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A Project Report on Cost ion for Various Truss Configurations
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Transcript of A Project Report on Cost ion for Various Truss Configurations
.AProject Report on :-
COST COMPARISON FOR. VARIOUS TRUSSCONFIGURATIONS
-: PROJECT GROUP :-
CHANDRA SINGHCHINTAN DAVEISHAK DALAJAGRUTI BHADRIKEK. VISHNUPRIYAMITA CHAUHANNEHA PATELNIKHIL JAINNUPUR JOSHIPRASHANT PATELTARAPRIYAVIJAY DHAMI
.: GUIDE :-
PROF. N. T. DESAI
APPLIED MECHANICS DEPARTMENT
s. ~ REGIONAL COLLEGE OF ENGINEERING g TECHNOLOGY
SURAT - 395 007. (GUJARAT)
1998 - 99
S.V.REGIONAL COLLEGE OF ENGINEERINGAND TECHNOLOGY, SURAT.
CERTIFICATE
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Date : \ S'. s. q ~ ~T ~\FACULTY ADVISOR
U\.HEAD OF THEDEPARTMENT
ACKNOWLEDGEMENT
Conventional words fall too short to express our innnense
grattitude to our respected guide Mr. N.T. Desai Prof., Applied
Mechanics Department, who continuously directed us during our
project work.
We are equally thankful to Dr. H.S. PatH Head of Applied
Mechnics Department, for providing us computer facility In our
project work.
We must mention our sincere thanks to Mr. S.A Vasanwala
Prof., Applied Meclmics Department, for helping us in getting
computer software.
At last, we are thankful to all, who directly or indirectly
contributed for our project work.
INDEX
1.0 INTRODUCTION
1.1 General
1.2 Definition of truss
1.3 Components of truss
1.4 Classification of truss
1.5 Materials used in construction of truss
1.6 Aims and scope of \,vork
2.0 TYPES OF TRUSSES
3.0 LOADS ON ROOF TRUSSES
3.1 Dead load
3.2 Live load
3.3 \JVindload
4.0 CONNECTIONS
4.1 Riveted connection
4.2 Bolted connection
4.3 Welded connection
5.0 ANALYSIS OF TRUSS
5.1 Method of joints
5.2 Method of section
5.3 Graphical method
6.0 INTORDUCTION TO STAAD-III
6.0 !NTORDUCTION TO STA~D-III
6.1 STAAD-III(Structural Analysis and Design Softvllare)
6.2 STAAD-III-Analysis and Design
6.3 STAAD-PRE-Graphica! input generation
6.4 STAAD-POST-Graphical post processing
6.5 STAAD-INTDES
7.0 PARAMETRIC STUDY OF 2-D TRUSSES
8.0 INPUT AND OUTPUT DATA FILE IN STAAD-III
9.0 ANALYSIS AND DESIGN OF TRUSSES FOR VARIOUS
CONFIGURATIONS
10.1 Comparative cost for various configuration of trusses
10.2 Discussion on results
11.0 CONCLUSION
SCOPE OF FUTURE WORK
REFERENCES
9.1 Fan truss
9.2 Pratt 1 truss
9.3 Compound fink truss
9.4 Howe truss
9.5 Pratt truss
10.0 INTERPRETATION OF RESULTS
ABSTRACT
Industrial trusses form one of the major structural systems,
Nhichrequire accurate analysis and design. Their span and corresponding cost
plays an important role in planning the industrial area.
The shape and configuration is decided upon the span, pitch,
spacing , various loads and naturally the cost,.
In this project an humble attempt is made to compare various truss
configurations with same span, pitch, spacing regarding the cost aspects.
Following trusses selected:
1) Fan truss
2) Pratt 1 truss
3) Compound fink truss
4) Howe truss
5) Pratt truss
All the above types of trusses have been analyzed, designed
and typical drawings are prepared for span ranging from 10 to 30 Mts. which are
the most common spans in practices.
Cost comparison between various configurations of trusses is
made graphs are drawn.
1.0 INTRODUCTION
1.1 General:
The majority of buildings constructed today may be classified structurally
as either load bearing or skeleton frame. As the least dimension of the building
becomes larger and thus impossible or uneconomical to span with simple beams
or joists, columns and roof support Such systems extend to the perimeter of
bearing walls or walls with integral load bearing piers. An alternative solution is to
span the distance between walls with trusses. The truss frequently offers the
added advantages of permitting a wider variety of roof shapes and greater
unobstructed interior floor area at less cost. In Industrial buildings,we use trusses
for roofing system ,where spans are larger.
1.2 Definition of truss
Whena roof is to be providedfor a buildingwhich does not have interior
supports,but the exteriorwalls of which are more than 12 meters apart, some
system of framing would be more economicalthan simple, beams, such a frame is
called a 'truss'.
The basic form of a truss is triangle,formed by three members joined
together at their common ends forming three joints .Such a triangle Is clearly rigid
Another two members connected to two of the joints with their far ends connected
member of such geometrically rigid triangles can be interconnected to give a
stable configuration .The joints may be bolted, welded or fastened together with
pins but in the present treatments,members are subjected to axial forces of
tension or compression only and are not subjected to bending.
1.3 Components of truss
. Some components of truss are defined as follows.
. Span :Thecenter to center distance between end bearings of truss.
. Rise :The overall height of the truss measured from the bearing level to its
peak.
. Pitch :The ratio of the truss rise to its span .
. SloPe:The ratio of the rise truss to half of its span.
. TopChord:The top chord is defined as the upper most line of
members extendingfrom one support to the other and that passes
throughoutthe peak of the truss,
. BottomChord:The bottom chord Is defined as the lower most line or
members of the truss extendingfrom one support to the other.
1.4 Classification of truss
There are great many steel truss forms used in buildingconstruction
However, they may be classified as follows:
(1) Plane truss
(2) Space truss
. Planetruss :
If all the members of the truss lies in one plane,( two dimensional)it is
called a planetruss.
. Space truss
A three dimensionaltruss is called space truss.
1.5 Materials used in construction of truss
In general, the materials used in the construction of truss are timber ,steel,
aluminum,concrete and plastics.Timber is one of the oldest buildingmaterials, and
it has high strength at low weight. Steel is most frequently used in truss
construction and is an ideal material for such trusses. Steel trusses may be
constructed of cold rolled sections, angles or tubes and riveted, bolted or welded
together or to suitably shaped gusset plates or connectors.Prestressed steel is
used for strengthening of building of very large span. Fibre reinforced plastic is
used in the constructionof airplane, helicopter, solar panel or space ship etc.
1.6 Aims and scope of the work
. To study the change in force with the change in span for a particular truss
configuration.
. To evaluate cost of different truss configuration.
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. · To utilize general computer program "STAAD-III "for truss analysis and
design.
· To plot the graphs and prepare tables for the better understandingof cost
benefit for different truss configurations.
2.0 TYPES OF TRUSSES
When a roof is to be providedfor a buildingwhich does not have any
interior supports the exterior walls and which are more than 12 m apart, some
system of framingwould be more economical than simple beams. Such a frame is
called a truss. The common types of buildingtrusses are as follows:
(1) King post truss
. The central post known as king post forms a support for the tie beam.
. The inclined members, known as struts, prevent the principal rafters
from bending in the middle.
. It is suitable for roofs of span varying from 5 -8 m.
. It is usually built of wood or of wood combinedwith steel.
. Steel rods are used as tension members.
(2) Queen post truss
. It has 2 vertical members known as queen posts.
. The upper ends of the queen posts are kept in position by means of a
horizontalmember known as straining beam.
. In this truss a straining sill is introduced on the tie beam between the
queen posts to constrict the throats of sturts.
. This truss is suitable for roof of spansvarying from 6 m - 9m
(3) Pratt truss
. The pratt truss has diagonals in tension under normal vertical loading so
that the shorter vertical web members are in compression
. For pratt roof truss the most economical span to depth ratio is between
4 and 5, with a span range of 6 m to 12 m.
. For a light pitched roof truss wind loads may cause a reversal
of load thus putting the longer web members in compression.
. The parallel ( or nearly parallel Le. flat) pratt trusses have on
economic span range between 6 m and 50 m ,with a span to
depth ratio between 15 and 25 dependingon the intensity of
applied loads.
. For the top end of the span range the bay width should be such that the
web members are inclinedat approximately 50° or slightly steeper.
. For long deep trusses the bay,width become too large and are often
subdividedwith secondary web members.
. Flat part trusses are used for flatter roofs.
. For longer spans the pitched trusses are used for drainage purposes.
. Pratt truss is not so economical for steep slopes.
(4) Howe Truss
. The tension chord is more heavily loaded than the compression chord at
mid-span under normal vertical loading.
· The most economical span to depth ratio is between 4 to 5 , with a
span range of 8 m to 12m.
. It can be used for steep slopes but they are usuallynot too economical.
(5) Compound Fink Truss
· The most economical span to depth ratio is between 4 and 5 with a
span range of 8m to 12 m.
. It is most economicalfor higher end of the span range.
. It is very popular for steep roofs.
· It is more economical as most of the members are in tension while
those that are in compression are very short.
· They can be divided into a large number of panels to suit almost any
span or purlin spacing.
· The disadvantage is that the number of panels can be increased only by
doublingthe previous numberof members.
(6) Fan truss
· It is a modification of the fink truss that permits greater flexibility in
number of panels.
(7) Mansard truss
. It is a variation of fink truss.
. For spans between 15 m and 30 m. the Mansard truss reduces the
unusableroof space.
(8) Warren truss
. It has equal length of compression and tension web members, resulting
in a net saving in steel weight for smaller span.
· Theyhaveeconomicspan rangebetween6 m to 50 m with a spanto
depth ratio between 15 and 25 dependingon intensityof applied loads.
(9) Modified Warren Truss
. It can be used for large spans.
. It may be adopted where additional restraint to the chords is required.
(10) Saw tooth truss or Butterfly truss
. It may be used when adequate natural lighting is desired from skylights
in wide building like factory.
(11) Bow-string truss
· If a curved roof is acceptable,bow string truss can be used
economicallyfor spans upto 35 m.
· When properly designed , this truss has the unusual feature of having
very small stresses in the web members.
· A recommended radius of curvaturefor the top chord is givenas.
. Radius = 4 X h2 + 4 X ,28h
I = span length
h = height of truss
(12) Scissors truss
· It is used for supporting short span structures like churches and other
buildingswith steep roofs.
(13) Quadrangular truss
· It Is a long span truss Whichis used for spans well over 30 m.
· Near the center line of this truss the diagonals are reserved for the
purpose of keeping as many of them in tension as possible.
(14) Hammer beam truss
· It Is used for long spans and also when more head room is required.
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3.0 LOADS ON ROOF TRUSSES
The roof trusses are subjected to normally,dead load ,live load.and wind
10ad.Andin addition to these loads, the roof trusses are also subjected to some
special loads such as ceiling suspendedfloors or heavy machinery.
