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Chapter 7
Design of Roof Truss
Content Outline:
7.1 Introduction
7.2 Properties of Trusses
7.3 Types of Trusses
7.3.1 Type-I Trusses
7.3.2 Type-II Trusses
7.3.3 Terms Related with Trusses
7.4 Loads on Truss Rooves
7.4.1 Dead Loads
7.4.2 Live Load
7.4.3 Wind Load
7.5 Selection of Members of Roof Trusses
7.6 Panel Loads
7.7 Table of Forces
7.8 Purlin Design
7.8.1 General Notes
7.8.2 Procedure for Purlin Design
7.8.3 Design of Sag Rod
7.9 Design of Corrugated Sheet
7.10 Bracing for Trusses
Objectives:
Upon completion of this chapter, the graduate students will be able to:
1. Familiarize readers with the concept of roof trusses and their importance in
structural design.
2. Highlight the role of roof trusses in providing support and stability to roofs in
various buildings.
3. Explain the fundamental properties of trusses, including their components and
behavior under different loads.
4. Introduce the concept of truss analysis and its significance in designing roof
trusses.
5. Describe the characteristics and applications of Type-I trusses, which could be
one of the common truss configurations.
6. Explain the features and uses of Type-II trusses, possibly a different truss
configuration than Type-I.
7. Define and elaborate on important terminology associated with truss design
and analysis.
8. Detail the dead loads that act on roof trusses, including the permanent weight
of the structure and materials.
9. Explain the live loads, which are variable loads on the roof truss due to
occupants, furniture, and other temporary factors.
10. Discuss the wind loads on roof trusses and their effects on the overall stability
of the structure.
11. Guide readers through the process of selecting appropriate members (top
chords, bottom chords, web members, connectors) for roof trusses based on
design requirements and load considerations.
12. Explore the concept of panel loads, which are loads transferred from the roofing
material to the truss members.
13. Provide a tabulated summary of forces acting on different truss members,
aiding designers in the structural analysis process.
14. Discuss general considerations and guidelines for purlin design in roof truss
systems.
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15. Outline a step-by-step procedure for designing purlins, which support the roof
covering and transfer loads to the truss.
16. Explain the design process for sag rods used in roof trusses to prevent
excessive deflection.
17. Guide readers on the design considerations for corrugated roofing sheets,
ensuring their compatibility with the truss system.
18. Describe the importance of bracing in roof trusses to enhance their stability and
resist lateral loads.
7.1 Introduction
- The first step in a roof truss design is to estimate various loads, which may act on
the roof. These loads included dead load, live load, rain load and wind load.
Magnitudes of all these loads may be selected depending on the guidelines given
in various references. The type of trusses is selected based on magnitude of
loads, locality, type of building and aesthetics. Some of the commonly used truss
along with their properties and range of span are given in section to follow.
- The uniformly distributed loads with respect to the horizontal or plan dimensions
are first converted into panel concentrated occurrence in various situations and
the associated factors of safety. Load analysis are carried out separately for
gravity and wind loads considering their unit magnitudes acting at the panel points
of the truss. The unit load forces and the already calculated panel loads are used
to evaluate the member forces for each combination and a table of forces is
prepared. Maximum values are chosen out of this table and the members are
designed for the result tension, compression or reversal of forces case.
- Connection design is then carried out for the same member forces according to
the detailed procedure given in the next chapter.
- The structural behavior resembles simultaneously to that of a beam and a column.
- Majority of the steel building frames have columns that carry sizable bending
moments in addition to the usual compressive loads.
- Some other members directly related with the roof truss are designed after the
design of the truss such as the purlin and the roof sheet. The definition, functions
and methods of construction of purlins, which are special type of beams, are given
later. Sag rods significantly affect the design of purlins and their types and
functions are also presented. Various types of roofing materials and detailed
properties for design of Galvanized Iron (GI) Corrugated Sheets may also be seen
in handbooks.
- Following is the comparison between rigid frames and trusses:
1. Joints are considered as having frictionless pins in trusses with no moment at
the member ends. In case of rigid frames, the members are rigidly connected
having appreciable moments at the member ends.
2. The forces in case of trusses are only axial and hence the members are equally
stressed throughout their cross-section. In rigid frames, due to the bending
moment, the fibers of the cross-section away from the neutral axis have
minimum stresses and the fibers close to the neutral axis have less stress.
3. Because of the above facts, the design of a member in a case of a truss is
economical as compared with the members of a rigid frame. Hence, trusses
become economical in those cases whereas the corresponding construction
cost is less as a percentage of the total cost.
