Civil Engineering (CE) Exam > Civil Engineering (CE) Notes > Structural Analysis > The Direct Stiffness Method: Beams - 5
The Direct Stiffness Method: Beams - 5 | Structural Analysis - Civil Engineering (CE) PDF Download
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1
(5)
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
-
- - -
- - -
-
-
=
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
6
5
4
3
2
1
6
5
4
3
1875 . 0 375 . 0 0 1875 . 0 0 375 . 0
375 . 0 0 . 1 0 375 . 0 0 5 . 0
0 0 1875 . 0 1875 . 0 375 . 0 375 . 0
1875 . 0 375 . 0 1875 . 0 375 . 0 375 . 0 0
0 0 375 . 0 375 . 0 0 . 1 5 . 0
375 . 0 5 . 0 375 . 0 0 5 . 0 2
67 . 6
0
u
u
u
u
u
u
EI
p
p
p
p
zz
We know that 0
6 5 4 3
= = = = u u u u . Thus solving for unknowns and , yields
1
u
2
u
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
=
?
?
?
?
?
?
?
?
?
?
2
1
0 . 1 5 . 0
5 . 0 0 . 2
67 . 6
0
u
u
EI
zz
(6)
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
-
=
?
?
?
?
?
?
?
?
?
?
67 . 6
0
0 . 2 5 . 0
5 . 0 0 . 1
75 . 1
1
2
1
zz
EI
u
u
?
?
?
?
?
?
?
?
?
? -
=
62 7
905 1
1
.
.
EI
zz
(7)
Thus displacements are,
zz zz
EI
u
EI
u
62 . 7
and
905 . 1
2 1
=
-
=
The unknown joint loads are given by,
?
?
?
?
?
?
?
?
?
? -
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
- -
=
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
62 . 7
905 . 1
1
0 375 . 0
0 5 . 0
375 . 0 375 . 0
375 . 0 0
6
5
4
3
zz
zz
EI
EI
p
p
p
p
Page 2
(5)
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
-
- - -
- - -
-
-
=
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
6
5
4
3
2
1
6
5
4
3
1875 . 0 375 . 0 0 1875 . 0 0 375 . 0
375 . 0 0 . 1 0 375 . 0 0 5 . 0
0 0 1875 . 0 1875 . 0 375 . 0 375 . 0
1875 . 0 375 . 0 1875 . 0 375 . 0 375 . 0 0
0 0 375 . 0 375 . 0 0 . 1 5 . 0
375 . 0 5 . 0 375 . 0 0 5 . 0 2
67 . 6
0
u
u
u
u
u
u
EI
p
p
p
p
zz
We know that 0
6 5 4 3
= = = = u u u u . Thus solving for unknowns and , yields
1
u
2
u
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
=
?
?
?
?
?
?
?
?
?
?
2
1
0 . 1 5 . 0
5 . 0 0 . 2
67 . 6
0
u
u
EI
zz
(6)
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
-
=
?
?
?
?
?
?
?
?
?
?
67 . 6
0
0 . 2 5 . 0
5 . 0 0 . 1
75 . 1
1
2
1
zz
EI
u
u
?
?
?
?
?
?
?
?
?
? -
=
62 7
905 1
1
.
.
EI
zz
(7)
Thus displacements are,
zz zz
EI
u
EI
u
62 . 7
and
905 . 1
2 1
=
-
=
The unknown joint loads are given by,
?
?
?
?
?
?
?
?
?
? -
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
- -
=
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
62 . 7
905 . 1
1
0 375 . 0
0 5 . 0
375 . 0 375 . 0
375 . 0 0
6
5
4
3
zz
zz
EI
EI
p
p
p
p
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
-
-
=
714 . 0
95 . 0
14 . 2
857 . 2
(8)
The actual support reactions are,
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
=
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
-
-
+
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
=
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
286 . 9
62 . 7
86 . 7
857 . 22
714 . 0
95 . 0
14 . 2
857 . 2
10
67 . 6
10
20
6
5
4
3
R
R
R
R
(9)
Member end actions for element 1
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
?
?
?
?
?
?
?
?
?
?
?
?
-
- - -
-
-
+
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
=
?
?
?
?
?
?
?
?
?
?
?
?
?
?
905 . 1
0
0
0
1
0 . 1 375 . 0 5 . 0 375 . 0
375 . 0 1875 . 0 375 . 0 1875 . 0
5 . 0 375 . 0 0 . 1 375 . 0
375 . 0 1875 . 0 375 . 0 1875 . 0
66 . 6
10
66 . 6
10
4
3
2
1
zz
zz
EI
EI
q
q
q
q
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
=
565 . 8
714 . 10
707 . 5
285 . 9
(10)
Member end actions for element 2
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
?
?
?
?
?
?
?
?
?
?
?
?