3.1 Dead Loads
Deadloads are loads which are constant in magnitude and fixed position
throughout the life time of the structure. Dead load on roof trusses includes the
weight of roof covering, the weight of purlins, the weight of bracing and the self fweight of trusses.
3.1.1 Weight of roof covering
It includes the weights of asbestos cement corrugated and semi
corrugated sheets, G.I Sheets, tiles, glass and slates. The weights of truss
materials are given in KN. per square meter of plan areas. The unit weights of
buildingmaterials have been given in IS: 875 ( PART I )- 1987 &Table I and II of
IS: 1991 -1967
3.1.2 Weight of bracing
The weight of bracing is assumed as 0.015 KNof plan area.
3.1.3 Weight of purllns
The weight of purlins is assumed as 0.070 to 0.150 KN. per meter of plan area.
3.1.4 Weight of trusses
For the design of roof trusses, the weight of truss is assumed . The weight of
truss varies with the span, and the rise of truss I the spacing of trusses, the type
of roof covering material, the geographical situation of the roof structure.The self
weight of truss is a small part of the total design for the roof truss. The self weight
of truss may be assumed as 0.090 to 0.150 km per square meter of plan area.
The self weight of truss can also be found by empirical
formula given below :
The self weight of truss in KN per square meter of plan area.
W = 11 100 ( U3 + 5) KN. 1m2
Where I is the span of truss in meters.
3.2 Live Loads
Live loads are the loads which very in magnitude and/or in positions. Live
loads are also known as imposed or transient loads. Live loads are expressed as
uniformly distributed static 10ads.Theimposed ( live) loads on various types of
roofs other than wind load and snow load. as per IS : 875-1987, for roofs with
slopes upto and including 10 degrees, is adopted as 1.5 KN I m2 of plan area
where access is provided to roof . The minimumlive load measured on plan shall
be 3.75 KN uniformly distributed over any span. of one meter width of the roof
slab and 9.0 KN uniformly distributed over the span in the case of all beams.
Where the access is not provided , except the maintenance , live load on roofs is
adopted as 0.150 KN/ m2of plan as in the case, the minimumlive load measured
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on plan shall be 1.9 KN uniformly distributed overly span of one meter width of
roof slab and 4.5 KN uniformly distributed over the span in the case of beams.
The live load for sloping roof with slopes greater than 10° is adopted as 0.75 KN
per square meter of plan area. less 0.020 KNlm2for every degree increase In
slope over 10° subjected to minimumof 0.400 KN I m2 per square meter of plan
area.
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3.3 Wind Load
The wind load is one of the most important loads that an engineer has to
deal with and is also one that is most difficult to evaluate properly . The magnitude
of wind pressure depends on wind velocity and the shape of the structure . The
magnitude of wind velocity varies with the geographical location of the structure
and the height of the structure.
3.3.1 Basic wind speed
The basic wind speed, Vb is the wind speed measured in a 50 year return
period,. The basic wind speed is based on peak gust velocityaveragedover a
short Internal of time of about 3 seconds and it corresponds to mean heights
above ground level In an open terrain (category)
As per IS : 815 (part 3) wind loads - 1987 , six wind zones have been
formed which corresponds to basic speed of 55,50,47,39 and 33 meter per
second, respectively shown in map in IS :875 .
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Afternoting the basic wind speed , it is modified to include the effects of risk,
level, terrain roughness, helght,slZe of the structure, and local topography., The
design wind speed, Vz may be mathematically expressed as under. The design
wind speed is the wind speed for which the structure is designed.
Vz = ( k1 . k2 . k3 ) Vb
Where Vz = designwind speed at any height in m /sec~
k1 = risk coefficient ( probability factor)
k2 = terrain, height and structure size factor
k3= topography factor
Above factors k1 , k2 and k3 have been described in IS :875 ( part 3) -1987 ,Is to
note that the design wind speed upto the height from the mean ground level shall
be considered constant.
3.3.3 Design wind pressure
The design wind pressure, pz depends upon the basic wind speed, Vb, the
height of structure above ground level, the terrain categories ,the local topography
,the aspect ratio ( viz.,length and breath of structures),the shape of structure and
the solidity ratio or opening in the structure.
The design wind pressure at any height above mean ground level shall be
obtained from the following expression.
pz = 0.6 <Vz)2 N 1m2
Where, Vz is the design wind speed in m/sec at height z . This coefficient 0.6 in
the above expressions depend on a number of factors and mainly on the
atmospheric pressure and air temperature.
4.0 CONNECTIONS
After design and investigation of different structural elements, each of
these members must be connected to adjacent members in order to form a
complete structure. Connection between two adjacent members should be strong
enoughto sustain various types of loads as the more common structural failures
occur in connection rather than in members.
Followingare the main types of connections used for framework:
4.1 Riveted connection
Rivets are made from mild steel rivet bars by a machine which forms the
head and cuts the rivet of the desired length.The different types of rivet are shown
in the fig.(4.1et)
Rivets are classified as :
. Power driven shop rivets
. Power driven field rivets
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. Riveted
. Bolted
. Welded
. Ball and socket Joint
. Joint with partial fixity
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. Hand driven rivets
Power driven shop rivets are the ones driven in fabrication shop under
better controlled.conditions. Therefore,they are stronger than the power driven
field rivets or hand driven rivets
When a rivet is ready for driving, it should be free from slag, scale and
other adhering matter. All rivets should be driven by hydraulic or pneumatic
process. This is the case when riveting is done by heating . The rivets can be
driven cold also with the use of special equipment and considerable success has
been obtained up to for 24 mm diameter rivets but at the present time cold driving
of rivets of diameter. greater than 10mm is not permissible.
4.1.1 Lap Joints
These are generally the simplest type of connection used when two
member are in the same plane. In this the planes to be connected together
The lap joints are usually of the following types.
overfap each other as shown in fig.(i./ l.b).
. Single riveted lap joints in which a single row of rivets parallel to the edges of
plates is used for the connection.Which is shown in fig.(~:lij.Double riveted lap
joint in which two parallel rows of rivets are used which may be in the form of
chain or in the zig - zag form which is shown in fig. (1:1.,,)
4.1.2 Butt joint
In the butt joint, the plates to be connected together are kept flush, their
central planes being just opposite to each other. These may be connected through
cover plates on one side only. Butt joint may be of single row of riveting or of
chain riveting or zig-zag riveting fig. ei:1-~. Transmission of load in a riveted joint
occurs either by friction between the connected plates due to large gapping forces
produced by the tension in rivet or by shearing action on the cross section of the
rivet and bearing stress on the rivet and plates in contact with each other fig.(4:~).
4.1.3 Failure of riveted Joint
If a riveted joint carrying one rivet in lap joint such as the one shown1nfig
(4-3) is subjected to load 'P' increasingfrom zero to the stage when the joint fails.
There are following ways in which the joint can fail, as shown in fig. (4 '3).
. Tearing of the connected plate along the line of rivets.
. Bearing of plate or rivets.
. Shearing of rivets.It
. Burstingand shearing at end of plate.
4.1.4 Efficiencyof joint
Due to rivet holes in the jointed plates, the original strength of the full
section is reduced. A joint which causes smaller reduction of strength is said to be !
more efficient. The efficiency of a joint. Is the ratio of the actual strength of the,t
connectionto the gross strength of the connected members and is expressed as a
percentage. For better efficiency,therefore,a section should have the least
possible number of holes at the critical section.
So for better efficiency,grouping of rivets should be done. The rivets should
be so grouped that a minimumloss of strength takes place due to rivet holes.
4.2 Bolted connections
Bolts are made from mild steel or high tensile steel and consists of a
hexagonalhead, a plain part of a shank and a threaded part as shown in fig. (Lj.4)
For connecting two steel plates together, holes are made in the parts, the parts Iare brought together, the bolt is passed through the holes and a nut Is threaded
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on the other end.
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. Black bolts.
. Fitted bolts.
. High strength friction grip bolts.f
. Turned bolts.
. Standard unfinishedbolts.
. Ribbed bolts.
4.2.1 Blackbolts
Black bolts are usually made from mild steel and the surface of the shank,.
is left unfinished, that is rough as rolled. The bearing of such bolts on the walls of I
the holes remains imperfect, hencethe allowable stress is kept less than the other .,
types of bolts. Also the joints remain quite loose resulting in large deflection of the..
the structure due to movements of the joints. Black bolts are commonly used
during erection and for temporary structures.
4.2.2 Fitted bolts
Fitted bolts are also usually made from mild steel but the surface of the
shank is finished by turning to a diameter which is larger than the nominaldiameter
ofthe bolt by 1.2 mm for bolts M8 to M16 and by 1.3 mm for larger sizes. These
bolts will fit the bolt holes, which are larger by 1.5 mm more readily and provide
much better bearing contact between the bolts and the holes.
4.2.3 Ribbed bolts
The Ribbed bolt Is a comparatively a recent innovation. It has the head of a
rivet and the thread and nut of a ballet as shown in fig( ~ .fa).The shank has
longitudinal ribs which project from its core and result in an over all diameter
slightly larger than the diameter of the hole. When driven into the hole, the ribs
are deformed wedging the bolt tightly and allowing the nut to be tightened. The
ribs, by gripping the sides of the fitted pieces, provide greater resistance to
vibration than ordinary bolts.
4.2.4 Highstrength bolts
High Strength bolts are the major type of fieldJastener used in steel
structural building.These bolts are made from high tensile steel and their surface
is kept unfinished, that is, as rolled and rough. Therefore,they remain loose fit in
holes like black bolts, but their action in the joint takes place differently..These
bolts are tightened to a very high tension, reaching their proof load,through
calibrated torque wrenches. Thus a very high compression is created between the
connected parts,which is equal to the proof load. The bolt of the joint is subjected
to a shear load, it is primarily resisted by the frictional force. Therefore the
bearing of bolt on the hole surface does not come to play at all. Suchjoints remain
fullytight .
4.2.5 Design of bolted Joints
The analysis and design of joints is exactly similar to the riveted joints
except that the allowable stresses in the bolt are different . The pitch and edge
distance for bolted joints are the same.
4.3 Welded connections
Welding consists of joining of two pieces of metal by establishing a
metallurgical bond between them. Many different welding processes may be used
to produce bending through the application of pressure or through fusion. The
bond between the metals is produced by reducing the surface to be joined to a
liquid state and than allowing the liquid to solidify.
4.3.1 Welding process
The shield Metal arc welding process is the most common type used for
structural welding. In this process, the intense heat required to reduce the metal
to a liquid state is produced by an electric arc fig. (Lj.5).
In all modern arc welding process t.hearc is shielded to control the complex
arc phenomenonand to improve the quality of the weld metal.
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4.3.2 Type of welds fig.(~ .6)
Welds are classified in three different ways :
(i) Accordingto their position,
flatweld .
horizontal weld .
vertical weld .
overhead weld.
(ii) Accordingto their type,.
groove weld .
fillet weld ...f
plug weld.
slot weld .
(iii) Accordingto the type of joint,
buttweld .
lap weld.
tee weld .
comer weld.
edge weld .