7.2 Properties of Trusses
- Truss is a frame structure in which all the members have axial forces due to the
following facts:
1. Members are arranged in triangles for stability.
2. All the joints of a truss are actually semi-rigid or fully rigid. However,
theoretically, these joints may be considered as pin joints. The analysis as a
pin-jointed frame is valid provided that the requirements given in No. 3 and 4
are satisfied.
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3. Centroidal axes of all the members meeting at a joint must intersect at a single
point.
4. The loads are only applied at the panel points.
- Following is the comparison between rigid frames and trusses:
1. Joints are considered as having frictionless pins in trusses with no moment at
the member ends. In case of rigid frames, the members are rigidly connected
having appreciable moments at the member ends.
2. The forces in case of trusses are only axial and hence the members are equally
stressed throughout their cross-section. In rigid frames, due to bending
moment, the fibers of the cross-section away from the neutral axis have
maximum stresses and the fibers close to the neutral axis have less stress.
3. Because of the above facts, the design of a member in a case of a truss is
economical as compared with the members of a rigid frame. Hence, trusses
become economical in those cases where the corresponding construction cost
is less as a percentage of the total cost.
7.3 Types of Trusses
- Trusses can broadly be divided into two categories, Type -I trusses are preferred
in those areas where snowfall is common and Type-II trusses used in cot climates
(Figure 7.1).
- The roofs of Type-I trusses are inclined at greater angles (10 to 60°) to drain part
of the snow falling on the roof surface. These may also be preferred if bending
moments are larger near the mid-span and zero at the ends.
- The roofs of Type-ll trusses are either nearly flat or are inclined at angles less
than 10°.
- If the forces in the diagonal members are all compressive and that in the vertical
members are all tensile, the truss is called Howe Truss.
- In a reverse way if the forces in all the diagonal members are tensile while the
forces in all the vertical members are compressive, the truss is called Pratt Truss.
- The difference between these two trusses is only the orientation of the diagonals
in relation to the applied loads.
- In case of Warren Truss, the diagonals alternate in orientation and also in the
sense of forces in them.
- For all the roof trusses, the loads are in general applied on the top chord.
7.3.1 Type-I Trusses
 Some typical Type-I trusses are shown in Figure 7.I.
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Problem Set:
Final Problem Set No. 2 (FPS-02)
1. Design all truss members and welded connections for the truss chosen
corresponding to the value of R from the trusses shown below. Also design the
corrugated sheet, purlins, sag rods and anchor bolts. Make a drawing showing
all the design results.
= 0.17
&
Self-weight of purlins = 0.12
&
Dead load of roofing
Insulation
Live load
a) % ≤ 770; = 2.5 +
% = 680 meters
= 0.05
= 0.59
•f®
-
&
&
(m); " = 10 +
•f®
-
(m)
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b) 770 < % ≤ 840;
% = 800 meters
= 2.5 +
•f¹¹
(m); " = 15 +
•f¹¹
(m)
c) 840 < % ≤ 910;
% = 888 meters
= 2.5 +
•f΃
(m); " = 20 +
•f΃
(m)
d) % > 910; = 3.0 +
% = 1000 meters
-
•fÄ
-
-
(m); " = 10 +
•fÄ
-
-
-
(m)
2. Design all truss members and welded connections for the truss chosen
corresponding to the value of R from the trusses shown below. Also design the
corrugated sheet, purlins, sag rods and anchor bolts. Make a drawing showing
all the design results.
= 0.17
&
Self-weight of purlins = 0.12
&
Dead load of roofing
Insulation
= 0.59
Live load
a) % ≤ 770;
= 0.05
= 2.5 +
•f®
-
&
&
(m); " = 10 +
•f®
-
(m)
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% = 680 meters
b) 770 < % ≤ 840;
% = 800 meters
= 2.5 +
•f¹¹
(m); " = 15 +
•f¹¹
(m)
c) 840 < % ≤ 910;
% = 888 meters
= 2.5 +
•f΃
(m); " = 20 +
•f΃
(m)
d) % > 910; = 3.0 +
% = 1000 meters
•fÄ
-
-
-
(m); " = 10 +
•fÄ
-
-
-
(m)
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3. Select a suitable section of purlin for the trusses, which are on 3.75 m centers.
Provide and design sag rods, if required, The roofing load is 28
& and live
load is 115
& . Angle of roof is 30 and the truss has a span length of 24 m
divided into 8 panels at the top.
