truss
TRANSCRIPT
Truss
1. Introduction
In architecture and structural engineering, a truss is a structure comprising one
or more triangular units constructed with straight members whose ends are
connected at joints referred to as nodes. External forces and reactions to those
forces are considered to act only at the nodes and result in forces in the
members which are either tensile or compressive forces. Moments (torques) are
explicitly excluded because, and only because, all the joints in a truss are
treated as revolutes.[1]
A structure that is composed of a number of bars pin connected at their
ends to form a stable framework is called a truss. It is generally assumed that
loads and reactions are applied to the truss only at the joints. A truss would
typically be composed of triangular elements with the bars on the upper chord
under compression and those along the lower chord under tension. Trusses are
extensively used for bridges, long span roofs, electric tower, and space
structures. Trusses are statically determinate when the entire bar forces can be
determined from the equations of statics alone. Otherwise the truss is statically
indeterminate. A truss may be statically (externally) determinate or indeterminate
with respect to the reactions.[2]
[1]
2. Characteristics of a Truss
A truss consists of straight members connected at joints. Trusses are composed of
triangles because of the structural stability of that shape and design. A triangle is the
simplest geometric figure that will not change shape when the lengths of the sides are
fixed. In comparison, both the angles and the lengths of a four-sided figure must be
fixed for it to retain its shape
Planar Truss
Space Frame Truss
2.1 Planar Truss
The simplest form of a truss is one single triangle. This type of truss is seen in a
framed roof consisting of rafters and a ceiling joist. and in other mechanical structures
such as bicycles. Because of the stability of this shape and the methods of analysis
used to calculate the forces within it, a truss composed entirely of triangles is known
as a simple truss. The traditional diamond-shape bicycle frame, which utilizes two
conjoined triangles, is an example of a simple trussA planar truss lies in a single
plane. Planar trusses are typically used in parallel to
form roofs and bridges.
2.2 Space Frame Truss
A space frame truss is a three-dimensional framework of members pinned at their
ends. A tetrahedron shape is the simplest space truss, consisting of six members
which meet at four joints. Large planar structures may be composed from tetrahedrons
with common edges and they are also employed in the base structures of large free-
standing power line pylons [2]
3. Truss Types
There are three basic types of truss:
The pitched truss, or common truss, is characterized by its triangular shape. It
is most often used for roof construction. Some common trusses are named
according to their web configuration. The chord size and web configuration
are determined by span, load and spacing.
The parallel chord truss, or flat truss, gets its name from its parallel top and
bottom chords. It is often used for floor construction.
A combination of the two is a truncated truss, used in hip roof construction. A
metal plate-connected wood truss is a roof or floor truss whose wood members
are connected with metal connector plates.[3]
.
[3]
4. Truss Types used in Bridges
4.1 Allan Truss
The Allan Truss, designed by Percy Allan, is partly based on the Howe truss. The
first Allan truss was completed on 13 August 1894 over Glennies Creek at
Camberwell, New South Wales . completed in March 1895. The Hampden Bridge in
Wagga Wagga, New South Wales, Australia, the first of the Allan truss bridges with
overhead bracing, was originally designed as a steel bridge but was constructed with
timber to reduce cost. In his design, Allan used Australian ironbark for its strength. A
similar bridge also designed by Percy Allen is the Victoria Bridge on Prince Street
Picton, New South Wales. Also constructed of ironbark, the bridge is still in use today
for pedestrian and light traffic.
4.2 Bailey Bridge
Designed for military use, the prefabricated and standardized truss elements may be
easily combined in various configurations to adapt to the needs at the site. In the
image at right, note the use of doubled prefabrications to adapt to the span and load
requirements. In other applications the trusses may be stacked vertically.
4.3 Baltimore Truss
The Baltimore truss is a subclass of the Pratt truss. A Baltimore truss has additional
bracing in the lower section of the truss to prevent buckling in the compression
members and to control deflection. It is mainly used for train bridges, boasting a
simple and very strong design.