-
- - -
-
-
+
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
=
?
?
?
?
?
?
?
?
?
?
?
?
?
?
62 . 7
0
905 . 1
0
1
0 . 1 375 . 0 5 . 0 375 . 0
375 . 0 1875 . 0 375 . 0 1875 . 0
5 . 0 375 . 0 0 . 1 375 . 0
375 . 0 1875 . 0 375 . 0 1875 . 0
66 . 6
10
66 . 6
10
4
3
2
1
zz
zz
EI
EI
q
q
q
q
?
?
?
?
?
?
?
?
?
?
?
?
?
?
=
0
856 . 7
565 . 8
14 . 12
Page 3
(5)
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
-
- - -
- - -
-
-
=
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
6
5
4
3
2
1
6
5
4
3
1875 . 0 375 . 0 0 1875 . 0 0 375 . 0
375 . 0 0 . 1 0 375 . 0 0 5 . 0
0 0 1875 . 0 1875 . 0 375 . 0 375 . 0
1875 . 0 375 . 0 1875 . 0 375 . 0 375 . 0 0
0 0 375 . 0 375 . 0 0 . 1 5 . 0
375 . 0 5 . 0 375 . 0 0 5 . 0 2
67 . 6
0
u
u
u
u
u
u
EI
p
p
p
p
zz
We know that 0
6 5 4 3
= = = = u u u u . Thus solving for unknowns and , yields
1
u
2
u
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
=
?
?
?
?
?
?
?
?
?
?
2
1
0 . 1 5 . 0
5 . 0 0 . 2
67 . 6
0
u
u
EI
zz
(6)
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
-
=
?
?
?
?
?
?
?
?
?
?
67 . 6
0
0 . 2 5 . 0
5 . 0 0 . 1
75 . 1
1
2
1
zz
EI
u
u
?
?
?
?
?
?
?
?
?
? -
=
62 7
905 1
1
.
.
EI
zz
(7)
Thus displacements are,
zz zz
EI
u
EI
u
62 . 7
and
905 . 1
2 1
=
-
=
The unknown joint loads are given by,
?
?
?
?
?
?
?
?
?
? -
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
- -
=
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
62 . 7
905 . 1
1
0 375 . 0
0 5 . 0
375 . 0 375 . 0
375 . 0 0
6
5
4
3
zz
zz
EI
EI
p
p
p
p
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
-
-
=
714 . 0
95 . 0
14 . 2
857 . 2
(8)
The actual support reactions are,
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
=
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
-
-
+
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
=
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
286 . 9
62 . 7
86 . 7
857 . 22
714 . 0
95 . 0
14 . 2
857 . 2
10
67 . 6
10
20
6
5
4
3
R
R
R
R
(9)
Member end actions for element 1
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
?
?
?
?
?
?
?
?
?
?
?
?
-
- - -
-
-
+
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
=
?
?
?
?
?
?
?
?
?
?
?
?
?
?
905 . 1
0
0
0
1
0 . 1 375 . 0 5 . 0 375 . 0
375 . 0 1875 . 0 375 . 0 1875 . 0
5 . 0 375 . 0 0 . 1 375 . 0
375 . 0 1875 . 0 375 . 0 1875 . 0
66 . 6
10
66 . 6
10
4
3
2
1
zz
zz
EI
EI
q
q
q
q
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
=
565 . 8
714 . 10
707 . 5
285 . 9
(10)
Member end actions for element 2
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
?
?
?
?
?
?
?
?
?
?
?
?
-
- - -
-
-
+
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
=
?
?
?
?
?
?
?
?
?
?
?
?
?
?
62 . 7
0
905 . 1
0
1
0 . 1 375 . 0 5 . 0 375 . 0
375 . 0 1875 . 0 375 . 0 1875 . 0
5 . 0 375 . 0 0 . 1 375 . 0
375 . 0 1875 . 0 375 . 0 1875 . 0
66 . 6
10
66 . 6
10
4
3
2
1
zz
zz
EI
EI
q
q
q
q
?
?
?
?
?
?
?
?
?
?
?
?
?
?
=
0
856 . 7
565 . 8
14 . 12
Summary
In the previous lesson the beam element stiffness matrix is derived from
fundamentals. Assembling member stiffness matrices, the global stiffness matrix
is generated. The procedure to impose boundary conditions on the load-
displacement relation is discussed. In this lesson, a few continuous beam
problems are analysed by the direct stiffness method.
