The document discusses shear force and bending moment in beams. It defines key terms like beam, transverse load, shear force, bending moment, and types of loads, supports and beams. It explains how to calculate and draw shear force and bending moment diagrams for different types of loads on beams including point loads, uniformly distributed loads, uniformly varying loads, and loads producing couples or overhangs. Sign conventions and the effect of reactions, loads and geometry on the shear force and bending moment diagrams are also covered.
Here presenting you the Introduction persentation of SFD and BMD. There are some concepts in the presentation. Easy to Understand...!!
Read N Xplore..!!
In this presentation you will get knowledge about shear force and bending moment diagram and this topic very useful for civil as well as mechanical engineering department students.
This document gives the class notes of Unit 6: Bending and shear Stresses in beams. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
Bending Stresses are important in the design of beams from strength point of view. The present source gives an idea on theory and problems in bending stresses.
Here presenting you the Introduction persentation of SFD and BMD. There are some concepts in the presentation. Easy to Understand...!!
Read N Xplore..!!
In this presentation you will get knowledge about shear force and bending moment diagram and this topic very useful for civil as well as mechanical engineering department students.
This document gives the class notes of Unit 6: Bending and shear Stresses in beams. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
Bending Stresses are important in the design of beams from strength point of view. The present source gives an idea on theory and problems in bending stresses.
This document gives the class notes of Unit 5 shear force and bending moment in beams. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
simple supported beams with shear force and bending moments diagrams, different types of loading conditions, everyday scenarios of simply supported beams, advantages and disadvantages of simple supported beams
What is Bending Moment?
What are its sign conventions?
What is BMD?
What is the difference between moment and bending moment?
Find out answers for these questions and many more in this presentation.
Introduction
Types of Beam
Types of Loads acting on beam
Types of Supports
Instrument used for finding “Support Reactions”
How to find “Support Reactions”
This document gives the class notes of Unit 5 shear force and bending moment in beams. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
simple supported beams with shear force and bending moments diagrams, different types of loading conditions, everyday scenarios of simply supported beams, advantages and disadvantages of simple supported beams
What is Bending Moment?
What are its sign conventions?
What is BMD?
What is the difference between moment and bending moment?
Find out answers for these questions and many more in this presentation.
Introduction
Types of Beam
Types of Loads acting on beam
Types of Supports
Instrument used for finding “Support Reactions”
How to find “Support Reactions”
TECHNICAL TRAINING MANUAL GENERAL FAMILIARIZATION COURSEDuvanRamosGarzon1
AIRCRAFT GENERAL
The Single Aisle is the most advanced family aircraft in service today, with fly-by-wire flight controls.
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Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
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.
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.
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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.
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.
Democratizing Fuzzing at Scale by Abhishek Aryaabh.arya
Presented at NUS: Fuzzing and Software Security Summer School 2024
This keynote talks about the democratization of fuzzing at scale, highlighting the collaboration between open source communities, academia, and industry to advance the field of fuzzing. It delves into the history of fuzzing, the development of scalable fuzzing platforms, and the empowerment of community-driven research. The talk will further discuss recent advancements leveraging AI/ML and offer insights into the future evolution of the fuzzing landscape.
Automobile Management System Project Report.pdfKamal Acharya
The proposed project is developed to manage the automobile in the automobile dealer company. The main module in this project is login, automobile management, customer management, sales, complaints and reports. The first module is the login. The automobile showroom owner should login to the project for usage. The username and password are verified and if it is correct, next form opens. If the username and password are not correct, it shows the error message.
When a customer search for a automobile, if the automobile is available, they will be taken to a page that shows the details of the automobile including automobile name, automobile ID, quantity, price etc. “Automobile Management System” is useful for maintaining automobiles, customers effectively and hence helps for establishing good relation between customer and automobile organization. It contains various customized modules for effectively maintaining automobiles and stock information accurately and safely.
When the automobile is sold to the customer, stock will be reduced automatically. When a new purchase is made, stock will be increased automatically. While selecting automobiles for sale, the proposed software will automatically check for total number of available stock of that particular item, if the total stock of that particular item is less than 5, software will notify the user to purchase the particular item.
