Civil Engineering (CE) Exam > Civil Engineering (CE) Notes > Structural Analysis > The Direct Stiffness Method: Truss Analysis - 7
The Direct Stiffness Method: Truss Analysis - 7 | Structural Analysis - Civil Engineering (CE) PDF Download
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1
The nodes and members are numbered in Fig. 25.6b. The global co-ordinate
axes are shown at node 3. At node 2, roller is supported on inclined support.
Hence it is required to use nodal co-ordinates " " y x - at node 2 so that
4
u could be
set to zero. All the possible displacement degrees of freedom are also shown in
the figure. In the first step calculate member stiffness matrix.
Member 1: . 00 . 5 , 87 . 6 , 13 . 143
"
m L
x x
= ° = ° = ? ? Nodal points 1-2
12 . 0 " ; 993 . 0 " ; 6 . 0 ; 80 . 0 = = = - = m l m l .
[]
4
3
2
1
014 . 0 119 . 0 072 . 0 096 . 0
119 . 0 986 . 0 596 . 0 794 . 0
072 . 0 596 . 0 36 . 0 48 . 0
096 . 0 794 . 0 48 . 0 64 . 0
0 . 5
4 3 2 1
1
?
?
?
?
?
?
?
?
?
?
?
?
-
-
- - -
-
=
EA
k
(1)
Page 2
The nodes and members are numbered in Fig. 25.6b. The global co-ordinate
axes are shown at node 3. At node 2, roller is supported on inclined support.
Hence it is required to use nodal co-ordinates " " y x - at node 2 so that
4
u could be
set to zero. All the possible displacement degrees of freedom are also shown in
the figure. In the first step calculate member stiffness matrix.
Member 1: . 00 . 5 , 87 . 6 , 13 . 143
"
m L
x x
= ° = ° = ? ? Nodal points 1-2
12 . 0 " ; 993 . 0 " ; 6 . 0 ; 80 . 0 = = = - = m l m l .
[]
4
3
2
1
014 . 0 119 . 0 072 . 0 096 . 0
119 . 0 986 . 0 596 . 0 794 . 0
072 . 0 596 . 0 36 . 0 48 . 0
096 . 0 794 . 0 48 . 0 64 . 0
0 . 5
4 3 2 1
1
?
?
?
?
?
?
?
?
?
?
?
?
-
-
- - -
-
=
EA
k
(1)
Member 2: . 00 . 4 , 30 , 0
"
m L
x x
= ° = ° = ? ? Nodal points 2-3
50 . 0 " ; 866 . 0 " ; 0 ; 1 = = = = m l m l .
Page 3
The nodes and members are numbered in Fig. 25.6b. The global co-ordinate
axes are shown at node 3. At node 2, roller is supported on inclined support.
Hence it is required to use nodal co-ordinates " " y x - at node 2 so that
4
u could be
set to zero. All the possible displacement degrees of freedom are also shown in
the figure. In the first step calculate member stiffness matrix.
Member 1: . 00 . 5 , 87 . 6 , 13 . 143
"
m L
x x
= ° = ° = ? ? Nodal points 1-2
12 . 0 " ; 993 . 0 " ; 6 . 0 ; 80 . 0 = = = - = m l m l .
[]
4
3
2
1
014 . 0 119 . 0 072 . 0 096 . 0
119 . 0 986 . 0 596 . 0 794 . 0
072 . 0 596 . 0 36 . 0 48 . 0
096 . 0 794 . 0 48 . 0 64 . 0
0 . 5
4 3 2 1
1
?
?
?
?
?
?
?
?
?
?
?
?
-
-
- - -
-
=
EA
k
(1)
Member 2: . 00 . 4 , 30 , 0
"
m L
x x
= ° = ° = ? ? Nodal points 2-3
50 . 0 " ; 866 . 0 " ; 0 ; 1 = = = = m l m l .
[]
4
3
6
5
014 . 0 119 . 0 072 . 0 096 . 0
119 . 0 986 . 0 596 . 0 794 . 0
072 . 0 596 . 0 36 . 0 48 . 0
096 . 0 794 . 0 48 . 0 64 . 0
0 . 4
4 3 6 5
2
?
?
?
?
?
?
?
?
?
?
?
?
-
-
- - -
-
=
EA
k
(2)
Member 3: . 00 . 3 , 90 m L
x
= ° = ? , 1 ; 0 = = m l Nodal points 3-1
.
[]
2
1
6
5
1 0 1 0
0 0 0 0
1 0 1 0
0 0 0 0
0 . 3
2 1 6 5
3
?
?
?
?
?
?
?
?
?
?
?
?
-
-
=
EA
k
(3)
For the present problem, the global stiffness matrix is of the order() 6 6 × . The
global stiffness matrix for the entire truss is.
[]
6
5
4
3
2
1
333 . 0 0 0 0 333 . 0 0
0 25 . 0 125 . 0 217 . 0 0 0
0 125 . 0 065 . 0 132 . 0 014 . 0 . 019 . 0
0 217 . 0 132 . 0 385 . 0 119 . 0 159 . 0
333 . 0 0 014 . 0 119 . 0 405 . 0 096 . 0
0 0 019 . 0 159 . 0 096 . 0 128 . 0
6 5 4 3 2 1
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
- -
-
- -
- - - -
-
= EA k
(4)
Writing load-displacement equation for the truss for unconstrained degrees of
freedom,
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
- -
-
=
?