[4]
4.4 Bollman Truss
The Bollman Truss Railroad Bridge at Savage, Maryland is the only surviving
example of a revolutionary design in the history of American bridge engineering. The
type was named for its inventor, Wendel Bollman, a self-educated Baltimore
engineer. The design employs wrought iron tension members and cast iron
compression members. The use of multiple independent tension elements reduces the
likelihood of catastrophic failure. The structure was also easy to assemble.
4.5 Bowstring Arch Truss (Tied Arch Bridge)
Thrust arches transform their vertical loads into a thrust along the arc of the arch. At
the ends of the arch this thrust may be resolved into two components, a vertical thrust
equal to a proportion of the weight and load of the bridge section, and a horizontal
thrust. In a typical arch this horizontal thrust is taken into the ground, while in a
bowstring arch the thrust is taken horizontally by a chord member to the opposite side
of the arch. This allows the footings to take only vertical forces, useful for bridge
sections resting upon high pylons.
4.6 Cantilevered Truss
Most trusses have the lower chord under tension and the upper chord under
compression. In a cantilever truss the situation is reversed, at least over a portion of
the span. The typical cantilever truss bridge is a balanced cantilever, which enables
the construction to proceed outward from a central vertical spar in each direction.
Usually these are built in pairs until the outer sections may be anchored to footings. A
central gap, if present, can then be filled by lifting a conventional truss into place or
by building it in place using a traveling support.
[5]4.7 Fink Truss
The Fink truss was designed by Albert Fink of Germany in the 1860s. This type of
bridge was popular with the Baltimore and Ohio Railroad. The Appomattox High
Bridge on the Norfolk and Western Railroad included 21 Fink deck truss spans from
1869 until their replacement in 1886.
4.8 Howe Truss
The relatively rare Howe truss, patented in 1840 by Massachusetts millwright William
Howe, includes vertical members and diagonals that slope up towards the center, the
opposite of the Pratt truss.[9] In contrast to the Pratt Truss, the diagonal web members
are in compression and the vertical web members are in tension. Examples include
Jay Bridge in Jay, New York, and Sandy Creek Covered Bridge in Jefferson County,
Missouri.
4.9 Kingpost Truss
A king post (or crown post) extends vertically from a crossbeam to the apex of a
triangular truss. King posts were used in roof construction in Medieval architecture in
buildings. The truss consists of two diagonal members that meet at the apex of the
truss, one horizontal beam that serves to tie the bottom end of the diagonals together,
and the king post which connects the apex to the horizontal beam below. For a roof
truss, the diagonal members are called rafters, and the horizontal member may serve
as a ceiling joist. A bridge would require two king post trusses with the driving
surface between them. A roof usually uses many side-by-side trusses depending on
the size of the structure
[6]4.10 Lattice Truss
A lattice bridge is a form of truss bridge that uses a large number of small and
closely spaced diagonal elements that form a lattice. Originally a design to allow a
substantial bridge to be made from planks employing lower–skilled labor, rather than
heavy timbers and more expensive carpenters, this type of bridge has also been
constructed using a large number of relatively light iron or steel members. The
individual elements are more easily handled by the construction workers, but the
bridge also requires substantial support during construction. A simple lattice truss will
transform the applied loads into a thrust, as the bridge will tend to change length
under load. This is resisted by pinning the lattice members to the top and bottom
chords, which are more substantial than the lattice members, but which may also be
fabricated from relatively small elements rather than large beams.
