The document discusses various topics related to trusses:
1. It defines the key features of a truss, including that it consists of slender straight members connected at joints, with pinned connections that allow only axial forces in the members.
2. External loads must be applied at the joints, as members cannot support lateral loads. Most structures use multiple trusses joined together to form a space framework.
3. Simple trusses are constructed by adding members and joints, following the rule that m = 2n - 3, where m is the number of members and n is the number of joints. Simple trusses are internally rigid.
4. Two common methods for analyzing trusses
Learn Online Courses of Subject Engineering Mechanics of First Year Engineering. Clear the Concepts of Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/Engineering-Mechanics
Learn Online Courses of Subject Engineering Mechanics of First Year Engineering. Clear the Concepts of Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/Engineering-Mechanics
An introduction to the module is given, including forces, moments, and the important concepts of free-body diagrams and static equilibrium. These concepts will then be used to solve static framework (truss) problems using two methods: the method of joints and the method of sections.
this PPT includes Definition
Classification Of Truss
Assumption Made In Analysis
Methods Of Analysis
Zero Force Member
procedure for analysis trusses using method of joint, ,procedure of method of section ,
graphical method, SPPU, Savitribai Phule pune university.
Truss is a framework, typically consisting of rafters, posts, and struts, supporting a roof, bridge, or other structure.
a truss is a structure that "consists of two-force members only, where the members are organized so that the assemblage as a whole behaves as a single object"
An introduction to the module is given, including forces, moments, and the important concepts of free-body diagrams and static equilibrium. These concepts will then be used to solve static framework (truss) problems using two methods: the method of joints and the method of sections.
this PPT includes Definition
Classification Of Truss
Assumption Made In Analysis
Methods Of Analysis
Zero Force Member
procedure for analysis trusses using method of joint, ,procedure of method of section ,
graphical method, SPPU, Savitribai Phule pune university.
Truss is a framework, typically consisting of rafters, posts, and struts, supporting a roof, bridge, or other structure.
a truss is a structure that "consists of two-force members only, where the members are organized so that the assemblage as a whole behaves as a single object"
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
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
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
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.
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1
Truss
Engineering Mechanics- Truss
Important Features of a Truss
• A truss consists of long and slender straight
members connected at joints. No member is
continuous through a joint.
• Bolted or welded connections (joints) are assumed
to be pinned together. Forces acting at the member
ends reduce to a single force and no couple. Only
two-force members are considered.
Engineering Mechanics- Truss
Formation of a truss is nothing more than
assemblage of triangles!
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2
External Loads on a Truss
Members of a truss are slender and not capable of supporting large lateral loads.
Loads must be applied at the joints. Members are light in weight and economical.
Engineering Mechanics- Truss
Most structures are made of several trusses joined together to form a space
framework. Each truss carries those loads which act in its plane and may be
treated as a two-dimensional structure.
Various Types of Truss
Engineering Mechanics- Truss
3. 11/29/2013
3
Simple Truss
• A simple truss is constructed by
successively adding two members and
one connection to the basic triangular
truss.
• A simple truss is not necessarily
made only of triangles.Although
triangles are always maintained in
practice
Engineering Mechanics- Truss
• In a simple truss, m = 2n - 3 where
m is the total number of members
and n is the number of joints.
basic truss
• A simple truss is always internally
rigid. Will not deform and collapse
under the action of load
Analysis of Trusses by the Method of Joints
• Dismember the truss and create a freebody
diagram for each member and pin.
• The two forces exerted on each member are
equal, have the same line of action, and
opposite sense.
• Forces exerted by a member on the pins or
joints at its ends are directed along the member
and equal and opposite.
• For simple Truss: m = 2n – 3
Total unknowns
member forces = m = 5
reactions = r = 3
Total no. of equilibrium equations
2n = 8 (2 force equilibrium equations per joint)
m+r=2n
The truss is said to be statically determinate
and completely constrained.
Engineering Mechanics- Truss
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4
Analysis of Trusses by the Method of Joints
Engineering Mechanics- Truss
Force Polygon for joint
equilibrium
Joints Under Special Loading Conditions
• Forces in opposite members intersectingin
two straight lines at a joint are equal.
• The forces in two opposite members are
equal when a load is aligned with a third
member. The thirdmember force is equal
to the load (includingzero load).
• The forces in two members connected at a
joint are equal if the members are aligned
and zero otherwise.
• Recognition of joints under special loading
conditions simplifies a truss analysis.
Engineers Mechanics- Truss
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5
Problem -1
For the given loading , determine the zero force member in the truss shown
Engineers Mechanics- Truss
Problem 2
Using method of joints, determine the forces in the members of the truss shown
below
Engineers Mechanics- Truss
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Problem 2
Engineers Mechanics- Truss
FAB=0=FBC
FAD= -5 (C)
FBD= FBF
2 FBD (1.6/3.4) + 20 + FBE = 0
FBD = FBF = -34 (C)
B
FEB=12 (T)
FED= FEF
D
FDE + FDB (3/3.4) = 0
FDE = 30 (T) = FEF
Check
+FAD + FBD (1.6/3.4) + 21 =0
21
2121
Problem 3
Using the method of joints,
determine the force in each
member of the truss.
SOLUTION:
• Based on a free-body diagram of the
entire truss, solve the 3 equilibrium
equations for the reactions at E and C.
• JointA is subjected to only two unknown
member forces. Determine these from the
joint equilibrium requirements.
• In succession, determine unknown
member forces at joints D, B, and E from
joint equilibrium requirements.
• All member forces and support reactions
are known at joint C. However, the joint
equilibriumrequirements may be applied
to check the results.