Flat weld is one which is made right on top,the electrode being downward
in a vertical plane.
Horizontal weld is made on a horizontal side, the electrode being in a
horizontal plane or only slightly inclined.
Verticalweld is made from bottom upward on a verticaljoint.Overhead
weld is made from lookingup, the electrode being upward in almost vertical plane.
The flat weld is the easiest to make and overhead weld the most
inconvenient.
Butt and fillets welds are the ones most commonly used for structural work.
plug and slot welds are generallyused where it is not possible to providethe
required weld area by butt or filletwelds and additional area is required.
Buttwelds
These are used in joints between two abutting parts lying in approximately
in the same plane. They are classified according to the method of grooving or
preparing the base metal before weld metal is deposited.
Fillet welds
Lap, tee or corner joints require fillet type welds.Such welds are usually in
the shape of a rightangledtrianglewithequal or unequal legs. Different types of
fillet are shown in the fig. ('1.6).
The size of the fillet welds Is denoted by the sizes of the sides of the right
angle. The strength of a fillet weld is determined by the throat dimension;
therefore. small fillet welds are the most economical. This is true because the
throat dimension is proportional to the leg size,while the amount of weld metal
varies approximately, as the square of the leg size.
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Welds of this type fail through the throat as a result of the combined effect
of shear and tension or compression. For design purpose,it is generally assumed
that strength per linear inch of fillet weld is the shearing strength .
Plug and slot welds
If a sufficient length of fillet weld can not be provided in a joint, the
connection can be strengthened by the use of plug or slot welds. Plug and slot
welds are made by filling with weld, metal in a circular or slotted hole cut in one of
the two parts to be jointed, or by forming a fillet weld around the edge of the hole
or slot. The strength of such a weld is equal to mean length of weld times the
Followingmethods are employed the design of steel framework :
throat dimensiontimes the permissible stress.
Ball and socket Joints
This is the joint where all the loads are supported by the end reactions in all
the three directions, As shown in the fig. (it-f) In the figure all components of the
force are shown along x, y and z direction.
Method of design
(1) Simple design :
This method applies to structures in which the end connections between
members are such that they will not develop restraint moment.and for the purpose
of design pin joints are to be assumed .
(2) Semi rigid design :
This method,as compared with the simple design method, permits a
reduction in the maximum bending moment in beams suitably connected to their
supports, so as to provide a degree of direction fixity, and in case of triangulated
frames, it permits account being taken of the rigidity of the connections and the
moment of interactions of members.
(3) Fully rigid design :
This method gives the greatest rigidity and economy in the weight of steel
In the absence of more exact analysis, the effective length of column in
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as compared to the pervious method. The end connections of members of the
frame shall have sufficient rigidity to hold the original angles between such
members and the members they connect virtually unchanged.
Effective length of column
firmed structure may be obtained from the ratio .IILof effective length I to
unsupported length L given in fig. (Lt-¥q)When relative displacement of the ends is
not prevented .In the later case the ratio ilL shouldnot be less than 1.2 .
Po, = P02 = EKe I E Ke + Ekb
Where, kc = flexure stiffness for column.
kb = flexure stiffness for beam.
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I 5.0 ANALYSIS OF TRUSS~
5.1 Method of joints
In this method, to determine the forces in the members of a statically
determinate truss. The whole truss is consider as a free body to obtain reaction
and then each joint as a free body to obtain the axial forces at a time. The joints
Nhere the number of unknowns are two or less than two should be solved first.
For example the truss ABC shown in fig find the forces in member AB, BC and AC
Taking moment @ B
R2X L - P X L1 = 0
~"e~~c.
R2 = PL1 I L KN
/~e,Lj'r L.1 -~
r - L
RI
I<.N
R2 = ( P - R2 ) KN
1
H~
1<1"\
~fy = 0
R1 + FASsin 81 = 0
FAS = R1sin 8 1( compression)
~Fx = 0
Fsc + FAS COS81 = 0
FBC+ ( -R1 J sin 81 ) x cas 81 = 0
/1 FHB
~/B 6L
iR I ~ F13 Co
FBC = R1J tan 81 (Tension)
1:FY=0
R2 + FACsin 82 =0
.(F8C
"\ AC.
~."""
GzGciR~ kt-\
FAC = R2/ sin 81 ( compression)
EFX = 0
FAC cas 82 + FBC = 0
!
t
i
(-R2/ sin 82) cas 82 + FBc= 0
Fac = R2/ tan 82 ( tension)
i.
5.2 Method of section
In this method the truss is cut in to two parts and equilibriumequations areI1
formed for either one of the parts of the truss treating it as a free body. The
method of section is superior if we see the forces only in some of the member
sectionAA cuts the trusses in to the parts . The left part of the truss takes in to
consideration the equilibrium condition
V, t@
/./'\; ~----
\,\ fA) v ~
"
I
:~I -
0"/
'''"''"
~,
"
,
L,""
>-~-'--1.-3
P3 Irlfl
1 R~
iRo,
To find the reaction (Truss is symmetrical)
R, = R2= Total forcesl 2
= P, + P2 + P32
To find force in member U,U2
Taking moment about the intersection of the other two forces.
L;ML2= ( R, x U 2) - ( P, x U4) + FU,U2x h = 0
FU,U2=( P, x L / 4 ) - (R, x L I 2 )11
Similarly to find force in member L,L2,taking moment about U,
L;Mu,= ( R, x U4) - ( FU,U2X h ) = 0
To find the force in member U,U2
L;FY= R, - P, - FU,U2sin 8, = 0
F U~U2= (R~ - P~) I sin e~
5.3 Graphical method
The member forces in a stability determine truss can be determined by
graphical method.
This method of analysis is based on two assumptions.
(1) If only there non parallel forces act one body they must pass through a
common point and,
(2) If the magnitude of two forces acting on a body are the only unknownthe
closures of force polygon determines their magnitudes.
Graphical solution of a truss is done in following steps:
(1) Construction of space diagram
(2) Construction of vector diagram.
Bow's notationsa
R(B)
///
,//
/c /
Rl(N)
Rl (D) IRR
Bow's Notations
(A), (B), (C) ,(D) ad = RLbd = RR
',,-.~ ","
RR(N)
SPACE DIAGRAM
ad = Parallel to W -Weightbc = Parallel to R - Right rafter
. bac = Parallel to L- Left raftercd = Parallel to T - Tie
VECTOR DIAGRAM
....
I':.a"
t'ctJ
IJ
6.0 INTRODUCTION TO STAAD-III
6.1 STAAD-III ( Structural Analysis and Design Software )
It is a popular and widely used structural engineering software. Equipped
\A,~thDowerful analysis, design, graphics and visualization capabilities it is a
favorite choice of structural engineers. Data Exchange with CAD programs for
import/export of dra\"Iing data is also possible. STAAD-III is a comprehensive
structural software that addresses all aspects of structural engineering - model
development, analysis, design, verifIcation and visualization. So it is easy for
anyone to build one's model, verify it graphically, perform analysis and design,
review the results, sort and search the data to create a report - all \,'.~thinthe
same graphical based environment.
STAAD-III uses a unique script language that allows you to build a
customized structural engineering solution using STAAD. The language used is
knO\'vnas STAPLE. It stands for STAAD-III Application Programming Language
Extension. STAPLE utilizes an English-like command language format. For an
engineer to use STAAD software it is extremely essential to learn STAPLE. Only
using STAPLE, you can access the STAAD-III database to extract all structural
data - geometry, section/material properties, forces, moments and more. So the
engineer has use STAPLE to integrate and execute his in-house, company-
standard programs seamlessly with STAAD-III.
In STAAD-III the following are the main options available from the
graphical Environment -..
STAAD-III Analysis and Design
STAAD-PRE Graphical Input Generation
STAAD-POST Graphical Post-Processing
STAAD-INTDES Interactive Design of Structural Components
6.2 STAAD-III -Analysis and Design
It performs the analysis and design of the structure. The processes of
analysis and design are integrated and can be performed in the same run. The
input file can be created through a text editor or STAAD-PRE input generation
facility. For structures it is capable for analyzing and designing structures
consisting both frame and plate/shell elements, most general is space( 3D )
structures and plane( 20 ) structures. But it also is capable in analyzing floor
structural components. Geometric modeling is done by assigning nodes at
structure, truss structure and columns. In STAAD a structure is an assemblage of
elements. So frame elements and plate elements may be used to model the
elements. But care should be taken that nodes be specified either clockwise or
anti-clockwise direction. Elements are numbered sequentially.
6.3 STAAD-PRE- Graphical Input Generation
This option can be used either to create a file or for adding additional
data before the completion of the input file. It allows generation of structural
models graphically. Powerful geometry generation facilities in the system helps
in generation and viewing of structural models for both 20 and 3D situations. The
facilities for the specifications of section properties, material constants, supports,
loads, analysis/design requirements, printing/plotting requirements etc. are
available. In addition to facilities for conventional member/element generation
STAAD-PRE includes a Library option. This option includes a number of common
structural components that can be customized, and used as building blocks to
create a complex model.
6.4 STAAD-POST- Graphical Post Processing
As suggested from its name it is an option to be invoked either after
processing ( i.e. after running) the input file or for processing the input file. It is a
powerful graphics facility for verification of the model and display of the results.
The model verification capabilities include complete graphics verification and
visualization of all items. Results verification capabilities include display and
plotting of structure geometry, deflected/mode shapes, bending moment/shear
force diagrams, stress contours etc. A versatile query facility allows generation of
cl:Istomized reports. Powerful icon-based graphics tools provide extremely user-~
friendly navigation and manipulation capabilities.
6.5 STAAD-INTDES
This option contains a set of interactive design facilities for structural
components. The currently available options include design of Cantilever
Retaining Walls, Footings and Slabs.
.
". PARAMETRIC STUDY OF 2 D TRUSSES.
Parametric study of roof truss is done using STADD -III package.An
input file for a typical roof truss is given in the following pages. The
output results of this truss containing analysis results i.e. forces in
members & displacement of joints and design results i.e. member sizes &
overall weight of truss obtained ftom STAAD III are shown in later pages.
The explanation of various connnands related to creation of input data file
is given below.
Input me
The purpose of explainingthe input files is:
. to explain,what type of data is required to be give as input for
standard analysis software for the analysis of 3- dimensional and 2-
dimensional structures.
. To explore the sophisticated features available with such softwares.
STADD TRUSS
Every STADD-III input has to start with the word STADD. the word
TRUSS signifies that the trusses are pin-joined and carry only axial loads.J
~
UNIT METER KG ,
it
t~
This command allows the user to specify or change length force units for
input and output.
INPUT WIDTH 72
This command is used to specify width of lines of input. The default
input width is 72.
Geometrical modelling of roof truss.
Mathematical modelling of the truss is an important step
truss. Once the configuration of the truss is decided,
generation is a prerequisite for any truss analysis.
m the design of
the configuration
JOINT COORDINATES
This command allows the user to specify and generate the co-ordinated of
the joints of the Truss. All joints numbers are assigned globally. In global
axts,
x -> + left.
y -> + Ve upward
Z -> + Ve outward
MEMBER INCIDENCES
This command defmes the members by the joints to which they are .
comected.
The general configuration of truss with joint numbers and member numbers
is shown in the latter pages.
MEMBER PROPERTY INDIAN
All members of a truss have properties from the Indian table.
INPUT WIDTH 72
This connnand is used to specify width of lines of input. The default
input width is 72.
Geometrical modelling of roof truss.
Mathematical modelling of the truss is an important step
truss. Once the configuration of the truss is decided,
generation is a prerequisite for any truss analysis.
in the design of
the configuration
JOINT COORDINATES
This connnand allows the user to specify and generate the co-ordinated of
the joints of the Truss. All joints numbers are assigned globally. In global
axts,
x -> + left
y -> + Ve upward
Z -> + Ve outward
MEMBER INCIDENCES
This connnand defmes the members by the joints to which they are
cormected.
The general configuration of truss with joint numbers and member numbers
is shown in the latter pages.
MEMBER PROPERTY INDIAN
All members of a truss have properties from the Indian table.
~
SELECT ALL
By this command , selection of member sizes is done using the last
results ftom analysis and iterating on sections until a least weight size is
obtained for most critical load combination.
SELECT OPTIMTZFTI
BY this command, analysis of the structure is done a number of times
and corresponding iteration of sizes until an overall structure of least
weight is obtained.
GROUP MEMB it to i5 ..Although the program selects the most economical section for all members,
it is not always practical to use many different sizes in one structure.
Truss members are classified into different types such as tie members,
rafters and strut members. Generally for the pmpose of design work,
members of same type at a particular level, at different faces of truss,
are grouped together and same is adopted. The GROUP command groups
the members by their input listing i.e. the members in one group have
same size (largest of grouped members.)
r
,.
PERFORM ANALYSIS
Since the member sizes are now all different, it is necessary to reanalyze
the structure to get new values of forces in the members.
JOINT LOAD
This command specifies that. all - loads are acting at the joints of a
member
LOAD liST AIL
This connnand activates all load for analysis and design.
PERFORM ANALYSIS
This connnand directs the program to penonn the analysis of a truss for
member sizes as initially specified which includes.
· checking whether all .infonnation is provided for the analysis;
. fOIming the joints stiffness matrix;
· checking the stability of the structure;
· solving simultaneous equations, and
· computing the member forces and displacement.
CHECK COAD ALL
The purpose of code checking is to verify whether the specified section
is capable of satisfying applicable design code requirements. The code
checking is based on the IS: 800(1984) requirements. The code checking
output labels the members as PASSed or FAILed . In addition, the critical
condition governing forces are also printed out.
After the generation of a roof truss on the screen . the initial member
sIZes are specified before going into complex 3D analysis of the actual
truss.
\~
,
CONSTANTS
E STEEL ALL
Material constant such as Modulus of Elasticity (E) are provided followingthe CONSTANT connnand to all truss members.
SUPPORTS
il to i4 FIXED
This connnand specifies that the joints il to i4 are fixed, meaning the
support has both transitional and rotational restraints.
LOADi
The load combination that we have considered for the analysis of the roof
truss is that of wind load and dead load.
SELECT ALL
Again for grouped members, the program selects member sizes using last
results of analysis for most critical load combination.
PRINT MEMBER FORCES
This connnand prints forces in all members of truss for a specific load
cases.
PRINT JOINT DISPLACEMENT AU.
This connnand prints X-translation, Y-translation and Z-translation of all the
truss joints.
PRINT SUPPORT REACTIONS
f\.s we ~m~ ~~~~~ \~ ~~ ~~~ ~\. ~~~\t\\ ,~~ ~,~~ \~~~i.e. Fx, Fy and Fz for the load case.
STEEL TAKE OFF
This conunand gives summary of all steel sections being used along with
their lengths and weights.
FINISH
This command tenninates the STADD-ill / ISDS run.
8.0 INPUT AND OUTPUT FILE IN STAAD-III
In this chapter, the input file for pratt truss of 9 m span in STAAD-II/is included in
the followingpages. And output file for the same is also included in the following
pages in the same format which STAAD-IIIgives.
-~
STAAD TRUSSINPUT WIDTH 72UNIT METER KNSJOINT COORDINATES1 .002 3.303 6.604 9.905 13.206 16.507 19.808 16.509 13.2010 9.9011 6.6012 3.30MEMBER INCIDENCES1122233344455566677788899 9 1010 10 1111 11 1212 1 1213 2 1214 3 1215 3 1116 4 1117 4 1018 4 919 5 920 5 821 6 8MEMBER PROPERTY INDIAN1 TO 21 TABLE ST ISA20X20X3SUPPORT1 7 FIXEDCONSTANTE STEEL ALLDENSITY STEEL ALL
LOAD 1 (DEAD LOAD + WIND LOAD)JOINT LOAD1 7 IT 7.968 TO 12 FY 15.931 7 FX 4.998 TO 12 FX 9.98PRINT PROBLEM STATISTICSPERFORM ANALYSIS
CHECK CODE ALLSELECT ALL.SELECT OPTIMIZEDPRINT MEMBER FORCES ALL
.000
.000
.000
.000
.000
.000
.0001.6503.3004.9503.3001.650
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
PRINT JOINT DISPLACEMENTS ALLPLOT DISPLACEMENT FILE
STEEL TAKE OFFFINISH
STAAD TRUSS -- PAGE NO. 3
STAAD-III CODE CHECKING - (ISA )***********************
UNITS ARE - KNS METE (UNLESS OTHERWISE NOTED)
ER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/FX MY MZ LOCATION
----------------------------------------------------------------------------------------------------------------------------------------
1 ST ISA20X20X3 FAIL SLENDERNESS 2.2304.67 T
2 ST ISA20X20X3 FAIL SLENDERNESS 2.2304.67 T
3 ST ISA20X20X3 FAIL SLENDERNESS 2.23015.61 T
4 ST ISA20X20X3 FAIL SLENDERNESS 2.2305.63 T
5 ST ISA20X20X3 FAIL SLENDERNESS 4.95515.29 C
6 ST ISA20X20X3 FAIL SLENDERNESS 4.95515.29 C
7 ST ISA20X20X3 FAIL SLENDERNESS 2.49372.31 T
8 ST ISA20X20X3 FAIL SLENDERNESS 2.49360.08 T
9 ST ISA20X20X3 FAIL SLENDERNESS 2.49347.85 T
10 ST ISA20X20X3 FAIL SLENDERNESS 2.49359.01 T
11 ST ISA20X20X3 FAIL SLENDERNESS 2.49382.40 T
12 ST ISA20X20X3 FAIL SLENDERNESS 2.493105.79 T
13 ST ISA20X20X3 PASS SLENDERNESS .000 1.00 T .00 .00 .00
14 ST ISA20X20X3 FAIL SLENDERNESS 2.49312.23 T
'" 15 ST ISA20X20X3 FAIL SLENDERNESS 4.9555.47 C
16 ST ISA20X20X3 FAIL SLENDERNESS 3.15315.47 T
'" 17 ST ISA20X20X3 FAIL SLENDERNESS 7.43231. 86 C
* 18 ST ISA20X20X3 FAIL SLENDERNESS 3.15329.59 T
* 19 ST ISA20X20X3 FAIL SLENDERNESS 4.95510.46 C
... 20 ST ISA20X20X3 FAIL SLENDERNESS 2.49323.39 T
21 ST ISA20X20X3 PASS SLENDERNESS .000 1.00 T
-.00 .00 .00
STAAD TRUSS
STAAD-III MEMBER SELECTION - (ISA )**************************
TABLE
ALL UNITS ARE - KNS METE (UNLESS OTHERWISE NOTED)
MEMBER RESULT/FX
CRITICAL COND/MY
RATIO/MZ
-- PAGE NO.
=======================================================================
LOADING/LOCATION
1 ST ISA45X45X3 PASS4.67 T
2 ST ISA45X45X3 PASS4.67 T
3 ST ISA45X45X3 PASS15.61 T
4 ST ISA45X45X3 PASS5.63 T
5 ST ISA100XIOOX6 PASS15.29 C
6 ST ISA100XI00X6 ~~S15.29 C
7 ST ISA65X45X5 PASS72.31 T
8 ST ISA50X50X5 ~~S60.08 T
~ ST ISA50X50X4 PASS47.85 T
10 ST ISA50X50X5 ~~S59.01 T
11 ST ISA70X45X5 PASS82.40 T
12 ST ISA75X50X6 ~~SS1 "I: .,n rn,LV.,J.IJ .I.
13 ST ISA20X20X3 PASS.00 TP.ZI.sS
1") ")':) m..LL..L..,J ..L
14 ST IS.ZI.50X50X3
15 ST ISA100X100X6 PASS5.47 C
16 ST ISA65X65X5 P~.ss, I; .II"7 'T'I..L,.~, ..L
17 ST ISA150X150X10 PASS31. 86 C
18 ST ISA65X65X5 P~.sS")n 1:0 mLoJ..JJ .L
19 ST ISA100X100X6 PASS10.46 C
20 ST ISA50X50X3 ~~S..,~ ~o 'T'ILo.,Je ,J .L
21 ST ISA20X20X3 PASS.00 T
TENSION.00
TENSION.00
TENSION.00
TE."lSION
.00COMPRESSION
.00COMPRESSION
.00TENSION
.00TENSION
.00TENSION
.00TENSION
.00TENSION
.00TENSION
''''.vv
TENSION.00
TENSION.00
COMPRESSION.00
TE."!SION''''.vv
COMPRESSION.00
TENSION''''.vv
COiviPRESSION
.00TENSION
roro.vvTENSION
.00
.118
.00
.118
.00
.394
.00
.142
.00
.353
.00
.353
.00
.917
.00
.836
.00
.822
.00
.821
.00
.995
.00
.985roro
.vv
.000
.00
.276roro.vv
.126
.00
.165
.00
.295
.00
.316roro.vv
.242
.00
.529roro.vv
.000
.00
1.001.001.001.001.001.001.001.001.001.001.001roro
.vv
1.001roro
.vv
1.001roro
.vv
1.001roro
.vv
1.001roro.vv
1
.00,.
2
ST.n..n.D TRUSS p.n.GE NO.
************** END OF TABULATED RESULT OF DESIGN **************
56. SELECT OPTIMIZED
++ Processing Element Stiffness Matrix. 5:50:495:50:495:50:49
++ Processing Global Stiffness Matrix.++ Processing Triangular Factorization.++ Calculating Joint Displacements.++ Calculating Member Forces.
5:50:495:50:49
3
ST.nun.D TRUSS -- PAGE NO. 4
ST_-III ER SELECTION - (IS.**************************
ALL UNITS ARE - KNS METE (UNLESS OTHERWISE NOTED)
MEMBER TABLE RESULT/ CRITIC.'\L CONDI Rl\.TIO/ L01\.DINGI
FX MY MZ LOCATION=======================================================================
1 ST ISAI00XI00X6 PASS COMPRESSION .015 1.64 C .00 .00 .00
2 ST ISA100X100X6 PASS COMPRESSION .015 1.64 C .00 .00 .00
3 ST ISA45X45X3 PASS TENSION .260 110.30 T .00 .00 .00
4 ST ISA45X45X3 PASS TENSION .008 1.32 T .00 .00 .00
5 ST ISAI00XI00X6 PASS COMPRESSION .476 120.60 C .00 .00 .00
6 ST ISA100X100X6 PASS COMPRESSION .476 120.60 C .00 .00 .00
7 ST ISA65X45XS PASS TENSION .917 172.31 T .00 .00 .00
8 ST ISA50XSOX5 PASS TENSION .836 160.08 T .00 .00 .00
9 ST ISA50X50X4 PASS TENSION .822 147.85 T .00 .00 .00
10 ST ISA50X50X5 PASS TENSION .821 159.01 T .00 .00 .00
11 ST ISA70X45X5 PASS TENSION .995 182.40 T .00 .00 .00
12 ST ISA75X50X6 PASS TENSION .985 1105.79 T .00 .00 .00
13 ST ISA20X20X3 PASS TENSION .000 1.00 T .00 .00 .00
14 ST ISA50X50X3 PASS TENSION .276 112.23 T .00 .00 .00
15 ST ISAI00XI00X6 PASS COMPRESSION .126 15.47 C .00 .00 .00
16 ST ISA65X65X5 PASS TENSION .165 115.47 T .00 .00 .00
17 ST ISA150X150XI0 PASS COMPRESSION .295 131. 86 C .00 .00 .00
18 ST ISA65X65X5 PASS TENSION .316 129.59 T .00 .00 .00
19 ST ISA100XIOOX6 PASS COMPRESSION .242 110.46 C .00 .00 .00
20 ST ISA50X50X3 PASS TENSION .529 123.39 T .00 .00 .00
21 ST ISA20X20X3 PASS TENS10N .000 1.00 T .00 .00 .00
STAAD TRUSS -- PAGE NO.
************** END OF TABULATED RESULT OF DESIGN **************
57. PRINT MEMBER FORCES ALL
5
STAAD TRUSS -- PAGE NO. 6
MEMBER END FORCES STRUCTURE TYPE = TRUSS-----------------
ALL UNITS ARE -- KNS METE
EMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y MOM-Z
1 1 1 .64 .00 .00 .00 .00 .002 -.64 .00 .00 .00 .00 .00
2 1 2 .64 .00 .00 .00 .00 .003 -.64 .00 .00 .00 .00 .00
3 1 3 -10.30 .00 .00 .00 .00 .004 10.30 .00 .00 .00 .00 .00
4 1 4 -.32 .00 .00 .00 .00 .005 .32 .00 .00 .00 .00 .00
5 1 5 20.60 .00 .00 .00 .00 .006 -20.60 .00 .00 .00 .00 .00
6 1 6 20.60 .00 .00 .00 .00 .007 -20.60 .00 .00 .00 .00 .00
7 1 7 -72.31 .00 .00 .00 .00 .008 72.31 .00 .00 .00 .00 .00
8 1 8 -60.08 .00 .00 .00 .00 .009 60.08 .00 .00 .00 .00 .00
9 1 9 -47.85 .00 .00 .00 .00 .0010 47.85 .00 .00 .00 .00 .00
10 1 10 -59.01 .00 .00 .00 .00 .0011 59.01 .00 .00 .00 .00 .00
11 1 11 -82.40 .00 .00 .00 .00 .0012 82.40 .00 .00 .00 .00 .00
12 1 1 -105.79 .00 .00 .00 .00 .0012 105.79 .00 .00 .00 .00 .00
13 1 2 .00 .00 .00 .00 .00 .0012 .00 .00 .00 .00 .00 .00
14 1 3 -12.23 .00 .00 .00 .00 .0012 12.23 .00 .00 .00 .00 .00
-15 1 3 5.47 .00 .00 .00 .00 .00
11 -5.47 .00 .00 .00 .00 .00
STAAD TRUSS -- PAGE NO. 7
MOM-Z
MEMBER END FORCES STRUCTURE TYPE = TRUSS-----------------
ALL UNITS ARE -- KNS METE
MEMBER LOAD JT AXIAL SHEAR-Y SHEAR-Z TORSION MOM-Y
16 1 4 -15.47 .00 .00 .00 .00 .0011 15.47 .00 .00 .00 .00 .00
17 1 4 31. 86 .00 .00 .00 .00 .0010 -31. 86 .00 .00 .00 .00 .00
18 1 4 -29.59 .00 .00 .00 .00 .009 29.59 .00 .00 .00 .00 .00
19 1 5 10.46 .00 .00 .00 .00 .009 -10.46 .00 .00 .00 .00 .00
20 1 5 -23.39 .00 .00 .00 .00 .008 23.39 .00 .00 .00 .00 .00
21 1 6 .00 .00 .00 .00 .00 .008 .00 .00 .00 .00 .00 .00
************** END OF LATESTANALYSIS RESULT **************
58. PRINT JOINT DISPLACEMENTS ALL
STAAD TRUSS -- PAGE NO. 8
JOINT DISPLACEMENT (CM AADIANS) STRUCTURE TYPE = TRUSS------------------
lINT LOAD X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN
1 1 .0000 .0000 .0000 .0000 .0000 .0000
2 1 -.0039 1.1979 .0000 .0000 .0000. .0000
3 1 -.0079 1.6185 .0000 .0000 .0000 .0000
4 1 .0549 1.7939 .0000 .0000 .0000 .0000
5 1 .0568 1.7589 .0000 .0000 .0000 .0000
6 1 .0284 1.3996 .0000 .0000 .0000 .0000
7 1 .0000 .0000 .0000 .0000 .0000 .0000
8 1 .3960 1.3996 .0000 .0000 .0000 .0000
9 1 .2568 1.7444 .0000 .0000 .0000 .0000
10 1 .0201 1.7674 .0000 .0000 .0000 .0000
11 1 -.2077 1.6109 .0000 .0000 .0000 .0000
12 1 -.3016 1.1979 .0000 .0000 .0000 .0000
************** END OF LATEST ANALYSIS RESULT **************
59. PLOT DISPLACEMENT FILE60. STEEL TAKE OFF
STAAD TRUSS -- PAGE NO.
STEEL TAKE-OFF--------------
PROFILE LENGTH (METE) WEIGHT(KNS
ST ISA100X100X6ST ISA45X45X3
ST ISA65X45X5ST ISA50X50X5ST ISASOX50X4ST ISA70X45X5ST ISA75X50X6ST ISA20X20X3ST ISA50X50X3ST ISA65X65X5ST ISA150X150X10
1.775.134.149.272.110.156.203.028.167.448
1.104
19.806.603.697.383.693.693.693.307.389.334.95
----------------
TOTAL = 4.55
************ END OF DATA FROM INTERNAL STORAGE ************
61. FINISH
*************** END OF STAAD-III ***************
**** DATE= JUN 12,1999 TIME= 5:50:50 ****
************************************************************
* FOR QUESTIONS REGARDING THIS VERSION OF PROGRAM PLEASE ** CONTACT: RESEARCH ENGINEERS PVT LTD ** CB-67, SALT LAKE CITY, SECTOR - 1 ** CALCUTTA - 700 064 **PH: (033)321-3047/3486,334-0079/80 FAX: (033)3219913/3376290**Ernail:[email protected]/ [email protected]** NEW DELHI ** --------- *
*E-882, First floor, Chittaranjan Park, New Delhi - 110 019** TEL:(011)6210612 ** MUMBAI ** *------
*3AJ2, Ram Manohar Lohia Nagar, Kurla (W), Mumbai - 400 070** TEL: (022) 5147385; Ernail:[email protected] ** CHENNAI ** ------- *
*No. 5, Ground Floor, 48th Street, 9th Avenue, Ashoke Nagar** Chennai - 600 083; TELEFAX: (044) 489-6097 ********************************~****************************
9
In this project various configurations of trusses for different spans have
been analysed and designed with the help of STAAD III Computer Programme
Software. The results of the various member sections of trusses and the
corresponding cost of that truss are tabulated below..
9.1 FANTRUSS
All section dimensions are in mm
!I 1015 20 25 30
: Memb '
100x100x6 150x150x10 200x200x12 200x200x25 200x200x25!
1245 x 45x 3 65 x 65x 5 90x90x 6 11Ox11Ox8 I 130x130x8
!3 100x100x6 1 150x150x10 200x200x12 200x200x25 200x200x25:
1470 x 45x 6 75 x 50x 6 70x45x 8 75x75x5 75x75x5
!5 65 x 45x 5 70 x45x 5 70x70x 5 : 65x65x5 75x75x5I
is 65 x 45x 5 60 x 40x 6 70x70x 5 65x65x5 75x75x5I
! i 65 x 45x 5 65 x 45x 5 70x70x 5 65x65x5 75x75x5;
'8 65 x 45x 5 65 x 45x 5 70x 70x 5 65x65x5 75x75x5I
19 70 x45x 6 70 x 45x 6 65 x 45x 8 75x75x 5 75x75x5I110 25 x 25x 3 40 x 40x 3 55 x 55x 5 65 x65x 5 75x75x5Ii
I 11 25 x 25x 3 35 )( 35)( 3 45 )( 45)(3 55)(55)(5 65)(65x5I! 12 90x90x 6 130x130x8 200x200x12 200x200x25 200x200x25I
113 90 x 90x 6 130x130x8 200x200x12 200x200x25 200x200x25i114 25 x 25x 3 35 x 35x 3 45x 45x 3 55)( 55)( 5 65)(65)(5j
11525)( 25)( 3 35)(35)( 3 50)(50)(3 65)(65x5 75)(75)(5
Fan Truss ( Cost Table)
Span (m)
10
15
20
25
30
Total Cost (Rs.)
