The document discusses the moment distribution method for analyzing statically indeterminate structures. It begins by outlining the basic principles and definitions of the method, including stiffness factors, carry-over factors, and distribution factors. It then provides an example problem, showing the calculation of fixed end moments, establishment of the distribution table through successive approximations, and determination of shear forces and bending moments. Finally, it discusses extensions of the method to structures with non-prismatic members, including using tables to determine necessary values for analysis.
information on types of beams, different methods to calculate beam stress, design for shear, analysis for SRB flexure, design for flexure, Design procedure for doubly reinforced beam,
Design and Detailing of RC Deep beams as per IS 456-2000VVIETCIVIL
Visit : https://teacherinneed.wordpress.com/
1. DEEP BEAM DEFINITION - IS 456
2. DEEP BEAM APPLICATION
3. DEEP BEAM TYPES
4. BEHAVIOUR OF DEEP BEAMS
5. LEVER ARM
6. COMPRESSIVE FORCE PATH CONCEPT
7. ARCH AND TIE ACTION
8. DEEP BEAM BEHAVIOUR AT ULTIMATE LIMIT STATE
9. REBAR DETAILING
10. EXAMPLE 1 – SIMPLY SUPPORTED DEEP BEAM
11. EXAMPLE 2 – SIMPLY SUPPORTED DEEP BEAM; M20, FE415
12. EXAMPLE 3: FIXED ENDS AND CONTINUOUS DEEP BEAM
13. EXAMPLE 4 : FIXED ENDS AND CONTINUOUS DEEP BEAM
information on types of beams, different methods to calculate beam stress, design for shear, analysis for SRB flexure, design for flexure, Design procedure for doubly reinforced beam,
Design and Detailing of RC Deep beams as per IS 456-2000VVIETCIVIL
Visit : https://teacherinneed.wordpress.com/
1. DEEP BEAM DEFINITION - IS 456
2. DEEP BEAM APPLICATION
3. DEEP BEAM TYPES
4. BEHAVIOUR OF DEEP BEAMS
5. LEVER ARM
6. COMPRESSIVE FORCE PATH CONCEPT
7. ARCH AND TIE ACTION
8. DEEP BEAM BEHAVIOUR AT ULTIMATE LIMIT STATE
9. REBAR DETAILING
10. EXAMPLE 1 – SIMPLY SUPPORTED DEEP BEAM
11. EXAMPLE 2 – SIMPLY SUPPORTED DEEP BEAM; M20, FE415
12. EXAMPLE 3: FIXED ENDS AND CONTINUOUS DEEP BEAM
13. EXAMPLE 4 : FIXED ENDS AND CONTINUOUS DEEP BEAM
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
ANALYSIS OF FRAMES USING SLOPE DEFLECTION METHODSagar Kaptan
slope deflection equations are applied to solve the statically indeterminate frames without side sway. In frames axial deformations are much smaller than the bending deformations and are neglected in the analysis.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
ANALYSIS OF FRAMES USING SLOPE DEFLECTION METHODSagar Kaptan
slope deflection equations are applied to solve the statically indeterminate frames without side sway. In frames axial deformations are much smaller than the bending deformations and are neglected in the analysis.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Deflection of structures using double integration method, moment area method, elastic load method, conjugate beam method, virtual work, castiglianois second theorem and method of consistent deformations
Event Management System Vb Net Project Report.pdfKamal Acharya
In present era, the scopes of information technology growing with a very fast .We do not see any are untouched from this industry. The scope of information technology has become wider includes: Business and industry. Household Business, Communication, Education, Entertainment, Science, Medicine, Engineering, Distance Learning, Weather Forecasting. Carrier Searching and so on.
My project named “Event Management System” is software that store and maintained all events coordinated in college. It also helpful to print related reports. My project will help to record the events coordinated by faculties with their Name, Event subject, date & details in an efficient & effective ways.
In my system we have to make a system by which a user can record all events coordinated by a particular faculty. In our proposed system some more featured are added which differs it from the existing system such as security.
