrium is equal to the virtual work done by internal forces. By considering the deflection of each member as a virtual displacement, the theorem allows the calculation of internal forces and deflections in a truss.
| 3. What are the advantages of using Engesser's Theorem in truss deflection analysis? | |
Engesser's Theorem provides a simplified approach to determine truss deflections compared to more complex methods such as the flexibility matrix method. It is particularly useful for trusses with relatively simple geometry and loads. Additionally, Engesser's Theorem can be easily applied to solve deflection problems by hand calculations.
| 4. Are there any limitations to using Engesser's Theorem for truss deflection analysis? | |
Yes, Engesser's Theorem has some limitations. It assumes that the truss structure is statically determinate, meaning that the number of unknown forces and displacements is equal to the number of equilibrium equations. It also assumes that the truss members behave linearly elastically and that the deflections are small.
| 5. Can Engesser's Theorem be applied to more complex structures beyond trusses? | |
Engesser's Theorem is specifically formulated for truss structures, which are composed of straight members connected at joints. While it may not directly apply to more complex structures, the principles of virtual work can be extended to analyze other types of structures, such as beams, frames, and even three-dimensional structures, using appropriate modifications and assumptions.
Related Exams
About this Document
|
4.96/5 Rating |
|
Dec 19, 2024 Last updated |
Document Description: Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 for Civil Engineering (CE) 2024 is part of Structural Analysis preparation.
The notes and questions for Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 covers topics
like and Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 Example, for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Engesser Theorem & Truss Deflections by Virtual Work Principles - 2.
Introduction of Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 in English is available as part of our Structural Analysis
for Civil Engineering (CE) & Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 in Hindi for Structural Analysis course.
Download more important topics related with notes, lectures and mock test series for Civil Engineering (CE)
Exam by signing up for free. Civil Engineering (CE): Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 | Structural Analysis - Civil Engineering (CE)
Description
Full syllabus notes, lecture & questions for Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 | Structural Analysis - Civil Engineering (CE) - Civil Engineering (CE) | Plus excerises question with solution to help you revise complete syllabus for Structural Analysis | Best notes, free PDF download
Information about Engesser Theorem & Truss Deflections by Virtual Work Principles - 2
In this doc you can find the meaning of Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 defined & explained in the simplest way possible. Besides explaining types of
Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 theory, EduRev gives you an ample number of questions to practice Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 tests, examples and also practice Civil Engineering (CE)
tests
|
Explore Courses for Civil Engineering (CE) exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
Free
,Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 | Structural Analysis - Civil Engineering (CE)
,Extra Questions
,Important questions
,shortcuts and tricks
,Semester Notes
,ppt
,Summary
,video lectures
,past year papers
,Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 | Structural Analysis - Civil Engineering (CE)
,Exam
,Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 | Structural Analysis - Civil Engineering (CE)
,Objective type Questions
,practice quizzes
,mock tests for examination
,Viva Questions
,study material
,MCQs
,Previous Year Questions with Solutions
,Sample Paper
;
Additional Information about Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 for Civil Engineering (CE) Preparation
Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 Free PDF Download
The Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 is an invaluable resource that delves deep into the core of the Civil Engineering (CE) exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner,
allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material,
or toppers' notes, this PDF has got you covered. Download the Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 now and kickstart your journey towards success in the Civil Engineering (CE) exam.
Importance of Engesser Theorem & Truss Deflections by Virtual Work Principles - 2
The importance of Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 cannot be overstated, especially for Civil Engineering (CE) aspirants.
This document holds the key to success in the Civil Engineering (CE) exam.
It offers a detailed understanding of the concept, providing invaluable insights into the topic.
By knowing the concepts well in advance, students can plan their preparation effectively.
Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.
Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 Notes
Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to Engesser Theorem & Truss Deflections by Virtual Work Principles - 2.
It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation.
Practice papers and question papers enable you to assess your progress effectively.
Additionally, the paper analysis provides valuable tips for tackling the exam strategically.
Access to Toppers' notes gives you an edge in understanding complex concepts.
Whether you're a beginner or aiming for advanced proficiency, Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 Notes on EduRev are your ultimate resource for success.
Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 Civil Engineering (CE) Questions
The "Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 Civil Engineering (CE) Questions" guide is a valuable resource for all aspiring students preparing for the
Civil Engineering (CE) exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 on the App
Students of Civil Engineering (CE) can study Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Engesser Theorem & Truss Deflections by Virtual Work Principles - 2,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Engesser Theorem & Truss Deflections by Virtual Work Principles - 2 is prepared as per the latest Civil Engineering (CE) syllabus.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup