Civil Engineering (CE) Exam > Civil Engineering (CE) Notes > Structural Analysis > The Slope Deflection Method: Frames with Sidesway - 4
The Slope Deflection Method: Frames with Sidesway - 4 | Structural Analysis - Civil Engineering (CE) PDF Download
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1
curve " AB rotates by an angle
AB
? , rotates by " "C B
BC
? and rotates by DC
CD
? as shown in figure. Due to symmetry,
AB CD
? ? = . From the geometry of the
figure,
AB AB
AB
L L
BB
1
" ?
- = = ?
But
a cos
1
?
= ?
Thus,
5 cos
?
- =
?
- =
a
?
AB
AB
L
5
?
- =
CD
?
5
tan
2
tan 2
2
2
?
= ? =
?
=
?
= a
a
?
BC
(1)
We have three independent unknowns for this problem
C B
? ? , and . The ends ?
A and are fixed. Hence, D . 0 = =
D A
? ? Fixed end moments are,
. 0 ; 0 ; . 50 . 2 ; . 50 . 2 ; 0 ; 0 = = - = + = = =
F
DC
F
CD
F
CB
F
BC
F
BA
F
AB
M M m kN M m kN M M M
Now, writing the slope-deflection equations for the six beam end moments,
[]
AB A AB
I E
M ? ? 3
1 . 5
) 2 ( 2
- =
? + = EI EI M
B AB
471 . 0 784 . 0 ?
? + = EI EI M
B BA
471 . 0 568 . 1 ?
? - + + = EI EI EI M
C B BC
6 . 0 2 5 . 2 ? ?
? - + + - = EI EI EI M
C B BC
6 . 0 2 5 . 2 ? ?
? + = EI EI M
C CD
471 . 0 568 . 1 ?
? + = EI EI M
C DC
471 . 0 784 . 0 ? (2)
Now, considering the joint equilibrium of B andC , yields
Page 2
curve " AB rotates by an angle
AB
? , rotates by " "C B
BC
? and rotates by DC
CD
? as shown in figure. Due to symmetry,
AB CD
? ? = . From the geometry of the
figure,
AB AB
AB
L L
BB
1
" ?
- = = ?
But
a cos
1
?
= ?
Thus,
5 cos
?
- =
?
- =
a
?
AB
AB
L
5
?
- =
CD
?
5
tan
2
tan 2
2
2
?
= ? =
?
=
?
= a
a
?
BC
(1)
We have three independent unknowns for this problem
C B
? ? , and . The ends ?
A and are fixed. Hence, D . 0 = =
D A
? ? Fixed end moments are,
. 0 ; 0 ; . 50 . 2 ; . 50 . 2 ; 0 ; 0 = = - = + = = =
F
DC
F
CD
F
CB
F
BC
F
BA
F
AB
M M m kN M m kN M M M
Now, writing the slope-deflection equations for the six beam end moments,
[]
AB A AB
I E
M ? ? 3
1 . 5
) 2 ( 2
- =
? + = EI EI M
B AB
471 . 0 784 . 0 ?
? + = EI EI M
B BA
471 . 0 568 . 1 ?
? - + + = EI EI EI M
C B BC
6 . 0 2 5 . 2 ? ?
? - + + - = EI EI EI M
C B BC
6 . 0 2 5 . 2 ? ?
? + = EI EI M
C CD
471 . 0 568 . 1 ?
? + = EI EI M
C DC
471 . 0 784 . 0 ? (2)
Now, considering the joint equilibrium of B andC , yields
0 0 = + ? =
?
BC
BA B
M M M
5 . 2 129 . 0 568 . 3 - = ? - + EI EI EI
C B
? ? (3)
0 0 = + ? =
?
CD
CB C
M M M
5 . 2 129 . 0 568 . 3 = ? - + EI EI EI
B C
? ? (4)
Shear equation for
Column AB
0 ) 1 ( 5
1 1
= + - - V M M H
BA AB
(5)
Column CD
0 ) 1 ( 5
2 2
= + - - V M M H
DC CD
(6)
Beam BC
0 10 2 0
1
= - - - =
?
CB BC C
M M V M (7)
Page 3
curve " AB rotates by an angle
AB
? , rotates by " "C B
BC
? and rotates by DC
CD
? as shown in figure. Due to symmetry,
AB CD
? ? = . From the geometry of the
figure,
AB AB
AB
L L
BB
1
" ?
- = = ?
But
a cos
1
?
= ?
Thus,
5 cos
?
- =
?
- =
a
?
AB
AB
L
5
?
- =
CD
?
5
tan
2
tan 2
2
2
?
= ? =
?
=
?
= a
a
?
BC
(1)
We have three independent unknowns for this problem
C B
? ? , and . The ends ?
A and are fixed. Hence, D . 0 = =
D A
? ? Fixed end moments are,
. 0 ; 0 ; . 50 . 2 ; . 50 . 2 ; 0 ; 0 = = - = + = = =
F
DC
F
CD
F
CB
F
BC
F
BA
F
AB
M M m kN M m kN M M M
Now, writing the slope-deflection equations for the six beam end moments,
[]
AB A AB
I E
M ? ? 3
1 . 5
) 2 ( 2
- =
? + = EI EI M
B AB
471 . 0 784 . 0 ?
? + = EI EI M
B BA
471 . 0 568 . 1 ?
? - + + = EI EI EI M
C B BC
6 . 0 2 5 . 2 ? ?
? - + + - = EI EI EI M
C B BC
6 . 0 2 5 . 2 ? ?
? + = EI EI M
C CD
471 . 0 568 . 1 ?
? + = EI EI M
C DC
471 . 0 784 . 0 ? (2)
Now, considering the joint equilibrium of B andC , yields
0 0 = + ? =
?
BC
BA B
M M M
5 . 2 129 . 0 568 . 3 - = ? - + EI EI EI
C B
? ? (3)
0 0 = + ? =
?
CD
CB C
M M M
5 . 2 129 . 0 568 . 3 = ? - + EI EI EI
B C
? ? (4)
Shear equation for
Column AB
0 ) 1 ( 5
1 1
= + - - V M M H
BA AB
(5)
Column CD
0 ) 1 ( 5
2 2
= + - - V M M H
DC CD
(6)
Beam BC
0 10 2 0
1
= - - - =
?
CB BC C
M M V M (7)
?
= + = 5 0
2 1
H H F
X
(8)
?
= - - = 0 10 0
2 1
V V F
Y
(9)
From equation (7),
2
10
1
+ +
=
CB BC
M M
V
From equation (8),
2 1
5 H H - =
From equation (9), 10
2
10
10
1 2
-
+ +
= - =
CB BC
M M
V V
Substituting the values of and in equations (5) and (6),
1 1
,H V
2
V
0 2 2 10 60
2
= + + - - -
CB BC BA AB
M M M M H (10)
0 2 2 10 10
2
= + + - - + -
CB BC DC CD
M M M M H (11)
Eliminating in equation (10) and (11),
2
H
25 = - - + + +
CB BC DC CD BA AB
M M M M M M (12)
Substituting the values of in (12) we get the required third
equation. Thus,
DC CD BA AB
M M M M , , ,
+ ? + EI EI
B
471 . 0 784 . 0 ? + ? + EI EI
B
471 . 0 568 . 1 ? + ? + EI EI
C
471 . 0 568 . 1 ?
? + EI EI
C
471 . 0 784 . 0 ? -( ? - + + EI EI EI
C B
6 . 0 2 5 . 2 ? ? )-
( ? - + + - EI EI EI
C B
6 . 0 2 5 . 2 ? ? ) 25 =
Simplifying,
25 084 . 3 648 . 0 648 . 0 = ? + - - EI EI EI
B C
? ? (13)
Solving simultaneously equations (3) (4) and (13), yields
205 . 1 ; 741 . 0 = - =
C B
EI EI ? ? and 204 . 8 = ? EI .
Substituting the values of
C B
EI EI ? ? , and ? EI in the slope-deflection equation
(3), one could calculate beam end moments. Thus,
3.28 kN.m
AB
M =
Page 4
curve " AB rotates by an angle
AB
? , rotates by " "C B
BC
? and rotates by DC
CD
? as shown in figure. Due to symmetry,
AB CD
? ? = . From the geometry of the
figure,
AB AB
AB
L L
BB
1
" ?
- = = ?
But
a cos
1
?
= ?
Thus,
5 cos
?
- =
?
- =
a
?
AB
AB
L
5
?
- =
CD
?
5
tan
2
tan 2
2
2
?
= ? =
?
=
?
= a
a
?
BC
(1)
We have three independent unknowns for this problem
C B
? ? , and . The ends ?
A and are fixed. Hence, D . 0 = =
D A
? ? Fixed end moments are,
. 0 ; 0 ; . 50 . 2 ; . 50 . 2 ; 0 ; 0 = = - = + = = =
F
DC
F
CD
F
CB
F
BC
F
BA
F
AB
M M m kN M m kN M M M
Now, writing the slope-deflection equations for the six beam end moments,
[]
AB A AB
I E
M ? ? 3
1 . 5
) 2 ( 2
- =
? + = EI EI M
B AB
471 . 0 784 . 0 ?
? + = EI EI M
B BA
471 . 0 568 . 1 ?
? - + + = EI EI EI M
C B BC
6 . 0 2 5 . 2 ? ?
? - + + - = EI EI EI M
C B BC
6 . 0 2 5 . 2 ? ?
? + = EI EI M
C CD
471 . 0 568 . 1 ?
? + = EI EI M
C DC
471 . 0 784 . 0 ? (2)
Now, considering the joint equilibrium of B andC , yields
0 0 = + ? =
?
BC
BA B
M M M
5 . 2 129 . 0 568 . 3 - = ? - + EI EI EI
C B
? ? (3)
0 0 = + ? =
?
CD
CB C
M M M
5 . 2 129 . 0 568 . 3 = ? - + EI EI EI
B C
? ? (4)
Shear equation for
Column AB
0 ) 1 ( 5
1 1
= + - - V M M H
BA AB
(5)
Column CD
0 ) 1 ( 5
2 2
= + - - V M M H
DC CD
(6)
Beam BC
0 10 2 0
1
= - - - =
?
CB BC C
M M V M (7)
?
= + = 5 0
2 1
H H F
X
(8)
?
= - - = 0 10 0
2 1
V V F
Y
(9)
From equation (7),
2
10
1
+ +
=
CB BC
M M
V
From equation (8),
2 1
5 H H - =
From equation (9), 10
2
10
10
1 2
-
+ +
= - =
CB BC
M M
V V
Substituting the values of and in equations (5) and (6),
1 1
,H V
2
V
0 2 2 10 60
2
= + + - - -
CB BC BA AB
M M M M H (10)
0 2 2 10 10
2
= + + - - + -
CB BC DC CD
M M M M H (11)
Eliminating in equation (10) and (11),
2
H
25 = - - + + +
CB BC DC CD BA AB
M M M M M M (12)
Substituting the values of in (12) we get the required third
equation. Thus,
DC CD BA AB
M M M M , , ,
+ ? + EI EI
B
471 . 0 784 . 0 ? + ? + EI EI
B
471 . 0 568 . 1 ? + ? + EI EI
C
471 . 0 568 . 1 ?
? + EI EI
C
471 . 0 784 . 0 ? -( ? - + + EI EI EI
C B
6 . 0 2 5 . 2 ? ? )-
( ? - + + - EI EI EI
C B
6 . 0 2 5 . 2 ? ? ) 25 =
Simplifying,
25 084 . 3 648 . 0 648 . 0 = ? + - - EI EI EI
B C
? ? (13)
Solving simultaneously equations (3) (4) and (13), yields
205 . 1 ; 741 . 0 = - =
C B
EI EI ? ? and 204 . 8 = ? EI .
Substituting the values of
C B
EI EI ? ? , and ? EI in the slope-deflection equation
(3), one could calculate beam end moments. Thus,
3.28 kN.m
AB
M =
2.70 kN.m
BA
M =
2.70 kN.m
BC
M = -
5.75 kN.m
CB
M = -
5.75 kN.m
CD
M =
4.81 kN.m
DC
M = . (14)
The bending moment diagram for the frame is shown in Fig. 17.5 d.
Summary
In this lesson, slope-deflection equations are derived for the plane frame
undergoing sidesway. Using these equations, plane frames with sidesway are
analysed. The reactions are calculated from static equilibrium equations. A
couple of problems are solved to make things clear. In each numerical example,
the bending moment diagram is drawn and deflected shape is sketched for the
plane frame.
Read More
|
34 videos|140 docs|31 tests
|
FAQs on The Slope Deflection Method: Frames with Sidesway - 4 - Structural Analysis - Civil Engineering (CE)
| 1. What is the slope deflection method in civil engineering? |  |
Ans. The slope deflection method is a structural analysis technique used in civil engineering to determine the bending moments and rotations at various points in a frame structure. It can be used to analyze frames with sidesway, where the lateral deflection of the frame influences the distribution of internal forces.
| 2. How does the slope deflection method handle frames with sidesway? | |
Ans. The slope deflection method handles frames with sidesway by considering the influence of lateral deflection on the distribution of internal forces. It allows for the calculation of bending moments and rotations at various points in the frame, taking into account the sidesway effects. This method is particularly useful for analyzing tall and slender structures that are prone to lateral deflection.