?
?
?
?
?
?
?
?
? -
3
2
1
385 . 0 119 . 0 159 . 0
119 . 0 405 . 0 096 . 0
159 . 0 096 . 0 128 . 0
0
5
5
u
u
u
(5)
Solving ,
AE
u
AE
u
AE
u
12 . 33
;
728 . 3
;
408 . 77
3 2 1
= =
-
=
(6)
Page 4
The nodes and members are numbered in Fig. 25.6b. The global co-ordinate
axes are shown at node 3. At node 2, roller is supported on inclined support.
Hence it is required to use nodal co-ordinates " " y x - at node 2 so that
4
u could be
set to zero. All the possible displacement degrees of freedom are also shown in
the figure. In the first step calculate member stiffness matrix.
Member 1: . 00 . 5 , 87 . 6 , 13 . 143
"
m L
x x
= ° = ° = ? ? Nodal points 1-2
12 . 0 " ; 993 . 0 " ; 6 . 0 ; 80 . 0 = = = - = m l m l .
[]
4
3
2
1
014 . 0 119 . 0 072 . 0 096 . 0
119 . 0 986 . 0 596 . 0 794 . 0
072 . 0 596 . 0 36 . 0 48 . 0
096 . 0 794 . 0 48 . 0 64 . 0
0 . 5
4 3 2 1
1
?
?
?
?
?
?
?
?
?
?
?
?
-
-
- - -
-
=
EA
k
(1)
Member 2: . 00 . 4 , 30 , 0
"
m L
x x
= ° = ° = ? ? Nodal points 2-3
50 . 0 " ; 866 . 0 " ; 0 ; 1 = = = = m l m l .
[]
4
3
6
5
014 . 0 119 . 0 072 . 0 096 . 0
119 . 0 986 . 0 596 . 0 794 . 0
072 . 0 596 . 0 36 . 0 48 . 0
096 . 0 794 . 0 48 . 0 64 . 0
0 . 4
4 3 6 5
2
?
?
?
?
?
?
?
?
?
?
?
?
-
-
- - -
-
=
EA
k
(2)
Member 3: . 00 . 3 , 90 m L
x
= ° = ? , 1 ; 0 = = m l Nodal points 3-1
.
[]
2
1
6
5
1 0 1 0
0 0 0 0
1 0 1 0
0 0 0 0
0 . 3
2 1 6 5
3
?
?
?
?
?
?
?
?
?
?
?
?
-
-
=
EA
k
(3)
For the present problem, the global stiffness matrix is of the order() 6 6 × . The
global stiffness matrix for the entire truss is.
[]
6
5
4
3
2
1
333 . 0 0 0 0 333 . 0 0
0 25 . 0 125 . 0 217 . 0 0 0
0 125 . 0 065 . 0 132 . 0 014 . 0 . 019 . 0
0 217 . 0 132 . 0 385 . 0 119 . 0 159 . 0
333 . 0 0 014 . 0 119 . 0 405 . 0 096 . 0
0 0 019 . 0 159 . 0 096 . 0 128 . 0
6 5 4 3 2 1
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
- -
-
- -
- - - -
-
= EA k
(4)
Writing load-displacement equation for the truss for unconstrained degrees of
freedom,
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
-
- -
-
=
?
?
?
?
?
?
?
?
?
? -
3
2
1
385 . 0 119 . 0 159 . 0
119 . 0 405 . 0 096 . 0
159 . 0 096 . 0 128 . 0
0
5
5
u
u
u
(5)
Solving ,
AE
u
AE
u
AE
u
12 . 33
;
728 . 3
;
408 . 77
3 2 1
= =
-
=
(6)
Now reactions are evaluated from the equation
?
?
?
?
?
?
?
?
?
?
-
?
?
?
?
?
?
?
?
?
?
-
- =
?
?
?
?
?
?
?
?
?
?
12 . 33
728 . 3
40 . 77
1
0 333 . 0 0
217 . 0 0 0
132 . 0 014 . 0 . 019 . 0
6
5
4
AE
AE
p
p
p
(6)
45 6
2.85 kN ; 7.19 kN ; 1.24 kN pp p ==- =-
Summary
Sometimes the truss is supported on a roller placed on an oblique plane. In such
situations, the direct stiffness method as discussed in the previous lesson needs
to be properly modified to make the displacement perpendicular to the roller
support as zero. In the present approach, the inclined support is handled in the
analysis by suitably modifying the member stiffness matrices of all members
meeting at the inclined support. A few problems are solved to illustrate the
procedure.