4.11 Lenticular Truss
A lenticular truss bridge includes a lens-shape truss, with trusses between an upper
arch that curves up and then down to end points, and a lower arch that curves down
and then up to meet at the same end points. Where the arches extend above and below
the roadbed, it is a lenticular pony truss bridge. The Royal Albert Bridge (United
Kingdom) uses a single tubular upper chord. As the horizontal tension and
compression forces are balanced these horizontal forces are not transferred to the
supporting pylons .This in turn enables the truss to be fabricated on the ground and
then to be raised by jacking as supporting masonry pylons are constructed. This truss
has been used in the construction of a stadium with the upper chords of parallel
trusses supporting a roof that may be rolled back.
[7]
4.12 Long Truss
Designed by Stephen H. Long in 1830; one surviving example is the Old Blenheim
Bridge. The design resembles a Howe truss, but is entirely made of wood instead of a
combination of wood and metal.
4.13 Parker Truss
A Parker truss bridge is a Pratt truss design with a polygonal upper chord. A
"camelback" is a subset of the Parker type, where the upper chord consists of exactly
five segments. An example of a Parker truss is the Traffic Bridge in Saskatoon.
4.14 Pegram Truss
The Pegram truss is a hybrid between the Warren and Parker trusses where the upper
chords are all of equal length and the lower chords are longer than the corresponding
upper chord. Because of the difference in upper and lower chord length, each panel
was not square. The members which would be vertical in a Parker truss vary from
near vertical in the center of the span to diagonal near each end (like a Warren truss).
George H. Pegram, while the chief engineer of Edge Moor Iron Company in
Wilmington, Delaware, patented this truss design in 1885.The Pegram truss consists
of a Parker type design with the vertical posts leaning towards the center at an angle
between 60 and 75°. The variable post angle and constant chord length allowed steel
in existing bridges to be recycled into a new span using the Pegram truss design. This
design also facilitated reassembly and permitted a bridge to be adjusted to fit different
span lengths. There are ten remaining Pegram span bridges in the United States with
seven in Idaho.
[8]
4.15 Post Truss
A Post truss is a hybrid between a Warren truss and a double-intersection Pratt truss.
Invented in 1863 by Simeon S. Post, it is occasionally referred to as a Post patent
truss although he never received a patent for it.[14] The Ponakin Bridge and the Bell
Ford Bridge are two examples of this truss.
4.16 Pratt truss
A Pratt truss includes vertical members and diagonals that slope down towards the
center, the opposite of the Howe truss.It can be subdivided, creating Y- and K-shaped
patterns. The Pratt Truss was invented in 1844 by Thomas and Caleb Pratt. This truss
is practical for use with spans up to 250 feet and was a common configuration for
railroad bridges as truss bridges moved from wood to metal. They are statically
determinate bridges, which lend themselves well to long spans.
4.17 Queenpost Truss
The queenpost truss, sometimes queen post or queenspost, is similar to a king post
truss in that the outer supports are angled towards the center of the structure. The
primary difference is the horizontal extension at the center which relies on beam
action to provide mechanical stability. This truss style is only suitable for relatively
short spans
4.18 Truss Arch
A truss arch may contain all horizontal forces within the arch itself, or alternatively
may be either a thrust arch consisting of a truss, or of two arcuate sections pinned at
the apex. The latter form is common when the bridge is constructed as cantilever
segments from each side as in the Navajo Bridge
[9]4.19 Warren Truss
It consists of longitudinal members joined only by angled cross-members, forming
alternately inverted equilateral triangle-shaped spaces along its length, ensuring that
no individual strut, beam, or tie is subject to bending or torsional straining forces, but
only to tension or compression. Loads on the diagonals alternate between
compression and tension (approaching the center), with no vertical elements, while
elements near the center must support both tension and compression in response to
live loads. This configuration combines strength with economy of materials and can
therefore be relatively light.
4.20 Whipple Pratt Truss
A whipple truss is usually considered a subclass of the Pratt truss because the
diagonal members are designed to work in tension. The main characteristic of a
whipple truss is that the tension members are elongated, usually thin, at a shallow
angle and cross two or more bays (rectangular sections defined by the vertical
members).An example of a Pratt Truss bridge is the Fair Oaks Bridge in Fair Oaks,
California.