Also when the user tries to sale items which are not in stock, the system will prompt the user that the stock is not enough. Customers of this system can search for a automobile; can purchase a automobile easily by selecting fast. On the other hand the stock of automobiles can be maintained perfectly by the automobile shop manager overcoming the drawbacks of existing system.
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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
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
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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.
2. SHEAR FORCE AND BENDING MOMENT
Beam: It is a structural member which is subjected to transverse
load.
Transverse load: The load which is perpendicular or it has non
zero component perpendicular to longitudinal axis of beam.
Shear force: it is the unbalanced force on either side of a section
parallel to cross section.
Moment: It is the product of force and perpendicular distance
between line of action of the force and the point about which
moment is required to be calculated.
Bending moment: It is the unbalanced moment on either side of
section, in the plane of beam.
3. TYPES OF LOAD
Sr. No. Type of load Example Description
1. Point Load Concentrated Load acts at a point.
2.
Uniformly Distributed
Load
UDL:- uniform load distribution
over wide area. Rate of loading per
unit length.
3.
Uniformly Varying
Load (Triangular
Distributed Load)
UVL:- Intensity of load at one point
to that at the other, eg. w1/m at C
to w2/m at D
4. Couple
A beam may be subjected to a
couple.
5. Oblique Load
The effect of Horizontal
components is to cause a thrust in
the beam. Vertical components of
the load cause bending and shear
& are treated as usual vertical
loads on a beam
4. TYPES OF SUPPORTS
Sr. No. Type of support Example Description
1.
Knife Edge
Support
Contact Area Insignificant.
Provides only vertical reaction
No resistance to turning or lateral
displacement
2.
Roller Support
(Horizontal
Plane)
Rollers on Horizontal Plane
Support reaction is vertical.
No resistance to turning or lateral
displacement
3.
Roller Support
(Inclined Plane)
Rollers on Inclined Plane
Support reaction is perpendicular to
inclined plane.
Allow turning or lateral
displacement.
4.
Hinged/Pin
Support
Allows turning but doesn’t allow any
lateral movement.
Support reaction could be in any
direction.
Can be determined by resolving applied
in horizontal. & Vertical. direction
5. Fixed Support
Doesn’t allow rotation or
translation.
5. TYPES OF BEAMS
Sr. No. Type of Beam Example Description
1. Cantilever Beam
Beams have one end rigidly
built into the support.
Large span or heavy loads
provided by additional support
are known as propel and beam
as a propped cantilever.
2.
Simply Supported
Beam
Beams with knife edge
supports or roller supports at
ends.
3.
Beams with
Overhangs
Portion of a beam that goes
beyond the support is called
overhanging, may be on one or
both ends.
4. Fixed Beams
Rigidly built-in-supports at
both ends. Beam have support
reaction and a fixing moments
at each end.
5. Continuous Beams
Beams that cover more than
one span.
6. Both shear force and bending moment are vector quantities
requiring a convention of signs in order that values of opposite sense
may be separated. Mathematical signs are chosen since it is in
calculation problems that it becomes necessary to use such a
convention
TABEL 1. Sign convention and units for shearing force and bending moment
N·mm
kN·m
(top fibers in tension)(bottom fibers in tension)
MBending
moment
N
KN
Q, V, SShear
force
NEGATIVE (-)POSITIVE (+)
UNITS
SIGN CONVENTION
SYMBOL
LOAD
EFFECT
BEAMS IN BENDING
7. BEAMS IN BENDING
The shearing force, at any transverse section in a loaded beam, is the
algebraic sum of all the forces acting on one (either) side of the
section.
The bending moment, at any transverse section in a loaded beam, is
the algebraic sum of the moments about the sections of all the forces
acting on one (either) side of the section.
RA RB
A
V1 V2 V3 V4
x
B
a4a3
a2
a1
a b
332211Ax
321Ax
aVaVaVaRM
VVVRQ
44Bx
4Bx
aVbRM
VRQ
Working to the left of x:
Working to the right of x:
8. THINGS TO REMEMBER FOR DRAWING OF S.F & B.M
Start from right hand section.