Read More
|
34 videos|140 docs|31 tests
|
FAQs on The Direct Stiffness Method: Truss Analysis - 7 - Structural Analysis - Civil Engineering (CE)
| 1. What is the direct stiffness method in truss analysis? |  |
Ans. The direct stiffness method is a numerical technique used to analyze truss structures. It involves breaking down the truss into individual elements and applying the principles of equilibrium and compatibility to solve for unknown forces and displacements. The method utilizes the stiffness matrix, which relates the forces and displacements of each element, to obtain the overall behavior of the truss.
| 2. How does the direct stiffness method work in truss analysis? | |
Ans. The direct stiffness method works by dividing the truss into smaller elements and representing each element with a stiffness matrix. The stiffness matrix relates the forces and displacements at each node of the truss element. By assembling these stiffness matrices for all elements and considering boundary conditions, a global stiffness matrix is formed. The unknown displacements and forces can then be solved by solving the system of equations formed by the global stiffness matrix.
| 3. What are the advantages of using the direct stiffness method in truss analysis? | |
Ans. The direct stiffness method offers several advantages in truss analysis. It allows for the efficient analysis of complex truss structures by breaking them down into smaller, more manageable elements. The method also accounts for the stiffness and flexibility of the truss members, making it applicable to real-world situations. Additionally, the direct stiffness method can handle different types of loading conditions and boundary conditions, providing accurate results for various scenarios.
| 4. What are the limitations of the direct stiffness method in truss analysis? | |
Ans. While the direct stiffness method is a powerful tool for truss analysis, it does have some limitations. One limitation is that it assumes linear behavior of the truss members, which may not hold true in certain cases. Additionally, the method requires a significant amount of computational resources and can become time-consuming for large and complex truss structures. Furthermore, the direct stiffness method may not be suitable for analyzing trusses with large displacements or nonlinear material properties.
| 5. How is the direct stiffness method used in practical applications of truss analysis? | |
Ans. The direct stiffness method is widely used in engineering practice for the analysis of truss structures. It is employed in the design and analysis of bridges, buildings, aerospace structures, and various mechanical systems. The method provides engineers with valuable insights into the behavior and performance of trusses under different loading conditions. By accurately predicting forces, displacements, and stresses, the direct stiffness method helps ensure the structural integrity and safety of truss-based systems.
Related Exams
About this Document
|
4.62/5 Rating |
|
Nov 15, 2024 Last updated |
Document Description: The Direct Stiffness Method: Truss Analysis - 7 for Civil Engineering (CE) 2024 is part of Structural Analysis preparation.
The notes and questions for The Direct Stiffness Method: Truss Analysis - 7 have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The Direct Stiffness Method: Truss Analysis - 7 covers topics
like and The Direct Stiffness Method: Truss Analysis - 7 Example, for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for The Direct Stiffness Method: Truss Analysis - 7.
Introduction of The Direct Stiffness Method: Truss Analysis - 7 in English is available as part of our Structural Analysis
for Civil Engineering (CE) & The Direct Stiffness Method: Truss Analysis - 7 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: Truss Analysis - 7 | Structural Analysis - Civil Engineering (CE)
Description
Full syllabus notes, lecture & questions for The Direct Stiffness Method: Truss Analysis - 7 | 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: Truss Analysis - 7
In this doc you can find the meaning of The Direct Stiffness Method: Truss Analysis - 7 defined & explained in the simplest way possible. Besides explaining types of
The Direct Stiffness Method: Truss Analysis - 7 theory, EduRev gives you an ample number of questions to practice The Direct Stiffness Method: Truss Analysis - 7 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
study material
,Sample Paper
,mock tests for examination
,The Direct Stiffness Method: Truss Analysis - 7 | Structural Analysis - Civil Engineering (CE)
,Exam
,shortcuts and tricks
,Free
,Viva Questions
,Important questions
,practice quizzes
,video lectures
,The Direct Stiffness Method: Truss Analysis - 7 | Structural Analysis - Civil Engineering (CE)
,ppt
,MCQs
,Objective type Questions
,Summary
,The Direct Stiffness Method: Truss Analysis - 7 | Structural Analysis - Civil Engineering (CE)
,Semester Notes
,past year papers
,Extra Questions
,Previous Year Questions with Solutions
;
Additional Information about The Direct Stiffness Method: Truss Analysis - 7 for Civil Engineering (CE) Preparation
The Direct Stiffness Method: Truss Analysis - 7 Free PDF Download
The The Direct Stiffness Method: Truss Analysis - 7 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: Truss Analysis - 7 now and kickstart your journey towards success in the Civil Engineering (CE) exam.
Importance of The Direct Stiffness Method: Truss Analysis - 7
The importance of The Direct Stiffness Method: Truss Analysis - 7 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: Truss Analysis - 7 Notes
The Direct Stiffness Method: Truss Analysis - 7 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: Truss Analysis - 7.
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: Truss Analysis - 7 Notes on EduRev are your ultimate resource for success.
The Direct Stiffness Method: Truss Analysis - 7 Civil Engineering (CE) Questions
The "The Direct Stiffness Method: Truss Analysis - 7 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: Truss Analysis - 7 on the App
Students of Civil Engineering (CE) can study The Direct Stiffness Method: Truss Analysis - 7 alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the The Direct Stiffness Method: Truss Analysis - 7,
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: Truss Analysis - 7 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