4043.75
11772.00
20950.16
64064.11
78308.00
9.2 PRATT 1 TRUSS
10 15 20 25 30Member
1 50x 50x 4 65 x 65x 5 100 x75x 6 125x 95x 6 1OOx 11 Ox 8
2 50 x50x 4 65 x 65x 5 100 x75x 6 125x95x 6 100x1 OOx8
3 35x 35x 3 50 x 50x 4 65 x 65x 5 75 x 75x 6 90 x 90x 6
4 20x 20x 3 30 x 20x 3 30 x 30x 3 35 x 35x 3 40 x 40x 3
5 25 x 25x 4 40 x 25x 4 40 x 25x 5 40 x 40x 5 40 X 40x 6
6 25 x 25x 4 40 x 25x 4 40 x 25x 5 40 x 40x 5 40 x 40x 6
7 20x 20x 3 30 x 20x 3 30 x 30x 3 35 x 35x 3 40 x 40x 3
8 35x 35x 3 50 x 50x 4 65 x 65x 5 75 x 75x 6 90x90x 6
9 50x 50x 4 65 x 65x 5 100 x 75x 6 125x95x 6 11Ox 11Ox 8
10 50x 50x 4 65 x 65x 5 100 x 75x 6 125 x 95x 6 11Ox 11Ox 8
11 125x75x 6 150 x 75x 8 125 x 95x 12 200x120x10 200x150x10
12 90x 90x 6 125 x 75x 8 90 x 90x 12 125 x 95x 12 130x130x12
13 80x 80x 6 100x75 x 8 80 X 80x 12 100x100x12 200x100x10
14 70x70x 10 75 x 50x 10 125x 75x 8 125x 75x 10 100x100x12
15 70 x 45x 6 100 x 65x 5 125x 95x 6 1OOx 75x 10 125x 75x 10
16 70x 45x 6 1OOx 65x 5 125x 95x 6 100 x 75x10 125x 75x 10
17 70x 70x 6 75 X 50x 10 12_5x75x 6 125x 75x 10 100x100x12
18 80x.80x 6 100 x 75x 8 80 x 80x 12 100x100x12 200x100x10
19 90x 90x 6 125 x 75x 8 90 x 90x12 125x 95x 12 130x130x12
All section dimensions are in mm
Pratt 1 Truss ( Cost Table)
Span (m)
10
15
20
25
30
Total Cost (Rs.)
4512.50
10913.75
21091.42
34065.09
57879.00
10 15 20 25 30Member
20 125x75x 6 150x75x8 125x 95x 12 200x100x10 200x150x10
21 30x 20x 3 35 x 35x 3 45x45x 3 50 X 50x 4 55 x 55x 5
22 30x 20x 3 35x35x 3 45x45x 3 45x45x4 50x50x4
23 45x 45x 3 55 x 55x 5 75x75x5 100x75x 6 1 OOx 1 OOx 6
24 30x 30x 3 45x45x 3 45x45x 4 50x50x5 60x60x5
25 55 x 5x 5 80x80x 6 100x100x 6 130x130x8 130x130x10
28 45)( 3D)( 3 40 x 40x 4 50 x 50x 5 60x60x 5 70x70x 5
21 l 1--' '\1.'K1. I 1.Qx13Qx 8 I 150x150x10 I ZooxZOOx1 Z I
28 45x 45x 3 50 x 50x 4 60 x 60x 5 75x75x5 90x90x6
29 125x95x6 130x130x10 200)(150x12 200x200x12 200x200x25
:\ 45')( 45')( '3 50 x 50x 4 60 X 60x 5 75 x 75x 5 90 x 90x 6
31 75x 75x 5 125 x 95x 6 130x130x 8 150x150x10 200x200x12
32 45x30x3 40 x 40x 4 50 X 50x 5 60x60x 5 70x70x 5
33 55x55x5 80 x 80x 6 100x100x 6 130x130x 8 130x130x10
. 34 30x30x3 45 x 45x 3 45 x 45x 4 50 x 50x 5 60x60x5
35 45x45x3 55 x 55x 3 75 x 75x 5 100x75x 6 100x100x 6
36 30x20x3 35 x 35x 3 45 x 45x 3 45 x 45x 4 50 x 50x 4
37 30x20x3 35 x 35x 3 45 x 45x 3 50 x 50x 4 55 x 55x 5
- -
9.4 HOWE TRUSS
I 10 15 20 25 30Mamba
1 35x 35x 3 50 x 50x 3 60 x 60x 5 75 x 75x 5 90 x 90x 6
2 35x 35x 3 50 x 50x 3 60 x 60x 5 75 x 75x 5 90 x 90x 6
3 30 x30x 3 45 x 45x 3 60 x 60x 5 75 x 75x 5 90 x 90x 6
4 20x 20x 3 30 x 20x 3 30 x 30x 3 35 x 35x 3 40 x 40x 3
5 30x 30x 3 40 x 40x 3 55 x 55x 5 65 x 65x 5 80 x 80x 6
6 20x 20x 3 30 x 20x 3 30 x 30x 3 35 x 35x 5 40 x 40x 3
7 30x 30x 3 45 x 45x 3 60 x 60x 5 75 x 75x 5 90 x 90x 6
8 35x 35x 3 50 x 50x 3 60 x 60x 5 75 x 75x 5 100x100x 6
9 35x 35x 3 50 x 50x 3 60 X 60x 5 75 x 75x 5 75 x 75x 5
10 45x 30x 6 75 x 50x 5 70 x 70x 6 100 x 75x 6 90 x 90x 6
11 45x 30x 6 75 X 50x 5 70 X 70x 6 100 x 65x 6 90 x 90x 6
12 40x 25x 6 55 x 55x 5 75 x 50x 6 90 x 60x 6 100 x 65x 6
13 35x 35x 5 60 x 40x 5 65 x 65x 5 70 x 70x 6 65 x 45x 8
14 . 35x 35x 5 60 x 40x 5 65 x 65x 5 70 x 70x 6 65 x 45x 8
15 40 x 25x 6 55 x 55x 5 75 x 50x 6 90 X 60x 6 100 x 65x 6
16 45x 30x 6 75 x 55x 5 70 x 70x 6 100 x 65x 6 90 x 90x 6
17 45x 30x 6 75 x 55x 5 70 x 70x 6 100 x 75x 6 90 x 90x 6
18 20x 20x 3 20 x 20x 3 20 x 20x 3 20 x 20x 3 20 x 20x 3
19 20x 20x 3 30 X 20x 3 30 X 20x 3 35 x 35x 3 40 x 40x 3
20 55x 55x 5 80 x 80x 6 125 x 95x6 130x130x8 200x150x10
21 30x 20x 3 30 x 30x 3 40 X 40x 3 50 x 50x 3 60 X 60x 6
22 65x 65x 5 100x100x 6 130x130x 8 200x200x10 200x200x12
23 30x 30x 3 40 X 40x 3 55 x 55 x 5 65x65x 5 80 x 80x 6
24 80x 80x 6 130x130x 8 200x150x10 200x200x12 200x200x25
25 80x 80x 6 130x 130x 8 200 150x1 0 200x200x12 200x200x25
26 30x 30x 3 40 x 40x 3 55x55x 5 65x65x 5 80x80x 6
All section dimensions are in mm
Howe Truss ( Cost Table)
9.5 Pratt Truss
10 15 20 25 30Mamba
27 65x 65x 5 100x1OOx6 130x130x 8 200x150x10 100x200x12
28 30x 20x 3 30 x 30x 3 40 x 40x 3 50x50x3 60x60x5
29 55x 55x 5 80 x 80x 6 125x95x 6 130x130x 8 200x150x10
30 20x 20x 3 30 x 20x 3 30 x 30x 3 35 x 35x 3 40 x 40x 3
31 20x 20x 3 20 x 20x 3 20 x 20x 3 20 x 20x 3 20 x 20x 3
Span (m) Total Cost Rs.
10 3280.25
15 8559.25
20 18295.05
25 32078.75
30 61778.05
10 15 20 25 30M9mb9
1 25 x 25x 3 75 x 75x 5 100x100x6 130x130x8 150x150x10
2 25 x 25x 3 75 x 75x 5 100x100x6 130x130x8 150x150x10
3 25 x 25x 3 35 x 35x 3 45x45x3 55x55x5 65 x 65x 5
4 25 x 25x 3 35 x 35x 3 45x45x3 55x55x5 65 x 65x 5
5 50 x 50x 4 75 x 75x 3 100x100x6 130x130x8 150x150x10
6 50 x 50x 4 75 x 75x 3 100x100x6 130x130x8 150x150x10
7 50 x 50x 3 45 x 45 x 5 65 x 45x 5 65 x 65x 5 75 x 75x 6_.8 40 x 25x 4 40 x 40x 3 50 X 50x 5 65 x 65x 5 75 x 75x 5
9 35 x 35x 3 50 x 50x 3 50 x 50x 4 65 x 65x 5 75 x 75x 5
All section dimensions are in mm
Steel Take- off (10 m span)
10 15 20 25 30Mamba
10 40 X 40x 3 45 x 45x 4 50 X 50x 5 65 x 65x 5 75 x 75x 5
11 35 x 35x 5 45 x 45x 6 70 x 45x 5 75 x 75x 5 75 x 75x 6
12 45 x 30x 6 65 x 65x 6 75x50x6 80 x 80x 6 75 x 75x 8
13 20 x 20x 3 20 x 20x 3 20 x 20x 3 20 x 20x 3 20 X 20x 3
14 25 x 25x 3 40 X 40x 3 50 X 50x 3 65 x 65x 5 75 x 75x 5
15 50 x 50x 3 75 x 75x 5 100x100x 6 130x130x 8 150x150x10
16 35 x 35x 3 50 x 50x 3 65 x 65x 5 80 x 80x 6 100x100x6
17 75 x 75x 5 11Ox 11Ox 8 150x150x10 200x200x12 200x200x25
18 35 x 35x 3 50 x 50x 3 65 x 65x 5 80 x 80x 6 100x100x6
19 50 x 50x 3 75 x 75x 5 100x100x 6 130x130x8 150x150x10
20 25 x 25x 3 40 x 40x 3 50 x 50x 3 65 x 65x 5 75 x 75x 5
21 20 x 20x 3 20 x 20x 3 20 x 20x 3 20 x 20x 3 20 x 20x 3
Sections (mm) Length(m) Weight (kn)
ST ISA 25 x 25x 3 10.35 0.112
ST ISA 50 x 50x 4 3.36 0.100
ST ISA 50 x 50x 3 5.21 0.118
ST ISA 40 x 25x 4 1.86 0.085
ST ISA 35 x 35x 3 6.56 0.102
ST ISA 40 x 40x 3 1.86 0.133
ST ISA 35 x 35x 3 1.86 0.047
ST ISA 45 x 30x 6 1.86 0.059
ST ISA 20 x 20x 3 1.66 0.014
ST ISA 75 x 75x 5 2.50 0.140_.
ITotal 0.760
Steel Take-off ( 25 m span )
Sections (mm) length(m)
ST ISA 130x130x 8 24.99
ST ISA 55 x 55x 5 8.33
ST ISA 65 x 65x 5 27.95
ST ISA 75 x 75x 5 4.66
ST ISA 80 x 80x 6
ST ISA 90 x 90x 3
ST ISA 100x100x 3
16.43
4.16
6.25
Total
Weight (kn)
3.881
0.337
1.342
0.260
1.173
0.036
2.238
9.270
Steel Take-off ( 30 m span)
Sections ( mm) length(m)
ST ISA 150x150x10 30.08
ST ISA 65 x 65x 5 10.00
ST ISA 75)( 75)( 6 11.20
ST ISA 75 x 75x 5 27.94
ST ISA 75)( 75)( 8 5.60
ST ISA 20 x 20x 3 5.04
ST ISA 100)(100)(6 14.20
ST ISA 200x200x25 7.50
Total
Weight(kn)
6.708
0.480
0.745
1.561
0.489
0.043
1.273
5.404
16.700
Pratt Truss
Span(m)
10
15
20
25
30
Total ost (Rs)1936.79
5708.46
11595.31
23623.85
42558.61
---
----
....