Use Sign convention of the side which you are choosing i.e Right or Left.
If the thing are complicated use other side of section.
Start from zero and end to zero. B.M at the ends will be zero.
End point of S.F. will be equal and opposite to the reaction at that point.
Mark the points and draw the diagram considering the type of load.
At change in nature of forces there will be two points in shear force diagram.
At Couple there will be two points in B.M Diagram.
•Beams are assumed to be always straight, horizontal & of uniform c/s & structure,
unless otherwise specified.
•Self weight of Beam neglected unless its definite value is given.
S.F may be max. at supports or under point loads or where S.F. is zero where B.M.
may be maximum at point where S.F. is zero or where S.F. changes its nature.
•Where the B.M changes its nature is known as Point of Contra Flexure or Point of
Inflexion.
9. a
X
X
SHEAR FORCE DIAGRAM
BENDING MOMENT DIAGRAM
35
20
20
35
35
35
20
20
C
D
E
B
A
F
20
25.5
20
Draw S.F. and B.M. diagrams for the loaded Beam Point Load
20 kN
C D E
20 kN
B
1m 1.3m 1.3m 1m
LOADED BEAM
A
70 kN
RC RE
Shear Force
S.F at B = -20kN
S.F at E = 55 - 20 = 35 kN
S.F at D = -20 – 70 + 55 = -35 kN
S.F at C = -20 + 55 - 70 + 55 = 20 kN
Symmetrical loading
Rc = RE = 20 + 70 + 20 = 55 kN
2
Calculations
Bending Moment
BME = -20 X 1 = -20 kNm.
BMD = -20 X 2.3 + 55 X 1.3 = 25.5kNm.
BMC = -20(1.3 + 1.3 +1) + 55(1.3 + 1.3)
-70 X 1.3 = -20 kNm.
BMX = - 20 (a + 1) + 55a = 35 a – 20
Point of Contra flexure BMX = 0
a = 0.57
+ve
-ve
+ve
-ve
+ve-ve -ve+ve
Point of Contra flexure
10. UNIFORMLY DISTRIBUTED LOAD
WL
1/2 L
L
1/2 L
Load act centre of
UDL
W kN/m
wL
1/2 L
L
1/2 L
W kN
w = W/L kN/m
There will be Parabola in B.M. and inclined line in S.F.
diagram
11. 100 kN
2m 2m 2m
LOADED BEAM
SHEAR FORCE DIAGRAM
BENDING MOMENT DIAGRAM
A
EFFECT OF UNIFORMLY DISTRIBUTED LOAD
Reactions
RA +RB = 100 = 20 x 2 + 50 = 190
MA,
RB x 8 = 100 x 6 + 20 x 2 x 50 x 2
RB = 112.5 kN, RA = 77.5 kN
RB
Shear Force
S.F at B = 112.5 kN (+ ve)
S.F at C = 112.5 -100 = 12.5 kN
S.F at D = 112.5 -100 – 20 x 2 = -27.5 kN
S.F at E = 112.5 – 100 – 20 X 2 – 50 =
-77.5 kN
S.F. at A = – 77.5 kN
Calculations
Bending Moment
BMA = 0 , BMB = 0
BMC = 112.5 X 2 = 225 kN.