Read More
|
34 videos|140 docs|31 tests
|
FAQs on The Direct Stiffness Method: Beams - 5 - Structural Analysis - Civil Engineering (CE)
| 1. What is the direct stiffness method for beams? |  |
Ans. The direct stiffness method is a numerical technique used to analyze the behavior of beams. It involves breaking down the beam into smaller elements and determining the stiffness matrix for each element. These stiffness matrices are then assembled to form the global stiffness matrix, which can be used to solve for displacements, forces, and moments in the beam.
| 2. How does the direct stiffness method handle boundary conditions? | |
Ans. The direct stiffness method handles boundary conditions by applying constraints or known displacements at the ends of the beam. These constraints are incorporated into the global stiffness matrix through the use of boundary condition equations. By solving the resulting system of equations, the method can determine the unknown displacements, forces, and moments at any point along the beam.
| 3. What are the advantages of using the direct stiffness method for beam analysis? | |
Ans. The direct stiffness method offers several advantages for beam analysis. Firstly, it allows for the analysis of complex beam structures with varying material properties, cross-sections, and loading conditions. Secondly, it provides accurate results by considering the stiffness of each individual element, rather than assuming a constant stiffness throughout the beam. Lastly, it can handle both linear and nonlinear behavior, making it versatile for a wide range of applications.
| 4. What are the limitations of the direct stiffness method for beam analysis? | |
Ans. While the direct stiffness method is a powerful tool for beam analysis, it does have some limitations. One limitation is that it assumes linear elastic behavior, which may not accurately represent the actual behavior of some materials. Additionally, it requires dividing the beam into discrete elements, which can be time-consuming for complex structures. Lastly, the method may become computationally expensive for large-scale analyses due to the need to solve a system of equations.
| 5. How does the direct stiffness method differ from other methods of beam analysis? | |
Ans. The direct stiffness method differs from other methods of beam analysis, such as the flexibility method or finite element method, in its approach to solving the beam equations. While the flexibility method focuses on determining the flexibility matrix of each element, the direct stiffness method calculates the stiffness matrix. The finite element method, on the other hand, uses a similar approach but allows for more complex element shapes and behaviors. Each method has its own advantages and limitations, making them suitable for different types of beam analysis problems.
Related Exams
About this Document
|
4.93/5 Rating |
|
Nov 15, 2024 Last updated |
Document Description: The Direct Stiffness Method: Beams - 5 for Civil Engineering (CE) 2024 is part of Structural Analysis preparation.
The notes and questions for The Direct Stiffness Method: Beams - 5 have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The Direct Stiffness Method: Beams - 5 covers topics
like and The Direct Stiffness Method: Beams - 5 Example, for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for The Direct Stiffness Method: Beams - 5.
Introduction of The Direct Stiffness Method: Beams - 5 in English is available as part of our Structural Analysis
for Civil Engineering (CE) & The Direct Stiffness Method: Beams - 5 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 Direct Stiffness Method: Beams - 5 | Structural Analysis - Civil Engineering (CE)
Description
Full syllabus notes, lecture & questions for The Direct Stiffness Method: Beams - 5 | 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 Direct Stiffness Method: Beams - 5
In this doc you can find the meaning of The Direct Stiffness Method: Beams - 5 defined & explained in the simplest way possible. Besides explaining types of
The Direct Stiffness Method: Beams - 5 theory, EduRev gives you an ample number of questions to practice The Direct Stiffness Method: Beams - 5 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
The Direct Stiffness Method: Beams - 5 | Structural Analysis - Civil Engineering (CE)
,Previous Year Questions with Solutions
,Summary
,Extra Questions
,Sample Paper
,practice quizzes
,Important questions
,mock tests for examination
,study material
,Free
,The Direct Stiffness Method: Beams - 5 | Structural Analysis - Civil Engineering (CE)
,Objective type Questions
,Semester Notes
,shortcuts and tricks
,Viva Questions
,The Direct Stiffness Method: Beams - 5 | Structural Analysis - Civil Engineering (CE)
,past year papers
,Exam
,MCQs
,video lectures
,ppt
;
Additional Information about The Direct Stiffness Method: Beams - 5 for Civil Engineering (CE) Preparation
The Direct Stiffness Method: Beams - 5 Free PDF Download
The The Direct Stiffness Method: Beams - 5 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 Direct Stiffness Method: Beams - 5 now and kickstart your journey towards success in the Civil Engineering (CE) exam.
Importance of The Direct Stiffness Method: Beams - 5
The importance of The Direct Stiffness Method: Beams - 5 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 Direct Stiffness Method: Beams - 5 Notes
The Direct Stiffness Method: Beams - 5 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 Direct Stiffness Method: Beams - 5.
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 Direct Stiffness Method: Beams - 5 Notes on EduRev are your ultimate resource for success.
The Direct Stiffness Method: Beams - 5 Civil Engineering (CE) Questions
The "The Direct Stiffness Method: Beams - 5 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 Direct Stiffness Method: Beams - 5 on the App
Students of Civil Engineering (CE) can study The Direct Stiffness Method: Beams - 5 alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the The Direct Stiffness Method: Beams - 5,
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 Direct Stiffness Method: Beams - 5 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