Civil Engineering (CE) Exam > Civil Engineering (CE) Notes > Structural Analysis > The Moment Distribution Method: Frames with Sidesway - 3
The Moment Distribution Method: Frames with Sidesway - 3 | Structural Analysis - Civil Engineering (CE) PDF Download
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1
571 . 0 ; 429 . 0 = =
CD CB
DF DF
b) Calculate fixed end moments due to applied loading.
2
2
12 3 3
9.0 kN.m
6
F
AB
M
××
== ; 9.0 kN.m
F
BA
M =-
0kN.m
F
BC
M = ; 0kN.m
F
CB
M =
0kN.m
F
CD
M = ; 0kN.m
F
DC
M =
c) Prevent sidesway by providing artificial support at C. Carry out moment-
distribution ( Case . .e i A in Fig. 21.5b). The moment-distribution for this case is
shown in Fig. 21.5c.
Page 2
571 . 0 ; 429 . 0 = =
CD CB
DF DF
b) Calculate fixed end moments due to applied loading.
2
2
12 3 3
9.0 kN.m
6
F
AB
M
××
== ; 9.0 kN.m
F
BA
M =-
0kN.m
F
BC
M = ; 0kN.m
F
CB
M =
0kN.m
F
CD
M = ; 0kN.m
F
DC
M =
c) Prevent sidesway by providing artificial support at C. Carry out moment-
distribution ( Case . .e i A in Fig. 21.5b). The moment-distribution for this case is
shown in Fig. 21.5c.
Now calculate horizontal reaction at A and from equations of statics. D
()
1
11.694 3.614
6 7.347 kN
6
A
H
-
=+= ?
()
1
1.154 0.578
0.577 kN
3
D
H
--
==- ?
( ) 12 (7.347 0.577) 5.23 kN R=- - =- ?
d) Moment-distribution for arbitrary sidesway ' ? (case B, Fig. 21.5c)
Calculate fixed end moments for the arbitrary sidesway of
EI
150
' = ? .
6 (2 ) 12 150
( ) 50 kN.m ; 50 kN.m ;
66
F F
AB BA
EI EI
MM
L EI
? =- = × - =+ =+
Page 3
571 . 0 ; 429 . 0 = =
CD CB
DF DF
b) Calculate fixed end moments due to applied loading.
2
2
12 3 3
9.0 kN.m
6
F
AB
M
××
== ; 9.0 kN.m
F
BA
M =-
0kN.m
F
BC
M = ; 0kN.m
F
CB
M =
0kN.m
F
CD
M = ; 0kN.m
F
DC
M =
c) Prevent sidesway by providing artificial support at C. Carry out moment-
distribution ( Case . .e i A in Fig. 21.5b). The moment-distribution for this case is
shown in Fig. 21.5c.
Now calculate horizontal reaction at A and from equations of statics. D
()
1
11.694 3.614
6 7.347 kN
6
A
H
-
=+= ?
()
1
1.154 0.578
0.577 kN
3
D
H
--
==- ?
( ) 12 (7.347 0.577) 5.23 kN R=- - =- ?
d) Moment-distribution for arbitrary sidesway ' ? (case B, Fig. 21.5c)
Calculate fixed end moments for the arbitrary sidesway of
EI
150
' = ? .
6 (2 ) 12 150
( ) 50 kN.m ; 50 kN.m ;
66
F F
AB BA
EI EI
MM
L EI
? =- = × - =+ =+
6( ) 6 150
( ) 100 kN.m ; 100 kN.m ;
33
F F
CD DC
EI EI
MM
L EI
? =- =- × - =+ =+
The moment-distribution for this case is shown in Fig. 21.5d. Using equations of
static equilibrium, calculate reactions and .
2 A
H
2 D
H
) ( 395 . 12
6
457 . 41 911 . 32
2
? =
+
= kN H
A
) ( 952 . 39
3
285 . 73 57 . 46
2
? =
+
= kN H
D
) ( 347 . 52 ) 952 . 39 395 . 12 ( ? - = + - = kN F
e) Final results
Now, the shear condition for the frame is (vide Fig. 21.5b)
Page 4
571 . 0 ; 429 . 0 = =
CD CB
DF DF
b) Calculate fixed end moments due to applied loading.