BMD = 112.5 X 4 – 100 X 2 – 20 X 2 X 2/2
= 210 kN.m
BME = 112.5 X 6 – 100 X 4 – 20 X 2 X 3
= 155 kN.m
BMF = 112.5 X 2.625 – 100 X 0.625 – 20 X
0.625 X 0.625/2 = 228.9 kN.m
+ve
-ve
+ve
-ve
+ve-ve -ve+ve
20 kN/m
50 kN
E D F C
B
RA
2m
S.F. at F = 0
S.F. at F = 112.5 – 100 – 20 (x – 2)
X = 2.625 m
A
E D
F C
B
E D F C
B
A
x
112.5 kN
27.5 kN77.5 kN
225 kN.m
228.9 kN.m
210 kN.m
115 kN.m
12. SHEAR FORCE DIAGRAM
BENDING MOMENT DIAGRAM
EFFECT OF COUPLE
Reactions
RA + RB = 20 X 4 = 80
MA,
RB X 10 = 40 + 20 X 4 X 2
RB = 20 kN, RA = 60 kN
RB
Shear Force
S.F at B = 20 kN
S.F at C = 20 kN
S.F at A = -60 kN
Calculations
Bending Moment
BMA = 0, BMB = 0,
BMC = 20 x 5 = 100 kN.m (just before)
BMC = 100 – 40 = 60 (just after)
BMD = 20 x 6 – 40 = 80 kN.m
BME = 20 x 7 – 40 – 20 x 1 x 0.5
= 90 kN.m
+ve
-ve
+ve
-ve
+ve-ve -ve+ve
RA
X = 7m
40 kN-m
4m 5m
A
20 kN/m
E D C
B
1m
D C B
A + ve S.F.
- ve
+ ve BM
E
D C B
A
20 kN
60 kN
90 kN.m
80 kN.m
100 kN.m
60 kN.m
S.F at E = 0
S.F at E = 20 – 20 (x-6)
x = 7m
E
13. a = 1m
BENDING MOMENT DIAGRAM
OVERHANGING BEAM WITH UDL
Reactions
MA,
RB x 6 = 5 x 9 + 2 x 9 x 9/2
RB = 21 kN
RA + RB = 5 + 2 x 9 = 23, RA = 2 kN
RB
Shear Force
S.F at C = 5 kN
S.F at B = 5 + 2 x 3 = -11 kN (just right)
S.F at B = -11 + 21 = 10 kN (just left)
S.F at A = 2 kN (- ve)
Calculations
Bending Moment
BMC = 0, BMA = 0
BMB = - 5 x 3 – 2 x 3 x 3/2 = -24 kN.m
+ve
-ve
+ve
-ve
+ve-ve -ve+ve
RA
ED
3m
A
2 kN/m
B
C
6m
5 kN
A
D
B
C
10 kN
11 kN
5 kN
+ ve
- ve
2 kN
Point of Contra flexure
1 kNm
A
D E
B
C
24 kNm
S.F between B & A = 0
S.F at D = - 2 + 2 x a
0 = - 2 + 2 a, a = 1m
b = 4m
Point of Contra flexure BME = 0
-5 (b + 3) – 2 x (b+3) / 2 + 21 b = 0
b = 4 m (+ ve value)
2
14. BENDING MOMENT DIAGRAM
CANTILEVER WITH UDL
Shear Force
S.F at B = 10 kN
S.F at C = 10 + 5 x 2 = -20 kN
S.F at D = 10 + 5 x 2 + 20 = - 40 kN
S.F at A = 10 + 5 x 2 + 20 + 40 x 3
= - 160 kN
Calculations
Bending Moment
BMB = 0
BMC = 10 x 2 + 5 x 2 x 2/2 = -30 kNm.
BMD = 10 x 3 + 5 x 2 x (2/2 + 1)
= 50 kN.m
BME = 10 x 5 + 5 x 2 x ( 2/2 + 3) + 20
x 2
= - 130 k Nm
BMA = 10 x 8 + 5 x 2 x (2/2 + 6) + 20 x
5 + 40 x 3 x 3/2
= - 430 kN.m.
+ve
-ve
+ve
-ve
+ve-ve -ve+ve
20 kN
3m 2m
A
40 kN/m
E D C
B
2m
10 kN
5 kN/m
1m
- VE S.F.
A
E
D
C
B
20 kN
10 kN
40 kN
160 kN
430 kN.m
130 kN.m
50 kN.m
Parabolic curve
30 kN.m- VE B.M.