4.21 Vierendeel truss
The Vierendeel truss, unlike common pin-jointed trusses, imposes significant bending
forces upon its members — but this in turn allows the elimination of many diagonal
elements. While rare as a bridge type this truss is commonly employed in modern
building construction as it allows the resolution of gross shear forces against the
frame elements while retaining rectangular openings between column.[4]
[10]5. Statics of Truss
A truss that is assumed to comprise members that are connected by means of pin
joints, and which is supported at both ends by means of hinged joints or rollers, is
described as being statically determinate. Newton's Laws apply to the structure as a
whole, as well as to each node or joint. In order for any node that may be subject to an
external load or force to remain static in space, the following conditions must hold:
the sums of all (horizontal and vertical) forces, as well as all moments acting about
the node equal zero. Analysis of these conditions at each node yields the magnitude of
the forces in each member of the truss. These may be compression or tension forces.
Trusses that are supported at more than two positions are said to be statically
indeterminate, and the application of Newton's Laws alone is not sufficient to
determine the member forces.
In order for a truss with pin-connected members to be stable, it must be entirely
composed of triangles. In mathematical terms, we have the following necessary
condition for stability:
m = 2j - 3
where m is the total number of truss members, j is the total number of joints and r is
the number of reactions (equal to 3 generally) in a 2-dimensional structure.
When m = 2j − 3, the truss is said to be statically determinate, because the (m+3)
internal member forces and support reactions can then be completely determined by 2j
equilibrium equations. Given a certain number of joints, this is the minimum number
of members, in the sense that if any member is taken out (or fails), then the truss as a
whole fails. Their member forces depend on the relative stiffness of the members, in
addition to the equilibrium condition described.[5]
[11]6. Truss Analysis
For the truss analysis, it is assumed that: Bars are pin-connected.
Joints are frictionless hinges.
Loads are applied at the joints only.
Stress in each member is constant along its length.
The objective of analyzing the trusses is to determine the reactions and member
forces. The methods used for carrying out the truss analysis with the equations of
equilibrium and by considering only parts of the structure through analyzing its free
body diagram to solve the unknowns.
There are 3 basic methods for determination of axial forces in members:-
Method of joints
Methods of Sections
Graphical Method
[12]
6.1 Method of Joints
The first to analyze a truss by assuming all members are in tension reaction. A tension
member is when a member experiences pull forces at both ends of the bar and usually
denoted as positive sign. When a member experiencing a push force at both ends,
then the bar was said to be in compression mode and designated as negative sign.
In the joints method, a virtual cut is made around a joint and the cut portion is isolated
as a Free Body Diagram (FBD). Using the equilibrium equations of ∑ Fx = 0 and ∑ Fy
= 0, the unknown member forces could be solve. It is assumed that all members are
joined together in the form of an ideal pin, and that all forces are in tension (+ve) of
reactions.
An imaginary section may be completely passed around a joint in the truss. The joint
has become a free body in equilibrium under the forces applied to it. The equations ∑
H = 0 and ∑ V = 0 may be applied to the joint to determine the unknown forces in
members meeting there. It is evident that no more than two unknowns can be
determined at a joint with these two equations.
A simple truss model supported by pinned and roller support at its end. Each triangle
has the same length, L and it is equilateral where degree of angle, θ is 60° on every
angle. The support reactions, Ra and Rc can be determine by taking a point of moment
either at point A or point C, whereas Ha = 0 (no other horizontal force).