COLLEGE BUS MANAGEMENT SYSTEM PROJECT REPORT.pdfKamal Acharya
The College Bus Management system is completely developed by Visual Basic .NET Version. The application is connect with most secured database language MS SQL Server. The application is develop by using best combination of front-end and back-end languages. The application is totally design like flat user interface. This flat user interface is more attractive user interface in 2017. The application is gives more important to the system functionality. The application is to manage the student’s details, driver’s details, bus details, bus route details, bus fees details and more. The application has only one unit for admin. The admin can manage the entire application. The admin can login into the application by using username and password of the admin. The application is develop for big and small colleges. It is more user friendly for non-computer person. Even they can easily learn how to manage the application within hours. The application is more secure by the admin. The system will give an effective output for the VB.Net and SQL Server given as input to the system. The compiled java program given as input to the system, after scanning the program will generate different reports. The application generates the report for users. The admin can view and download the report of the data. The application deliver the excel format reports. Because, excel formatted reports is very easy to understand the income and expense of the college bus. This application is mainly develop for windows operating system users. In 2017, 73% of people enterprises are using windows operating system. So the application will easily install for all the windows operating system users. The application-developed size is very low. The application consumes very low space in disk. Therefore, the user can allocate very minimum local disk space for this application.
Courier management system project report.pdfKamal Acharya
It is now-a-days very important for the people to send or receive articles like imported furniture, electronic items, gifts, business goods and the like. People depend vastly on different transport systems which mostly use the manual way of receiving and delivering the articles. There is no way to track the articles till they are received and there is no way to let the customer know what happened in transit, once he booked some articles. In such a situation, we need a system which completely computerizes the cargo activities including time to time tracking of the articles sent. This need is fulfilled by Courier Management System software which is online software for the cargo management people that enables them to receive the goods from a source and send them to a required destination and track their status from time to time.
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Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Quality defects in TMT Bars, Possible causes and Potential Solutions.PrashantGoswami42
Maintaining high-quality standards in the production of TMT bars is crucial for ensuring structural integrity in construction. Addressing common defects through careful monitoring, standardized processes, and advanced technology can significantly improve the quality of TMT bars. Continuous training and adherence to quality control measures will also play a pivotal role in minimizing these defects.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
3. 7.1 MOMENT DISTRIBUTION METHOD - AN
OVERVIEW
• 7.1 MOMENT DISTRIBUTION METHOD - AN OVERVIEW
• 7.2 INTRODUCTION
• 7.3 STATEMENT OF BASIC PRINCIPLES
• 7.4 SOME BASIC DEFINITIONS
• 7.5 SOLUTION OF PROBLEMS
• 7.6 MOMENT DISTRIBUTION METHOD FOR STRUCTURES
HAVING NONPRISMATIC MEMBERS
4. 7.2 MOMENT DISTRIBUTION METHOD -
INTRODUCTION AND BASIC PRINCIPLES
7.1 Introduction
(Method developed by Prof. Hardy Cross in 1932)
The method solves for the joint moments in continuous beams and
rigid frames by successive approximation.
7.2 Statement of Basic Principles
Consider the continuous beam ABCD, subjected to the given loads,
as shown in Figure below. Assume that only rotation of joints
occur
at B, C and D, and that no support displacements occur at B, C and
D. Due to the applied loads in spans AB, BC and CD, rotations
occur at B, C and D.
15 kN/m 10 kN/m
150 kN
8 m 6 m 8 m
A B C D
I I I
3 m
5. In order to solve the problem in a successively approximating manner,
it can be visualized to be made up of a continued two-stage problems
viz., that of locking and releasing the joints in a continuous sequence.
7.2.1 Step I
The joints B, C and D are locked in position before any load is
applied on the beam ABCD; then given loads are applied on the
beam. Since the joints of beam ABCD are locked in position, beams
AB, BC and CD acts as individual and separate fixed beams,
subjected to the applied loads; these loads develop fixed end
moments.
8 m
-80 kN.m -80 kN.m15 kN/m
A B
6 m
-112.5kN.m 112.5 kN.m
B C 8 m
-53.33 kN.m
10 kN/m
C D
150 kN
53.33 kN.m
3 m
6. In beam AB
Fixed end moment at A = -wl2
/12 = - (15)(8)(8)/12 = - 80 kN.m
Fixed end moment at B = +wl2
/12 = +(15)(8)(8)/12 = + 80 kN.m
In beam BC
Fixed end moment at B = - (Pab2
)/l2
= - (150)(3)(3)2
/62
= -112.5 kN.m
Fixed end moment at C = + (Pab2
)/l2
= + (150)(3)(3)2
/62
= + 112.5 kN.m
In beam AB
Fixed end moment at C = -wl2
/12 = - (10)(8)(8)/12 = - 53.33 kN.m
Fixed end moment at D = +wl2
/12 = +(10)(8)(8)/12 = + 53.33kN.m
7. 7.2.2 Step II
Since the joints B, C and D were fixed artificially (to compute the the fixed-
end moments), now the joints B, C and D are released and allowed to rotate.