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TOTAL COST (RS.).... N Co) . c.n 0) ..... <» co0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 00
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0 0 0 0 0 0 0 0UI
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en
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TOTAL COST (RS.).. N to) (J'I 0) ..... CD0 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
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..0
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- N c:0UJUJ
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TOTAL COST (RS.).... N Co) .e. C1I 0)0 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 0
0 0 0 0 0 0 0 0.; C1I
Ii
\ :I:i
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UJI \
-I"V :u):. c:z en- eni:
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wo
TOTAL COST (Rs.)N N w w01 0 01 0 01 0 01 0 01
0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0'0
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10.0 INTERPRETATION OF RESULTS
In this chapter, the analysis of cost data for different types of trusses is
carried out . The cost tables for different types of trusses, for differents spans are
placed and on those results the graphs are plotted for,
. types of trusses vs. cost.
The discussionon the results of these graphs is as follows carried out." , .
10.1 Comparative costs for various configurations of trusses
For 10 m span
Type of truss Total cost (Rs.)
Fan.Truss
Pratt 1 Truss
Compound Fink Truss
Howe Truss
Pratt Truss
4043.75
4512.50
3311.00
3280.25
1936.79
For 15 m Span
Type of truss Total cost (Rs.)
Fan.Truss
Pratt 1 Truss
Compound Fink Truss
Howe Truss
Pratt Truss
11772.00
10913.75
8829.00
8559.25
5708.46
For 20 m Span
Type of tuss Total cost (Rs.)
Fan.Truss
Pratt 1 Truss
Compound Fink Truss
Howe Truss
Pratt Truss
20950.16
21091.42
20306.75
18295.50
11595.31
For Span 25 m
Type of truss Total cost (Rs.)
I Fan.TrussPratt 1 Truss
Compound Fink Truss
Pratt Truss
64064.11
34065.09
35168.75
32078.75
23623.85
I
I Howe TrussI
For Span 30 m
Type of truss Total cost (Rs.)
Fan.Truss
Pratt 1 Truss
. Compound Fink TrussIIHowe Truss
I Pratt Truss
78308.00
51879.00
72103.50
61778.50
42558.61
10.2 Discussion on results
. From the graph of howe truss, it can be seen that total cost of truss
varies almost linearly upto 25m span. The difference between the cost
of 30 m span & 25 m span is almost double.
. In compound fink truss, it can be observed that, this truss configuration
is suitable upto 25 m span. The cost of 30 m span is as high as 2.05
times than that of 25 m span. Secondly, it can be also observed that the
cost of 20m span be comes more than double for 15m span.
The economical span for fan truss is upto 20m because of the fact that
there is a large difference in cost of 25m and 20m span. As depicted in
the graph, there is a steep slope between 20 m & 25 m span.
. Pratt 1 type of truss can be used for spans ranging from 10m to 25 m
span because the cost curve varies smoothly for above span interval.
However, it gives exceptionally high cost for 30 m span
. For the pratt truss the cost comparison with pratt1 truss is very
interesting .The number of members in pratt truss are_less than that of
pratt 1 truss. The cost of pratt 1 truss for 10m span is 230% higher
than the cost of pratt truss. Such kind of trend can also be witnessed
for rest of the spans .
Now the study of graphs, plotted between various configurations of
trusses Vs cost for a particular span gives the following results.
.0 For 10m span pratt 1 type of truss gives the highest cost whereas the
difference between the cost of howe truss and compound fink truss is
almost negligible
. The least cost amongst the trusses studied,is for pratt truss. Its cost is
half than that of fan truss Moreover, pratt 1 truss is 2.32 times costlier
than pratt truss.
. For the span at 15 m fan truss comes out to be the costliest one. Again,
the cost difference between compound fink truss and howe truss is
almost negligible. Even for 15m span also pratt truss is the most
economical solution.
. For 20 m span, a little difference among the cost for trusses accept
pratt truss can be pointed out 36% cost reduction can be obtained by
adopting pratt truss than the rest of the trusses
. A sudden increase in the cost of fan truss can be seen for 25m span.
The costs of pratt 1,compoundfink and howe trusses are comparable.
But again,pratt truss,gives 37% less cost than fan truss. .
. For 30 m span the costs of compound fink truss & howe truss become
doubler than their costs for 25 m span, Fan truss gives the highest cost-
which is as much as 1.85 times higher than for pratt truss. For this case
also pratt truss is the most economical configuration..
0,
TOTAL COST (Rs.)
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0 0 0 0 0 0 0 00
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TOTAL COST (Rs.)
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TOTAL COST (Rs.).... N W . <11 (J) ....0 0 0 0 0 0 00 0 0 0 0 0 0- 0 - 0 0 0 -
0 (5 0 (5 0 0 0 (5
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TOTAL COST (Rs.)..... N W CJ1 <» ..... (XI CD0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
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11.0 CONCLUSION
This project gives the various cost comparison curves to get an idea
about the suitability of various configurationsfor different spans.
All the graphs pinpoint to the most economical configuration- as "
Pratt Truss" for all the spans studied since it gives us the least cost. Fink
and howe truss are useful for span range of 10 to 20m but they are the
second choice after pratt truss because beyond 20m span they become
uneconomical.
One more observation can be carried out from the cost tables that,
pratt truss is more economical than pratt1 truss. So it can be concluded
that, for the same configuration, by keeping span & pitch constant, the cost
increases with increase in number of members
J,
J
SCOPE OF FUTURE WORK
In this project work has been carried out by varying spans &
configurations whereas, spacing between trusses & pitch of truss are kept
constant. A cost comparison can also be made by varying the above stated
constant parameters. Effect of height of truss, (pitch) on cost can also be
checked out.
By varying spacing between trusses,there would be variation in the
quantity of purlins and similarly,number of supporting columns would
vary. Even by selecting channels. and I - sections in place of angle
sections,cost can be comparedfor various configurationwith different spans.
In the present construction practices prestressed concrete trusses are
also used in place of steel trusses. The major advantage they offer,is the
"costeffectiveness" .In appendix, a case study is incorporated which can be
used as a guideliner for further work.
.« F.:EFEF-:ENCES ..---------------------.--.--
(1) " Ramamt'utham s. "~ Design of Steel Structure.
,(2) " Ramchandt'a "* Design of Stael Structure.
,( '! \ At'ya ~_ A ,1amat' i "~ ___ign of Steel Structure.
'(4) " C.k.Wang "* Stability Indaterminate Structures.
(5) II Crawley, Stanley W. & Dillon, Robert M.* Steel Buildings: Analyses and Design.
"
(6' ,II Vazit'ani V.N. ~-<Ratwani M.M. "
* ~teel Structures & Timber Structures: Ana.lysis,Design& Details" Of Structures, Volume-III.
1(7) " National Building Ot'ganisation,New Delhi "* Steel Economy-In Building Construction.
k8)
~9)
II Kuzmanovlc, Bogdan O. & Williems, NIcholas"* Steel Design For Structural Engineers.
" Knowles, Peter R. & Dowling, Petrick J.~ Steel Design Manual.
"
kll) " Hibbelet', Russel C.* Structural Analysis.
"
,~1-1) " Bowels ~... Joseo]-. "
* Structural Steel .Design.
d2) .""
*r-JegI L.S. "Desigr. of Steel Stl'uctut'es.
1-:;) " Char-les E. Reynolds & James C. Steedman "* Reinforced Concrete DesIgner's Handbook.
14) " IS: 800 (1984) "* Indian Standar'd Code Of Pi'actice Fat, Genet'a.l Constt'uction
In Steel.
15> /" IS : 875, Par't:3 (1987) "~ Indian Standard Code Of Practice For Design Loads
( Other' Than Ear'thouaLe )
Fot' Building And StrLlct!':wes F'al"t:::::. ( Wind Loads
- - ---
APPENDIX
Table 5.1 PermissibleStresss ac (MPA) in Axial Compression for Steels
with Various Yield Stresses (Clause 5.5.1 IS : 800 - 1984)
fx 240 250 300 400 420 450 480 540
10 144 150 180 239 251 269 287 323
20 142 148 177 235 246 263 280 314
30 140 145 172 225 236 251 266 295
40 134 139 164 210 218 231 243 267
50 127 132 153 190 197 207 216 233
60 118 122 139 168 173 180 187 199
70 109 112 125 147 150 155 160 168
80 98 101 111 127 129 133 136 141
90 88 90 98 109 111 114 116 119
100 79 80 86 94 96 97 99 101
110 71 72 76 82 83 84 85 87
120 63 64 67 71 72 73 73 75
130 56 57 59 62 63 63 64 65
140 50 51 53 55 55 56 56 57
150 45 45 47 49 49 49 49 50
160 41 41 42 43 43 44 44 44
170 37 37 38 39 39 39 39 39
values of based s eo on Eq. 5.2 are given in Table 5.1 for convenience
corresponding to various values of yield stress fx and slenderness ratio I
Ir.
**********************************************************************
Design a roof truss of span 9.3 m at a spacing of 4 m for an
industrial shed. The height of eaves is 6.5m and it is situated near
Delhi. The roof truss is supported on 40 cm thick brick masonary.
Solution :
Use pratt truss of pitch 30° as shown in Fig.9.13.
Load:
(i) Imposed Loads (Table B-3 and sec. 9.2.2.1)
Imposed load = 0.75 - 20 x 0.02 = 0.35 kN/m 2
180 33 33 34 35 35 35 35 35
190 30 30 31 31 32 32 32 32
200 28 28 28 28 28 28 28 28
210 25 25 26 26 26 26 26 26
220 23 23 23 24 24 24 24 24
230 21 21 22 22 22 22 22 22
240 20 20 20 20 20 20 20 20
250 18 18 18 19 19 19 19 19
Take minimum load 0.4 kN/rtI 2 ( horizontal) for purlin and ( 2/3) x 0.4 N
=0.267 kN/m (horizontal) for trusses.
(ii) Wind Loads
For Delhi, basic wind speed, Vb = 47 m/sec.
Taking risk factor. k1=1.0
height and size factor. k2=0.88
and ,topography factor, 1<:3=1.0
Design wind speed., Vz=Vt> xk1c k2x k3 = 47x 1.0 x 0.88
x 1.0
= 41.36 m/ec
Design wind pressure, pz = 0.6x v/ = 1026.4 N/m
From Table 8 -7 and 8-9, wind load is evaluated assuming normal
premiability as follow.
1/2 < hlw = 650/930 < 3/2
Wind normal to ridge Total Pressure = ( Cpe- Cpi) Pz
Cpi =+ 0.2 Cpi = - 0.2
Windward = Cpe = -0.2 -410.6 N/m
- 718.5 N/m2
o
-308 N/m2Leeward Cpe= -0.5
Wind parallel to rigde on both I - 1026.4 N/m -616 N/m
slopes Cpe = -0.8
Maximum wind load = - 1026.4N/m2 uplifton boths slopes.