2
2
12 3 3
9.0 kN.m
6
F
AB
M
××
== ; 9.0 kN.m
F
BA
M =-
0kN.m
F
BC
M = ; 0kN.m
F
CB
M =
0kN.m
F
CD
M = ; 0kN.m
F
DC
M =
c) Prevent sidesway by providing artificial support at C. Carry out moment-
distribution ( Case . .e i A in Fig. 21.5b). The moment-distribution for this case is
shown in Fig. 21.5c.
Now calculate horizontal reaction at A and from equations of statics. D
()
1
11.694 3.614
6 7.347 kN
6
A
H
-
=+= ?
()
1
1.154 0.578
0.577 kN
3
D
H
--
==- ?
( ) 12 (7.347 0.577) 5.23 kN R=- - =- ?
d) Moment-distribution for arbitrary sidesway ' ? (case B, Fig. 21.5c)
Calculate fixed end moments for the arbitrary sidesway of
EI
150
' = ? .
6 (2 ) 12 150
( ) 50 kN.m ; 50 kN.m ;
66
F F
AB BA
EI EI
MM
L EI
? =- = × - =+ =+
6( ) 6 150
( ) 100 kN.m ; 100 kN.m ;
33
F F
CD DC
EI EI
MM
L EI
? =- =- × - =+ =+
The moment-distribution for this case is shown in Fig. 21.5d. Using equations of
static equilibrium, calculate reactions and .
2 A
H
2 D
H
) ( 395 . 12
6
457 . 41 911 . 32
2
? =
+
= kN H
A
) ( 952 . 39
3
285 . 73 57 . 46
2
? =
+
= kN H
D
) ( 347 . 52 ) 952 . 39 395 . 12 ( ? - = + - = kN F
e) Final results
Now, the shear condition for the frame is (vide Fig. 21.5b)
129 . 0
12 ) 952 . 39 395 . 12 ( ) 577 . 0 344 . 7 (
12 ) ( ) (
2 2 1 1
=
= + + -
= + + +
k
k
H H k H H
D A D A
Now the actual end moments in the frame are,
AB AB AB
M k M M ' ' ' + =
11.694 0.129( 41.457) 17.039 kN.m
AB
M=+ + =+
3.614 0.129( 32.911) 0.629 kN.m
BA
M =- + + =
3.614 0.129( 32.911) 0.629 kN.m
BC
M=+ - =-
1.154 0.129( 46.457) 4.853 kN.m
CB
M =- + - =-
1.154 0.129( 46.457) 4.853 kN.m
CD
M =- + + =+
0.578 0.129( 73.285) 8.876 kN.m
DC
M =- + + =+
The actual sway
EI
k
150
129 . 0 ' × = ? = ?
EI
35 . 19
=
The joint rotations can be calculated using slope-deflection equations.
[ ] ? ? ? 3 2
) 2 ( 2
- + + = -
B A
F
AB AB
L
I E
M M
or
[]
?
?
?
?
?
?
?
?
?
?
?
?
- - =
?
?
?
?
?
?
+ - = +
L
EI
M M
EI
L
L
EI
M M
EI
L
F
AB AB
F
AB AB B A
? ?
? ?
12
4
12
4
2
[]
?
?
?
?
?
?
?
?
?
?
?
?
- - =
?
?
?
?
?
?
+ - = +
L
EI
M M
EI
L
L
EI
M M
EI
L
F
BA BA
F
BA BA A B
? ?
? ?
12
4
12
4
2
17.039 kN.m
AB
M =+
Page 5
571 . 0 ; 429 . 0 = =
CD CB
DF DF
b) Calculate fixed end moments due to applied loading.
2
2
12 3 3
9.0 kN.m
6
F
AB
M
××
== ; 9.0 kN.m
F
BA
M =-
0kN.m
F
BC
M = ; 0kN.m
F
CB
M =
0kN.m
F
CD
M = ; 0kN.m
F
DC
M =
c) Prevent sidesway by providing artificial support at C. Carry out moment-
distribution ( Case . .e i A in Fig. 21.5b). The moment-distribution for this case is
shown in Fig. 21.5c.
Now calculate horizontal reaction at A and from equations of statics. D
()
1
11.694 3.614
6 7.347 kN
6
A
H
-
=+= ?
()
1
1.154 0.578
0.577 kN
3
D
H
--
==- ?
( ) 12 (7.347 0.577) 5.23 kN R=- - =- ?
d) Moment-distribution for arbitrary sidesway ' ? (case B, Fig. 21.5c)
Calculate fixed end moments for the arbitrary sidesway of
EI
150
' = ? .
6 (2 ) 12 150
( ) 50 kN.m ; 50 kN.m ;
66
F F
AB BA
EI EI
MM
L EI
? =- = × - =+ =+
6( ) 6 150
( ) 100 kN.m ; 100 kN.m ;
33
F F
CD DC
EI EI
MM
L EI
? =- =- × - =+ =+
The moment-distribution for this case is shown in Fig. 21.5d. Using equations of
static equilibrium, calculate reactions and .
2 A
H
2 D
H
) ( 395 . 12
6
457 . 41 911 . 32
2
? =
+
= kN H
A
) ( 952 . 39
3
285 . 73 57 . 46
2
? =
+
= kN H
D
) ( 347 . 52 ) 952 . 39 395 . 12 ( ? - = + - = kN F
e) Final results
Now, the shear condition for the frame is (vide Fig. 21.5b)
129 . 0
12 ) 952 . 39 395 . 12 ( ) 577 . 0 344 . 7 (
12 ) ( ) (
2 2 1 1
=
= + + -
= + + +
k
k
H H k H H
D A D A
Now the actual end moments in the frame are,
AB AB AB
M k M M ' ' ' + =
11.694 0.129( 41.457) 17.039 kN.m
AB
M=+ + =+
3.614 0.129( 32.911) 0.629 kN.m
BA
M =- + + =
3.614 0.129( 32.911) 0.629 kN.m
BC
M=+ - =-
1.154 0.129( 46.457) 4.853 kN.m
CB
M =- + - =-
1.154 0.129( 46.457) 4.853 kN.m
CD
M =- + + =+
0.578 0.129( 73.285) 8.876 kN.m
DC
M =- + + =+
The actual sway
EI
k
150
129 . 0 ' × = ? = ?
EI
35 . 19
=
The joint rotations can be calculated using slope-deflection equations.
[ ] ? ? ? 3 2
) 2 ( 2
- + + = -
B A
F
AB AB
L
I E
M M
or
[]
?
?
?
?
?
?
?
?
?
?
?
?
- - =
?
?
?
?
?
?
+ - = +
L
EI
M M
EI
L
L
EI
M M
EI
L
F
AB AB
F
AB AB B A
? ?
? ?
12
4
12
4
2
[]
?
?
?
?
?
?
?
?
?
?
?
?
- - =
?
?
?
?
?
?
+ - = +
L
EI
M M
EI
L
L
EI
M M
EI
L
F
BA BA
F
BA BA A B
? ?
? ?
12
4
12
4
2
17.039 kN.m
AB
M =+
0.629 kN.m
BA
M =
()
9 0.129(50) 15.45 kN.m
F
AB
M =+ =
()
9 0.129(50) 2.55 kN.m
F
BA
M =- + = -
1
change in near end + - change in far end
2
3
1
(17.039 15.45) (0.629 2.55)
2
0.0
3
6
A
EI
L
EI
?
??
??
??
=
??
-+- +
??
??
==
4.769
B
EI
? =
Example 21.3
Analyse the rigid frame shown in Fig. 21.6a. The moment of inertia of all the
members are shown in the figure.
Read More
|
34 videos|140 docs|31 tests
|
FAQs on The Moment Distribution Method: Frames with Sidesway - 3 - Structural Analysis - Civil Engineering (CE)
| 1. What is the Moment Distribution Method? |  |
Ans. The Moment Distribution Method is a structural analysis technique used in civil engineering to analyze frames with sidesway. It allows engineers to determine the distribution of moments and shears in the members of a frame subjected to lateral loads. The method is based on the principle of successive approximation, where the moments are distributed and redistributed until equilibrium is achieved.
| 2. How does the Moment Distribution Method handle frames with sidesway? | |
Ans. The Moment Distribution Method is specifically designed to handle frames with sidesway, which refers to the lateral deflection of a frame caused by horizontal loads. This method accounts for the flexibility of the frame by taking into consideration the moments and rotations at the joints. By distributing and redistributing the moments, the method accounts for the additional flexibility of the sidesway, providing a more accurate analysis of the frame's behavior.
| 3. What are the advantages of using the Moment Distribution Method for frames with sidesway? | |
Ans. The Moment Distribution Method offers several advantages for analyzing frames with sidesway. Firstly, it provides a more accurate representation of the frame's behavior under lateral loads compared to other methods. Secondly, it allows engineers to easily determine the distribution of moments and shears in the members, enabling them to assess the structural integrity and design of the frame. Lastly, the method is relatively straightforward and computationally efficient, making it a popular choice for structural engineers.