Here are some simple guidelines for this method of truss analysis:
[13]
1. Solve the reactions of the given structure,
2. Select a joint with a minimum number of unknown (not more than 2) and
analyze it with ∑ Fx = 0 and ∑ Fy = 0,
3. Proceed to the rest of the joints and again concentrating on joints that have
very minimal of unknowns,
4. Check member forces at unused joints with ∑ Fx = 0 and ∑ Fy = 0,
5. Tabulate the member forces whether it is in tension (+ve) or compression (-ve)
reaction
From fig.21, the forces in each member can be determine from any joint or point. The
best way to start by selecting the easiest joint like joint C where the reaction Rc is
already obtained and with only 2 unknown, forces of FCB and FCD. Both can be
evaluate with ∑ Fx = 0 and ∑ Fy = 0 rules. At joint E, there are 3 unknown, forces of
FEA, FEB and FED, which may lead to more complex solution compare to 2 unknown
values. For checking purposes, joint B is selected to shown that the equation of ∑ Fx is
equal to ∑ Fy which leads to zero value, ∑ Fx = ∑ Fy = 0. Each value of the member’s
condition should be indicate clearly as whether it is in tension (+ve) or in compression
(-ve) state.
Trigonometric Functions:
Taking an angle between member x and z…
Cos θ = x / z
Sin θ = y / z
Tan θ = y / x
[14]
6.2 Method of Sections
The section method is an effective method when the forces in all members of a truss
are being able to determine. Often we need to know the force in just one member with
greatest force in it, and the method of section will yield the force in that particular
member without the labor of working out the rest of the forces within the truss
analysis.
If only a few member forces of a truss are needed, the quickest way to find these
forces is by the method of sections. In this method, an imaginary cutting line called a
section is drawn through a stable and determinate truss. Thus, a section subdivides the
truss into two separate parts. Since the entire truss is in equilibrium, any part of it
must also be in equilibrium. Either of the two parts of the truss can be considered and
the three equations of equilibrium ∑ Fx = 0, ∑ Fy = 0, and ∑ M = 0 can be applied to
solve for member forces.Using the same model of simple truss, the details would be
the same as previous figure with 2 different supports profile. Unlike the joint method,
here we only interested in finding the value of forces for member BC, EC, and ED.
Few simple guidelines of section truss analysis:
1. Pass a section through a maximum of 3 members of the truss, 1 of which is the
desired member where it is dividing the truss into 2 completely separate parts,
2. At 1 part of the truss, take moments about the point (at a joint) where the 2
members intersect and solve for the member force, using ∑ M = 0,
3. Solve the other 2 unknowns by using the equilibrium equation for forces,
using ∑ Fx = 0 and ∑ Fy = 0.
[15]
In fig.23,a virtual cut is introduce through the only required members which is
along member BC, EC, and ED. Firstly, the support reactions of Ra and Rd should
be determine. Again a good judgment is require to solve this problem where the
easiest part would be consider either on the left hand side or the right hand side.
Taking moment at joint E (virtual pint) on clockwise for the whole RHS part
would be much easier compare to joint C (the LHS part). Then, either joint D or C
can be consider as point of moment, or else using the joint method to find the
member forces for FCB, FCE, and FDE. Note: Each value of the member’s condition
should be indicate clearly as whether it is in tension (+ve) or in compression (-ve)
state.
[16]
6.3 Graphical Method
The method of joints could be used as the basic for a graphical analysis of trusses.
The graphical analysis was developed by force polygons drawn to scale for each joint,
and then the forces in each member were measured from one of these force polygons.
The number of lines which have to be drawn can be greatly reduced, however, if the
various force polygons are superimposed. The resulting diagram of truss analysis is
known as the Maxwell’s Diagram.
In order to draw the Maxwell diagram directly, here are the simple guidelines:
1. Solve the reactions at the supports by solving the equations of equilibrium for
the entire truss,
2. Move clockwise around the outside of the truss; draw the force polygon to
scale for the entire truss,
3. Take each joint in turn (one-by-one), then draw a force polygon by treating
successively joints acted upon by only two unknown forces,
4. Measure the magnitude of the force in each member from the diagram,
5. Lastly, note that work proceed from one end of the truss to another, as this use
for checking of balance and connect to other end.