Design of Purlins
Spacing of purlins = 1.79 m
Weight of 20 gauge CGI sheets = 112.7 n/m2
Loads on purlins per meter length :
(i) Weight of sheeting = 112.7x 1.79 = 201.7 N/m
(ii) Weight of purlin (assuming) = 100 N/m
Total dead load = 301.7 N/m
Imposed load = 400 x1.79 cos 30° = 620 N/m
\f\Jind load = -1026.4 x 1.79 =-1837.3 N/m (uplift)
Dead + imposed load = 301.7 +620 = 921.7 N/m
Dead + Wind load = 301.7 -1837.3 = -1535.6 N/m
Since increase in permissible stresses is 33.33% when wind load
is considered. dead + wind load may be considered 33.33% less
effective.
1535.6/1.33 = 1154.6 N/m > 921.7 N/m
Therefore, the combination of dead and wind loads is critical.
Maximum bending moment = 1154.6 x 42 110 = 1847.3N.m
= 1847.3 x10 N3mm
For an angle purlin, Z required = 1847.3 x103/165 = 11.2 x 103 mm3
Minimum depth = L 145 = 4000 145 = 88.88mm
Minimum width = U60 =4000/60= 66.66 mm
Provide ISA 90 x 90,6 mm @ 8.2 kgf/m having Zx = 12.2 cm3 .
Design of roof truss
(1) Dead loads (assumed to be acting on top panel points):
CGI sheets = 112.7 x 4x 9.3/ cas 30° = 4841 N
Purlins= 82 x4x 8 = 2624 N
Trusses (assume @ 100 N/m horizontaly)
= 100x 4 x9.3 = 3720 N
Total dead load = 11185N
Dead load on at end each top panel = 1118516= 1864 N
Dead load at end panel points = 1864/2= 932 N
(2) Imposed load for trusses on top panel points = 267 x4 x9.3
= 9932 N
Imposed load per panel = 9932/6 =1655 N
(3) Wind load on each of the top panel
uplift = -1026.4 x1.79x 4=-7349N=7.35kN
Downward= 0
The force diagrams for truss under dead load and negative wind
load have been shown in Figs. 9.14 and 9.15 . Forces due to imposed
load are calculated by multlyplying
forces due to dead load by 1655/1864
Wrost load combinations are worked out in Table 9.1 for one half
of the due to symmetry.
Rafter, La U3 and Ls U3
Design load =17.4 x 10 N3( compression)
= 20.9 x10 N3(tension)
Main Sling U3Lz +3.2 +2.8 -14.8 +6.0 -8.7 -8.7
+6.0
Table 9.1 (Compression -ve, tension + ve)
Member Force (KN) due to Load Combination Design
Dead Imposed Wind (i + ii) (i + iii) Load
Load Load Load +1.33* ( Kn)
(i) (ii) (iii)
Principal LaU1 -9.2 -8.2 +32.6 -17.4 +17.6
Rafter U1U2 -9.2 -8.2 +37.0 -17.4 +20.9 -17.4
U2U3 -7.4 -6.6 32.3 -14.0 +18.7 +20.9
Main Tie LaL1 +7.9 +7.0 -26.6 +14.9 -14.0 -14.0
L1 L2 +6.3 +5.6 -19.1 +11.9 -9.6 +14.9
L2L3 +4.8 +4.3 -11.5 +9.1 -3.2
Since permissible stresses are increased due to wind by 33.3%
Using a minimum double angle section angle section 1 -ISA50 x
50, 6 mm thick connected on both sides of 8 mm gusset plate by 16
mm dia rivets as shown in Fig. 9.16.
A gross = 2 x5.68 = 11.36 cm2
a net = 11.36 -2x 1.75 x 0.6 = 9.26 cm2
rx = 1.51 cm
ry = Iy 1A = [2x 12.9 + 2 x5.68 ( 1.45+0.4 )2/2 x 5.68 ) 112
= 2.38 cm
Effective length about y -y axis, assuming purlins provide lateral restrain
Iy = 179 cm
Effective length about x-x-axis.
Ix = 0.7 x 179 = 125.3 cm
(since rafter is continuous over panel points)
.--'-,....,...
. .
Main Strut U2 L2 -2.8 -2.5 -12.7 -5.3 +7.4 -5.3
+7.4
Minor Sling U2 +2.46 +2.2 -14.4 +4.66 -6.7 -6.7
L1 +4.6
Minor Strut U1 -1.86 -1.65 +8.5 -3.51 +5.0 -3.5
21 +5.0
1
I x= I xl r x = 125.2 /1.51 = 82.98
Iy= 1x/rx=179/2.38=75.2
For! :(= 82.98, Sac= 97.7 Mpa ( Table 5.1)
Actual compressive stress,
Sac.cal= 17.4 x 103/11.36x 102 = 15.3 Mpa 97.7 Mpa
\I\fhich is safe.
Actual tensile stress,
Sac.cal= 20.9 x103 /9.26 x102 = 22.6 Mpa 150 Mpa
V"hich safe
Main tie, LaLs
Design load = 14.9 kN (tension)
= 14.0 kN ( compression)
Try 2-ISA 50 x 50,6 mm( A, rx , ryas earlier).
Ix= 0.75x 155 = 108.5 cm
Iy= 2 x155 = 310 cm (assuming bottom chords of trusses are
connected by bracing at nodes Lz and L3)
I x= 108.5/1.51 =71.85
I y = 310/2.38= 130.25
~ "",;_.. -",.-. . ...-'
.
. ' ,.
.. " ..ro" "";.:,;. -- .- '-. . -.<.~
For ! :~= 130.25 , Sac= 56.85 Mpa ( Table 5.1)
Actual compressive stress = 14.0 x 103/11.36 x 102 =12.3 Mpa 56.85
Mpa
\/Vhich is safe
Main sling, U3 L2, U3 L3
Design load = 6kN (tension)
= 8.7 kN ( compression)
Try a single 2-18A 50 x 50,6 mm thick connected by 16 mm dia rivets
Effective length 1= O.85x 3.1 = 2.635 cm
r = 1.51 cm
1= 2.635x 100/1.51 =174.5
Corresponding Sac= 32.2 Mpa
Sac.cal= 8.7 x 103/5.86 x 102 =15.3 Mpa 35.2 Mpa
\iVhich is safe.
For tension, area of connected leg,
A1 = ( 50 - 6/2 ) 6 - 6x 17.5 = 177 mm2
Area of outstandng leg,
A2 = ( 50 -6/2 ) 6 =282 mm 2
K = 3A1/3A1 + A2 = 3 x 177 /3x 177 + 282 = 0.65
Net effective area
Actual tensile stress = 177 + 0.65x 282 = 360.3 mm 2
Sac.cal = 6 x 103/360.3 =16.65 Mpa 150 Mpa
Which is safe
Since other members are not severally loaded, a single ISA 50 x
50,6 mm will be sufficient for main strut, minor sling and minor strut.
Design of joints
Using 16 mm dia pds rivets, strength of rivets,
in single shear = 100/1000 x p /4 x (17.5) 2 = 24 kN
in double shera = 2 x 24 = 48 kN
in bearing 6 mm leg = 300 /1000 x6 x 17.5 = 31.5 KN
in bearing a mm gusset = 300 /1000 x ax 17.5 = 42 KN
Only one rivets is required to connect each member with a mm
gusset plate. However a minimum 2 to 3 rivets are provided as given in
Table 9.2.
Table 9.2
Member Design Load Section provided Rivet Number
(kN) value (kN) of rivets
Rafter -17.4 2 ISA 50x 50x 6 42 2or3
+20.9
Main tie + 14.9 2 ISA 50x 50x 6 42 2or3
-14.0
Design of bearing plate
End reaction due to dead + imposed load = 11185 + 9932 12
= 10558.5 N
End reaction due to dead +wind load = 5.58-19.1
= -13.52 kN
Assumuming permissible bearing pressure on masonry
= 0.8 NI mm2
Bearing area required = 10558.5/0.8= 13198mm2
Provide 158 x 200 mm bearing plate
Intensity of pressure under bearing plate = 10558.5/158x 200
= 0.334 Mpa
Bending moment at critical section x -x ( Fig 9.18)
= 69 x200x 0.334x 69/2 = 159 x 10 N mm 2
Main Sling +6 ISA 50x 50x 6 24 2
-8.7
Main strut -5.3 ISA 50x 50x 6 24 2
+7.4
Main sling -6.7 ISA 50x 50x 6 24 2
+4.6
Minor strut -3.51 2 ISA 50x 50x 6 24 2
+5.0
Sectional modulus of plate = 200 x (216
premissible bending stress in bearing plate = 185 Mpa
= 185 x 200 (216 = 159 x 10316
t = 5 mm
Provide 6 mm thick bearing plate 2 -20 mm dia anchor bolts sufficient to
resist uplift force. The length of anchor bolt d should be such that the
weight of mansory is more than the uplift force.
Assuring the line of rupture in the masonary to be at 45° and
specific
weight of masonry is 20 kN I m3.
weight of masonry = (0.158 + d) dx O.4x 20 = 13.52 kN (Uplift force)
or d = 1.38 m ( say 1.4 m)
The base angles are provided with 22 mm wide x 28 mm long slotes to
permit expansion of truss due to temperature stresses.
Table b -1 Unit weight of materials.
Materials Weight kNI Materials Weight kN Im
m3
Steel 77 Brick masonry 20
Aluminium 28 Stone masonry 25
Timber 5-6 Plain Concrete 23
Table 8.3 Imposed loads on roofs
Type of roof UDL per m2 of area in Minimum load
plan kNI m2
Flat , sloping or curved
roof with slopes upto
10 degrees
(i) Access provided 1.50 3.75 kN uniformly
distributed over any
span of 1 m width of
roof slab and 9 kN
uniformly distributed
over the span of any
beam or truss or wall
(ii) access not 0.75 Half of above load
provided Sloping roofs For roofing and purlins Subjected to a
Earth 16-18 Reinforced Concerete 25
Sand 17-20 Abestos cement 120-155 N/m2i
Sand Stone 22-24 sheet 85 N 1m2
Marble 27 Glsheets( 1 mm
thick)
-
with slopes > 10 0.75 kNI m2 less one minimum of 0.4 kN/m2
degrees degree over 10
degrees. Subjected to a
Curved roof with slope (0.75 - 0.52 g2) where. minimum of 0.4 kN/m2
of line obtained by g = h/l
joining springing point
to the crown with the
horizontal , greater than
10 degrees.
WIND LOAD FACTORS
Table 8.4 Wind Force coefficient Cf for single frames.
Solidarity sections ratio , f Cf for Flat sided members
0.1 1.9 'I
0.2 1.8
0.3 1.7
0.4 1.7
0.5 1.6
0.75 1.6
1.00 2.0