| 3. What are the advantages of using the slope deflection method for frames with sidesway? | |
Ans. The slope deflection method offers several advantages for analyzing frames with sidesway. It allows for the accurate determination of internal forces, including bending moments and rotations, considering the effects of lateral deflection. This method also takes into account the stiffness and flexibility of the structure, providing a more realistic analysis. Additionally, the slope deflection method is suitable for both statically determinate and indeterminate frames.
| 4. Are there any limitations or assumptions associated with the slope deflection method? | |
Ans. Yes, there are some limitations and assumptions associated with the slope deflection method. One of the main assumptions is that the frame is linearly elastic, meaning that it behaves within the linear range of its material properties. Additionally, the method assumes that the frame is subjected to static loading conditions and neglects any dynamic effects. It also assumes that the frame members are connected rigidly at their joints, without any rotational or translational movements.
| 5. Can the slope deflection method be used for all types of frame structures? | |
Ans. The slope deflection method can be used for a wide range of frame structures, including both statically determinate and indeterminate frames. However, its applicability may depend on the complexity and size of the structure. For highly complex or large-scale frames, other analysis methods such as the matrix stiffness method or finite element method may be more suitable. It is important to consider the specific characteristics of the frame and consult structural engineering guidelines to determine the most appropriate analysis method.
Related Exams
About this Document
|
4.96/5 Rating |
|
Oct 31, 2024 Last updated |
Document Description: The Slope Deflection Method: Frames with Sidesway - 4 for Civil Engineering (CE) 2024 is part of Structural Analysis preparation.
The notes and questions for The Slope Deflection Method: Frames with Sidesway - 4 have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The Slope Deflection Method: Frames with Sidesway - 4 covers topics
like and The Slope Deflection Method: Frames with Sidesway - 4 Example, for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for The Slope Deflection Method: Frames with Sidesway - 4.
Introduction of The Slope Deflection Method: Frames with Sidesway - 4 in English is available as part of our Structural Analysis
for Civil Engineering (CE) & The Slope Deflection Method: Frames with Sidesway - 4 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 Slope Deflection Method: Frames with Sidesway - 4 | Structural Analysis - Civil Engineering (CE)
Description
Full syllabus notes, lecture & questions for The Slope Deflection Method: Frames with Sidesway - 4 | 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 Slope Deflection Method: Frames with Sidesway - 4
In this doc you can find the meaning of The Slope Deflection Method: Frames with Sidesway - 4 defined & explained in the simplest way possible. Besides explaining types of
The Slope Deflection Method: Frames with Sidesway - 4 theory, EduRev gives you an ample number of questions to practice The Slope Deflection Method: Frames with Sidesway - 4 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
Previous Year Questions with Solutions
,Objective type Questions
,practice quizzes
,ppt
,video lectures
,Viva Questions
,Extra Questions
,The Slope Deflection Method: Frames with Sidesway - 4 | Structural Analysis - Civil Engineering (CE)
,shortcuts and tricks
,Summary
,MCQs
,study material
,The Slope Deflection Method: Frames with Sidesway - 4 | Structural Analysis - Civil Engineering (CE)
,Important questions
,Semester Notes
,Exam
,mock tests for examination
,Free
,past year papers
,The Slope Deflection Method: Frames with Sidesway - 4 | Structural Analysis - Civil Engineering (CE)
,Sample Paper
;
Additional Information about The Slope Deflection Method: Frames with Sidesway - 4 for Civil Engineering (CE) Preparation
The Slope Deflection Method: Frames with Sidesway - 4 Free PDF Download
The The Slope Deflection Method: Frames with Sidesway - 4 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 Slope Deflection Method: Frames with Sidesway - 4 now and kickstart your journey towards success in the Civil Engineering (CE) exam.
Importance of The Slope Deflection Method: Frames with Sidesway - 4
The importance of The Slope Deflection Method: Frames with Sidesway - 4 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 Slope Deflection Method: Frames with Sidesway - 4 Notes
The Slope Deflection Method: Frames with Sidesway - 4 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 Slope Deflection Method: Frames with Sidesway - 4.
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 Slope Deflection Method: Frames with Sidesway - 4 Notes on EduRev are your ultimate resource for success.
The Slope Deflection Method: Frames with Sidesway - 4 Civil Engineering (CE) Questions
The "The Slope Deflection Method: Frames with Sidesway - 4 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 Slope Deflection Method: Frames with Sidesway - 4 on the App
Students of Civil Engineering (CE) can study The Slope Deflection Method: Frames with Sidesway - 4 alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the The Slope Deflection Method: Frames with Sidesway - 4,
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 Slope Deflection Method: Frames with Sidesway - 4 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!
within 7 days!
Takes less than 10 seconds to signup