| 4. Are there any limitations to the Moment Distribution Method for frames with sidesway? | |
Ans. While the Moment Distribution Method is a powerful tool for analyzing frames with sidesway, it does have some limitations. One limitation is that it assumes the frame remains within the elastic range, meaning it cannot accurately predict the behavior of frames that experience significant plastic deformation. Another limitation is that it may not provide accurate results for frames with complex geometry or irregular member stiffness. In such cases, more advanced analysis methods may be required.
| 5. What are some practical applications of the Moment Distribution Method for frames with sidesway? | |
Ans. The Moment Distribution Method finds extensive use in the analysis and design of various structural systems in civil engineering. It is commonly applied in the design of buildings, bridges, and other large structures subjected to lateral loads. By accurately predicting the distribution of moments and shears, engineers can ensure the structural integrity and stability of these systems. The method also allows for the optimization of member sizes and reinforcement, resulting in cost-effective and efficient designs.
Related Exams
About this Document
|
4.81/5 Rating |
|
Nov 15, 2024 Last updated |
Document Description: The Moment Distribution Method: Frames with Sidesway - 3 for Civil Engineering (CE) 2024 is part of Structural Analysis preparation.
The notes and questions for The Moment Distribution Method: Frames with Sidesway - 3 have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The Moment Distribution Method: Frames with Sidesway - 3 covers topics
like and The Moment Distribution Method: Frames with Sidesway - 3 Example, for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for The Moment Distribution Method: Frames with Sidesway - 3.
Introduction of The Moment Distribution Method: Frames with Sidesway - 3 in English is available as part of our Structural Analysis
for Civil Engineering (CE) & The Moment Distribution Method: Frames with Sidesway - 3 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): The Moment Distribution Method: Frames with Sidesway - 3 | Structural Analysis - Civil Engineering (CE)
Description
Full syllabus notes, lecture & questions for The Moment Distribution Method: Frames with Sidesway - 3 | 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 The Moment Distribution Method: Frames with Sidesway - 3
In this doc you can find the meaning of The Moment Distribution Method: Frames with Sidesway - 3 defined & explained in the simplest way possible. Besides explaining types of
The Moment Distribution Method: Frames with Sidesway - 3 theory, EduRev gives you an ample number of questions to practice The Moment Distribution Method: Frames with Sidesway - 3 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
video lectures
,ppt
,Free
,Exam
,Viva Questions
,The Moment Distribution Method: Frames with Sidesway - 3 | Structural Analysis - Civil Engineering (CE)
,Objective type Questions
,study material
,The Moment Distribution Method: Frames with Sidesway - 3 | Structural Analysis - Civil Engineering (CE)
,Previous Year Questions with Solutions
,Sample Paper
,Semester Notes
,Important questions
,shortcuts and tricks
,Extra Questions
,mock tests for examination
,The Moment Distribution Method: Frames with Sidesway - 3 | Structural Analysis - Civil Engineering (CE)
,past year papers
,MCQs
,practice quizzes
,Summary
;
Additional Information about The Moment Distribution Method: Frames with Sidesway - 3 for Civil Engineering (CE) Preparation
The Moment Distribution Method: Frames with Sidesway - 3 Free PDF Download
The The Moment Distribution Method: Frames with Sidesway - 3 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 The Moment Distribution Method: Frames with Sidesway - 3 now and kickstart your journey towards success in the Civil Engineering (CE) exam.
Importance of The Moment Distribution Method: Frames with Sidesway - 3
The importance of The Moment Distribution Method: Frames with Sidesway - 3 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.
The Moment Distribution Method: Frames with Sidesway - 3 Notes
The Moment Distribution Method: Frames with Sidesway - 3 Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to The Moment Distribution Method: Frames with Sidesway - 3.
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, The Moment Distribution Method: Frames with Sidesway - 3 Notes on EduRev are your ultimate resource for success.
The Moment Distribution Method: Frames with Sidesway - 3 Civil Engineering (CE) Questions
The "The Moment Distribution Method: Frames with Sidesway - 3 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 The Moment Distribution Method: Frames with Sidesway - 3 on the App
Students of Civil Engineering (CE) can study The Moment Distribution Method: Frames with Sidesway - 3 alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the The Moment Distribution Method: Frames with Sidesway - 3,
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 The Moment Distribution Method: Frames with Sidesway - 3 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