Parabolic curve
A E D C B
15. UNIFORMLY VARYING LOAD
W N/m
W N/m
1/3 L
L
2/3 L
Load Act the centroid of the
Triangular Area
There will be Parabola in both S.F. and B.M
16. +ve
-ve
+ve
-ve
+ve-ve -ve+ve
C
A
W
L D
E
x
W.x/L
B
5000 N/mC
A
4 m
D
E
x
B
Rate of Loading
S.F. = Triangular Load area = ½ X DE X DB
W x /2L
2
W L / 2
W x /6L
3W L / 6
2
B.M = Force X Perpendicular
= ½ X DE X DB X DB / 3 from point D to
the centroid
Cubic Parabola
13.33 kN.m
Parabola Curve
10 kN.m
DE / AC = DB / AB , DE = 5000x/4 = 1250 x
i.e rate loading at any distance x
S.F. at D = -1/2 X x 1250 x = - 625 x
S.F. at B = 0 where x= 0
S.F. at A , at x = 4 , -625 X 4 = 10 kN
B.M. at x = -1/2 X DB X DE X DB/3
= - 625 x X x/3, at x = 4 ,
B.M. at A = - 13.33 kN.m
2
2
2
17. Draw S.F. and B.M. diagrams for the loaded Beam
Reactions
RA + RB = 150 + 300
MA,
RB X 6 = 150 X 5 + 300 (2/3 X 3 + 1)
RB = 275 kN, RA = 175 kN
Shear Force
S.F at B = 275 kN
S.F at C = 275 – 150 = 125 kN
S.F at D = 125 kN
S.F at E = 275 – 150 – 300 = -175 kN
S.F at A = - 175 kN
Calculations
Rate of Loading at distance x
w = Wx/L = w = 200 x / 3
S.F at F = -175 + ½ 200x / 3 X x
x= 2.29 m
+ve
-ve
+ve
-ve
+ve-ve -ve+ve
RA
RB
300 kN
1m 1m
A
E D C
B
3m
150 kN
1m
F
½ WL = 300
= 200 kN/m
x
A E F D C
B
275 kN
125 kN
175 kN
+ ve S.F.
+ ve B.M.
175 kNm
442.32 kNm
400 kNm
275 kNm
A E F D C
B
Bending Moment
BMA = 0, BMB = 0,
BMC = 275 X 1 = 275 kN.m
BMD = 275 X 2 – 150 X 1 = 400 kN.m
BME = 175 X 1 = 175 kN.m
BMF = 175 X 3.29 – (200 X 2.29/3) ( 2.29/2 X
2.29/3)
= 442.32 kN.m
½ WL X L/3
18. Draw S.F. and B.M. diagrams for the loaded Beam
Reactions
MA,
RB X8= 200 X 8 X 4 + ½ X 400 X 8 X 8/3
RB = 1333.33 N
RA + RB = 200 X 8 + ½ X 400 X 8
RA = 1866.67 N
Rate of Loading at X-X = GH + GF
Rate of Loading at GH
DE/CD = GH/CG, GH = 400x /8 = 50x
Rate of Loading at GF = 200
Rate of Loading at X-X = GH + GF = 200 + 50x
Calculations
+ve
-ve
+ve
-ve
+ve-ve -ve+ve
Bending Moment
BMF = 1333.33x – 200x X x/2 – ½ X 50x X x X
x/3…….(GH = 50x)
We have x = 4.326
Max. B.M at F = 3436.14 N/m
200 N/m
RA
600 N/m
8m
A
B
RB
400 N/m
200 N/m 200 N/m
1333.3 N
1866.6 N x = 4.325 m
3222.18 N
H
G
F x
C
BA
D
E
X
X
Shear Force at P = 0
S.F. at F =1333.33 – (load BCGF + Load CGH
= 1333.33 – (200x + ½ X 50 x X x)
x = 4.326 (quadratic equation +ve value)
F
19. OBLIQUE OR INCLINED LOAD and Hinges
Consider the Vertical Component
θ
P kN
Horizontal Component = P cos θ kN
Vertical Component = P sin θ kN
P sin θ kN
a
b
P kN
Horizontal Component = P cos θ kN
= P X a/c kN
Vertical Component = P sin θ kN
= P X b/c kN
c
By Pythagoras theorem
P X b/c kN
For the Hinges consider the Vertical Support Reactions by the help of free body
diagram and solve as the regular process generally you will find at the UDL.
At the Hinges you will have Bending Moment is zero.