Due to the joint release, the joints rotate maintaining the continuous nature of
the beam. Due to the joint release, the fixed end moments on either side of
joints B, C and D act in the opposite direction now, and cause a net
unbalanced moment to occur at the joint.
15 kN/m 10 kN/m
8 m 6 m 8 m
A B C D
I I I
3 m
150 kN
Released moments -80.0 -112.5 +53.33 -53.33+112.5
Net unbalanced moment
+32.5 -59.17 -53.33
8. 7.2.3 Step III
These unbalanced moments act at the joints and modify the joint moments at
B, C and D, according to their relative stiffnesses at the respective joints. The
joint moments are distributed to either side of the joint B, C or D, according
to their relative stiffnesses. These distributed moments also modify the
moments at the opposite side of the beam span, viz., at joint A in span AB, at
joints B and C in span BC and at joints C and D in span CD. This
modification is dependent on the carry-over factor (which is equal to 0.5 in
this case); when this carry over is made, the joints on opposite side are
assumed to be fixed.
7.2.4 Step IV
The carry-over moment becomes the unbalanced moment at the joints
to which they are carried over. Steps 3 and 4 are repeated till the carry-
over or distributed moment becomes small.
7.2.5 Step V
Sum up all the moments at each of the joint to obtain the joint
moments.
9. 7.3 SOME BASIC DEFINITIONS
In order to understand the five steps mentioned in section 7.3, some words
need to be defined and relevant derivations made.
7.3.1 Stiffness and Carry-over Factors
Stiffness = Resistance offered by member to a unit displacement or rotation at a
point, for given support constraint conditions
θA
MA
MB
A BA
RA RB
L
E, I – Member properties
A clockwise moment MA is
applied at A to produce a +ve
bending in beam AB. Find θA
and MB.
10. Using method of consistent deformations
L
∆A
A
MA
B
L
fAA
A
B
1
EI
LM A
A
2
2
+=∆
EI
L
fAA
3
3
=
Applying the principle of
consistent
deformation,
↓−=→=+∆
L
M
RfR A
AAAAA 2
3
0
EI
LM
EI
LR
EI
LM AAA
A
42
2
=+=θ
L
EIM
khence
L
EI
M
A
A
AA
4
;
4
===∴
θ
θ θ
Stiffness factor = kθ = 4EI/L
11. Considering moment MB,
MB + MA + RAL = 0
∴MB = MA/2= (1/2)MA
Carry - over Factor = 1/2
7.3.2 Distribution Factor
Distribution factor is the ratio according to which an externally applied
unbalanced moment M at a joint is apportioned to the various members
mating at the joint
+ ve moment M
A C
B
D
A
D
B C
MBA
MBC
MBD
At joint B
M - MBA-MBC-MBD = 0
I1
L1
I3
L3
I2
L2
M
12. i.e., M = MBA + MBC + MBD
( )
( )
MFDM
K
K
M
MFDM
K
K
M
Similarly
MFDM
K
K
KM
K
M
KKK
M
KKK
L
IE
L
IE
L
IE
BD
BD
BD
BC
BC
BC
BA
BA
BBABA
BDBCBA
B
BBDBCBA
B
).(
).(
).(
444
3
33
2
22
1
11
=
=
=
=
=
==
=
++
=∴
++=
+
+
=
∑
∑
∑
∑
θ
θ
θ
θ
13. 7.3.3 Modified Stiffness Factor
The stiffness factor changes when the far end of the beam is simply-
supported.
θAMA
A B
RA RB
L
As per earlier equations for deformation, given in Mechanics of Solids
text-books.