In conclusion, the truss internal reaction as well as its member forces could be
determine by either of this 3 methods especially in mechanics of structures.[6]
[17]
7. Design of Members
A truss can be thought of as a beam where the web consists of a series of separate
members instead of a continuous plate. In the truss, the lower horizontal member (the
bottom chord) and the upper horizontal member (the top chord) carry tension and
compression, fulfilling the same function as the flanges of an I-beam. Which chord
carries tension and which carries compression depends on the overall direction of
bending. The diagonal and vertical members form the truss web, and carry the shear
force. Individually, they are also in tension and compression, the exact arrangement of
forces is depending on the type of truss and again on the direction of bending. In
addition to carrying the static forces, the members serve additional functions of
stabilizing each other, preventing bucklingThe inclusion of the elements shown is
largely an engineering decision based upon economics, being a balance between the
costs of raw materials, off-site fabrication, component transportation, on-site erection,
the availability of machinery and the cost of labor. In other cases the appearance of
the structure may take on greater importance and so influence the design decisions
beyond mere matters of economics. Modern materials such as prestressed concrete
and fabrication methods, such as automated welding, have significantly influenced the
design of modern bridges.
[18]
8. Design of Joints
After determining the minimum cross section of the members, the last step in the
design of a truss would be detailing of the bolted joints, e.g., involving shear of the
bolt connections used in the joints, see also shear stress. Based of the needs of the
project, truss internal connections (joints) can be designed as rigid, semi rigid, or
hinged. Rigid connections can allow transfer of bending moments leading to
development of secondary bending moments in the members.
9.Applications
Component connections are critical to the structural integrity of a framing system. In
buildings with large, clearspan wood trusses, the most critical connections are those
between the truss and its supports. In addition to gravity-induced forces , these
connections must resist shear forces acting perpendicular to the plane of the truss and
uplift forces due to wind. Depending upon overall building design, the connections
may also be required to transfer bending moment.
Wood posts enable the fabrication of strong, direct, yet inexpensive connections
between large trusses and walls. Exact details for post-to-truss connections vary from
designer to designer. Solid-sawn timber and glulam posts are generally notched to
form a truss bearing surface. The truss is rested on the notches and bolted into place.
A special plate/bracket may be added to increase connection load transfer capabilities.
[7]
[19]
Index
Topics Pg. No.
1. Introduction 1
2. Characteristics of a Truss 2
2.1 Planar Truss 2
2.2 Space Frame Truss 2
3. Truss Types 3
4. Truss Types used in Bridges 4
4.1 Allan Bridge 4
4.2 Bailey Bridge 4
4.3 Baltimore Truss 4
4.4 Bollman Truss 5
4.5 Bowstring Arch Truss 5
4.6 Cantilevered Truss 5
4.7 Flink Truss 6
4.8 Howe Truss 6
4.9 Kingpost Truss 6
4.10 Lattice Truss 7
4.11 Lenticular Truss 7
4.12 Long Truss 8
4.13 Parker Truss 8
4.14 Pegram Truss 8
4.15 Post Truss 9
4.16 Pratt Truss 9
4.17 Queenpost Truss 9
4.18 Truss Arch 9
4.19 Warren Truss 10