Engineers Mechanics- Truss
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Problem 3
SOLUTION:
• Based on a free-body diagram of the entire
truss, solve the 3 equilibrium equations for the
reactions at E and C.
m6m12N1000m24N2000
0
E
MC
N000,10E
xx CF 0 0xC
yy CF N10,000N1000-N20000
N7000yC
Engineers Mechanics- Truss
Problem -3
• Joint A is subjected to only two unknown
member forces. Determine these from the
joint equilibrium requirements.
534
N2000 ADAB FF
CF
TF
AD
AB
N2500
N1500
• There are now only two unknown member
forces at joint D.
DADE
DADB
FF
FF
5
32
CF
TF
DE
DB
N3000
N2500
Engineers Mechanics- Truss
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• There are now only two unknown member
forces at joint B. Assume both are in
tension.
N3750
250010000 5
4
5
4
BE
BEy
F
FF
CFBE N3750
N5250
3750250015000 5
3
5
3
BC
BCx
F
FF
TFBC N5250
• There is one unknown member force at
joint E. Assume the member is in
tension.
N8750
375030000 5
3
5
3
EC
ECx
F
FF
CFEC N8750
Engineers Mechanics- Truss
Problem -3
• All member forces and support reactions are
known at joint C. However, the joint
equilibrium requirements may be applied to
check the results.
checks087507000
checks087505250
5
4
5
3
y
x
F
F
Problem -3
Engineers Mechanics- Truss
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Analysis of Trusses by the Method of Sections
• When the force in only one member or the
forces in a very few members are desired, the
method of sections works well.
• To determine the force in member BD, pass a
section through the truss as shown and create
a free body diagramfor the left side.
• With only three members cut by the section,
the equations for static equilibrium may be
applied to determine the unknown member
forces, including FBD.
Engineering Mechanics- Truss
Problem 4
A Fink roof truss is loaded as shown. Use method of section to determine the
force in members CD, CE and BD
Engineers Mechanics- Truss
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Problem 4
Engineers Mechanics- Truss
Problem 5
Use method of section to determine the force in members GJ and IK of the
truss shown
Engineers Mechanics- Truss
100kN
100kN
100kN
Inverted K truss
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Problem-5
Engineers Mechanics- Truss
100kN
100kN
100kN
G
Solution JX = -300
KY = -JY = 100*(2.7 + 5.4 +8.1)/7.5 = 1620/7.5 = 216
Section XX, lower FBD,
∑MG = 0
-FKI [ 5.9( ] + JY(0.8) –JX(2.7) – KY(6.7) = 0
FKI = -143.19 kN (C )
∑MI = 0
FJG[ 5.9 ( ] + JY(6.7) –JX(2.7) – KY(0.8) = 0
FJG = 143.19 kN (T )
Compound Truss
• Compound trusses are composed of two or more
simple trusses . The trusses shown are statically
determinant, rigid, and completely constrained,
nrm 2
Engineers Mechanics- Truss
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12
Engineers Mechanics- Truss
Compound Truss
Determine the forces in bars 1. 2. and 3 of the plane truss supported and
loaded as shown in the figure
Problem 6
Engineers Mechanics- Truss
SOLUTION:
• Two simple trusses
ADE & BCF
• Detach to expose 6
unknowns (three
member forces at 1,
2,3 and three support
reactions)
• Draw free body
diagrams to find
forces in 1, 2 &3
E F
3
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14
Engineers Mechanics- Truss
Problem 6
Partially, Improperly and Properly Constrained Truss
Engineering Mechanics- Truss
• For a truss to be properly constrained:
– It should be able to stay in equilibrium for any combination
of loading.
– Equilibrium implies both global equilibrium and internal
equilibrium.
• Note that if m + r < 2n, the truss is most definitely
partially constrained (and is unstable to certain
loadings). But m + r ≥ 2n, is no guarantee that the
truss is stable, and may be termed improperly
constrained.
• If m + r < 2n, the truss can never be statically
determinate.
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• Fewer unknowns than
equations, partially
constrained
• Equal number unknowns
and equations but
improperlyconstrained
Partially, Improperly and Properly Constrained Truss
Inadequacy
of external
constraints
unstable
Simple Truss
(internally
rigid)
Engineering Mechanics- Truss
Partially, Improperly and Properly Constrained Truss
Engineering Mechanics- Truss
Check if partially constrained, fully constrained or improperly constrained
P
P
P
Statically determinate, properly constrained
A Simple Truss is always a rigid truss
m + r = 2n m=9, r = 3, n=6
m=9, r = 3, n=6m + r = 2n
improperly constrained (non rigid,
may collapse)
m + r < 2n
Partially constrained (non rigid, may
collapse)
m=8, r = 3, n=6
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Engineers Mechanics- Truss
Problem 7 : Partially, Improperly and Properly ConstrainedTruss
`
2n = 20, m = 16, r = 4.
The circled part is a simple truss that
is adequately supported with 3
reactions. So it is completely
constrained
We only have to worry about the
remaining portion. We can easily
show that no matter whatever loading
is applied at the joints of the
remaining part can be supported.
Completely constrained & Statically
determinate
Problem 7 : Partially, Improperly and Properly ConstrainedTruss
Engineering Mechanics- Truss
a) j = 7, m = 10, r = 3, 2n > m + r.
Partially Constrained
b) j = 8, r = 3, m = 13, 2n = m + r.
Clearly the truss cannot be equilibrium
with this loading.
Take equilibrium of joint C. BC is
tensile
Take a section as shown and moment
about left hinge is not balanced
Improperly Constrained.
B
C