fixedAB
A
A
AB
A
A
K
L
EI
L
EIM
K
EI
LM
)(
4
3
4
4
33
3
=
===
=
θ
θ
14. 7.4 SOLUTION OF PROBLEMS -
7.4.1 Solve the previously given problem by the moment
distribution method
7.4.1.1: Fixed end moments
mkN
wl
MM
mkN
wl
MM
mkN
wl
MM
DCCD
CBBC
BAAB
.333.53
12
)8)(10(
12
.5.112
8
)6)(150(
8
.80
12
)8)(15(
12
22
22
−=−=−=−=
−=−=−=−=
−=−=−=−=
7.4.1.2 Stiffness Factors (Unmodified Stiffness)
EI
EI
K
EIEI
EI
K
EI
EI
L
EI
KK
EI
EI
L
EI
KK
DC
CD
CBBC
BAAB
5.0
8
4
5.0
8
4
8
4
667.0
6
))(4(4
5.0
8
))(4(4
==
==
=
====
====
16. Joint A B C D
Member AB BA BC CB CD DC
Distribution Factors 0 0.4284 0.5716 0.5716 0.4284 1
Computed end moments -80 80 -112.5 112.5 -53.33 53.33
Cycle 1
Distribution 13.923 18.577 -33.82 -25.35 -53.33
Carry-over moments 6.962 -16.91 9.289 -26.67 -12.35
Cycle 2
Distribution 7.244 9.662 9.935 7.446 12.35
Carry-over moments 3.622 4.968 4.831 6.175 3.723
Cycle 3
Distribution -2.128 -2.84 -6.129 -4.715 -3.723
Carry-over moments -1.064 -3.146 -1.42 -1.862 -2.358
Cycle 4
Distribution 1.348 1.798 1.876 1.406 2.358
Carry-over moments 0.674 0.938 0.9 1.179 0.703
Cycle 5
Distribution -0.402 -0.536 -1.187 -0.891 -0.703
Summed up -69.81 99.985 -99.99 96.613 -96.61 0
moments
7.4.1.4 Moment Distribution Table
17. 7.4.1.5 Computation of Shear Forces
Simply-supported 60 60 75 75 40 40
reaction
End reaction
due to left hand FEM 8.726 -8.726 16.665 -16.67 12.079 -12.08
End reaction
due to right hand FEM -12.5 12.498 -16.1 16.102 0 0
Summed-up 56.228 63.772 75.563 74.437 53.077 27.923
moments
8 m 3 m 3 m 8 m
I I I
15 kN/m 10 kN/m
150 kN
A
B C
D
18. 7.4.1.5 Shear Force and Bending Moment Diagrams
56.23
3.74 m
75.563
63.77
52.077
74.437
27.923
2.792 m
-69.806
98.297
35.08
126.704
-96.613
31.693
Mmax=+38.985 kN.m
Max=+ 35.59 kN.m
3.74 m
84.92
-99.985
48.307
2.792 m
S. F. D.
B. M. D
19. Simply-supported bending moments at center of span
Mcenter in AB = (15)(8)2
/8 = +120 kN.m
Mcenter in BC = (150)(6)/4 = +225 kN.m
Mcenter in AB = (10)(8)2
/8 = +80 kN.m
20. 7.5 MOMENT DISTRIBUTION METHOD FOR
NONPRISMATIC MEMBER (CHAPTER 12)
The section will discuss moment distribution method to analyze
beams and frames composed of nonprismatic members. First
the procedure to obtain the necessary carry-over factors,
stiffness factors and fixed-end moments will be outlined. Then
the use of values given in design tables will be illustrated.
Finally the analysis of statically indeterminate structures using
the moment distribution method will be outlined
21. 7.5.1 Stiffness and Carry-over Factors
Use moment-area method to find the stiffness and carry-
over factors of the non-prismatic beam.
∆
A
B
PA MB
MA
θA
AABAA KP ∆= )( ( )
AABB
AABA
MCM
KM
=
= θθ
CAB= Carry-over factor of moment MA from A to B
22. A
B
M′A=CBAMB
=CBAKB
M′B(≡KB)MB=CABMA
=CABKA
MA(≡KA)
θA (= 1.0)
MA θB (= 1.0)
A
B
(a) (b)
Use of Betti-Maxwell’s reciprocal theorem requires that the work
done by loads in case (a) acting through displacements in case (b) is
equal to work done by loads in case (b) acting through displacements in
case (a)
( ) ( ) ( ) ( )
BA
BABA
KK
MMMM
BAAB CC
)0.0()0.1()1()0(
=
′+′=+
MB
23. 7.5.2 Tabulated Design Tables
Graphs and tables have been made available to determine fixed-end
moments, stiffness factors and carry-over factors for common
structural shapes used in design. One such source is the Handbook of
Frame constants published by the Portland Cement Association,
Chicago, Illinois, U. S. A. A portion of these tables, is listed here as
Table 1 and 2
Nomenclature of the Tables
aA ab = ratio of length of haunch (at end A and B to the length
of span
b = ratio of the distance (from the concentrated load to end A)
to the length of span
hA, hB= depth of member at ends A and B, respectively
hC = depth of member at minimum section