4.20 Whipple Pratt Truss 10
4.21 Vierendeel Truss 10
5. Statics of truss 11
6. Truss Analysis 12
6.1 Method of Joints 13
6.2 Method of Sections 15
6.3 Graphical Method 17
7. Design of Members 18
8. Design of Joints 19
9. Applications 19
Bibliography
1. http://en.wikipedia.org/wiki/Truss
2. http://www.civilcraftstructures.com/civil-subjects/3-methods-for-
truss-analysis/
3. http://en.wikipedia.org/wiki/Truss#Truss_types
4. http://en.wikipedia.org/wiki/
Truss_bridge#Truss_types_used_in_bridges
5. http://en.wikipedia.org/wiki/Truss#Statics_of_trusses
6. http://www.civilcraftstructures.com/civil-subjects/3-methods-for-
truss-analysis/
7. http://en.wikipedia.org/wiki/Truss#Applications
Pictures Reference
Fig.1 Railway Track
http://en.wikipedia.org/wiki/File:RRTrussBridgeSideView.jpg
Fig. 2 Planar Truss http://en.wikipedia.org/wiki/File:Trusses_008.jpg
Fig.3 Space Frame Truss http://en.wikipedia.org/wiki/File:SpaceFrame02.png
Fig.4 Allan Truss
http://en.wikipedia.org/wiki/File:Hampden_Bridge_Wagga_design.jpg
Fig.5 Bollman Bridge http://en.wikipedia.org/wiki/File:Bollman-bridge-1.jpg
Fig.6 Bowstring Arch Truss http://en.wikipedia.org/wiki/File:FortPittBridge.jpg
Fig.7 Cantilevered Truss
http://en.wikipedia.org/wiki/File:CooperRiverBridge.svg
Fig.8 Fink Truss http://en.wikipedia.org/wiki/File:Bridges_20.png
Fig.9 Howe Truss http://en.wikipedia.org/wiki/File:Howe_truss.PNG
Fig.10 Kingpost Truss http://en.wikipedia.org/wiki/File:King_post_truss.png
Fig.11 Lattice Truss http://en.wikipedia.org/wiki/File:Lattice_truss.png
Fig. 12 Long Truss
http://en.wikipedia.org/wiki/File:Long_Truss_Bushing_CB_(Versailles_SP)_000
03r.jpg
Fig.14 Post Truss http://en.wikipedia.org/wiki/File:Post_truss.svg
Fig.15 Pratt Truss http://en.wikipedia.org/wiki/File:Pratt_truss.PNG
Fig.16 Queenpost Truss http://en.wikipedia.org/wiki/File:Queen_post_truss.png
Fig.17 Warren Bridge http://en.wikipedia.org/wiki/File:Warren_truss.PNG
Fig.18 Vierendeel Truss http://en.wikipedia.org/wiki/File:Vierendeel_truss.png
Fig.19 Statics of Truss http://www.civilcraftstructures.com/civil-subjects/3-
methods-for-truss-analysis/
Fig.20 Method of Joints http://www.civilcraftstructures.com/civil-subjects/3-
methods-for-truss-analysis/
Fig.21 Joint B,C and E http://www.civilcraftstructures.com/civil-subjects/3-
methods-for-truss-analysis/
Fig.22 Method of Sections http://www.civilcraftstructures.com/civil-subjects/3-
methods-for-truss-analysis/
Fig.23 Cutting Section http://www.civilcraftstructures.com/civil-subjects/3-
methods-for-truss-analysis/
Fig.24 Graphical Method http://www.civilcraftstructures.com/civil-subjects/3-
methods-for-truss-analysis/
Acknowledgement
We are greatly indebted to Mr. Sukhvinder Singh, our worthy and
highly respected Mechanics Teacher who inspired us to undertake
this project and provided us with very valuable guidance in the
preparation of the report. We express our deep and sincere gratitude
to him
Abhishek Sharma (12811502810)
Ashish Kumar Singh (12911502810) Gaurav Nigam (13011502810)
Mridul Malik (13111502810)
Bharti Vidyapeeth’s College of Engineering A-4 , Paschim Vihar, New Delhi-110063
CERTIFICATE
This is to certify that the reportt entitled “Truss” submitted by
,Abhishek Sharma,Ashish Kumar Singh,Gaurav Nigam and Mridul
Malik, of branch ECE-2 is a record of the project was carried by
them. They have worked under my guidance and supervision and
has fulfilled the requirements for the submission of the report,
which to my knowledge has reached a requisite standard.
Head of Department Date Professor Incharge