4. Design G.I. corrugated sheet using ASD method for truss roof with trusses at
4.5 m on centers. Horizontal panel length is 2.25 m and the truss top chord angle
is 30 .
References:
1. Steel Design, 6th Edition, by William T. Segui, 2018
2. Structural Steel Design, 3rd Edition, by Abi Aghayere, Jason Vigil, 2020
3. Steel Structures Design and Behavior, 5th Edition, Charles G. Salmon, John E.
Johnson, Faris A. Malhas, 2009
4. Unified Design Steel Structures, 3rd Editon, by Louis F. Geeschwindner, Judy Liu
Charles J. Carter, 2017
5. Structural Steel Design, 5th Edition by Jack C. McCormac, Stephen F. Csernak,
Manojkumar V. Chitawadagi, 2012
6. Steel Structures, 4th Edition, by Zahid Amad Siddiqi, 2017
7. Structural Steel Design and its Applications, 1st Edition, by Ahmed Mohamed
Sayed Elngaoy, 2020
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Chapter 8
Connections
Content Outline:
8.1 Introduction
8.2 Types of Connections
8.2.1 Based on Means of Connection
8.2.2 Based on Forces to be Transferred
8.2.3 Types of Joints on Placement of Parts to be Joined
8.2.3.1 Butt Joints
8.2.3.2 Lap Joints
8.2.3.3 Tee Joints
8.2.3.4 Corner Joints
8.2.3.5 Edge Joints
8.3 Truss Connections
8.4 Building / Frame / Beam Connections
8.4.1 Moment Connections
8.4.1.1 Fully Restrained (FR)
8.4.1.2 Semi-Rigid / Partially Restrained (PR) / PR Connections
8.4.2 Simple / Shear / Flexible Connections
8.5 Splices
8.6 Brackets
8.7 Bearing Joints of Compression Members
8.8 Application of Bolted and Welded Connections
8.9 Welding
8.9.1 General Types of Welding
8.9.1.1 Gas Welding
8.9.1.2 Electric Arc Welding
8.9.2 Advantages of Welding
8.9.3 Types of Welds Depending Upon Weld Shape
8.9.3.1 Groove Welds
8.9.3.2 Fillet Welds
8.9.3.3 Slot and Plug Welds
8.9.4 Other Welding Symbols
8.9.5 Standard Welding Symbol
8.9.6 Intermittent Welds
8.9.7 Minimum Weld Size for Fillet Welds
8.9.8 Minimum Weld Size for Groove Welds
8.9.9 Maximum Fillet Weld Size
8.9.10 Practical Weld Size
8.9.11 End Return s or Boxing
8.9.12 Minimum Length of Fillet Weld
8.9.13 Recommend ed Maximum Weld Length
8.9.14 Strength of Weld
8.10 Stresses in Fillet Welds
8.10.1 Effective Throat of Fillet Welds
8.10.2 Adopted or Selected Weld Size ˆ¤
8.10.3 Selected Weld Length
8.11 Strength of Weld Material
8.12 Matching Weld Metal
8.13 Gusset Plate Thickness and Dimensions
8.14 Required Length of Weld
8.15 Procedure for Design of Welded Truss Connections
8.16 Riveted and Bolted Truss Connections
8.17 Type of Stresses in Fasteners
8.17.1 Bearing and Tearout Stresses
8.17.2 Shear Stresses
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8.18 Bearing Type Connections
8.19 Effective Bearing Area
8.20 Rivet and Bolt Value
8.20.1 Rivet Value in Case of Lap Joint
8.20.2 Rivet Value in Case of Half Butt Joint
8.21 Required Clearances
8.21.1 Minimum Edge Distance
8.21.2 Minimum Spacing of Fasteners
8.21.3 Maximum Edge Distance and Spacing
8.22 Placement of Welds and Fasteners
8.23 Minimum Strength of Connections
8.24 Diameter of Fastener
8.25 Anchor Bolts and Embedment (AISC LRFD J9)
8.26 Advantages of Bolts Over Rivets
8.27 Procedure for Design of Riveted Truss Connections
8.28 Design of Loaded Truss Joints
8.29 Design of Simple / Shear Connection
8.29.1 Procedure for Design of Riveted Simple Connections
8.29.2 Design of Welded Simple Connections
8.29.2.1 Types of Welds
8.29.2.2 Procedure
8.30 Moment Connections
8.30.1 Rigid Frame Knees
8.30.2 Strength of Connecting Elements in Compression
8.30.3 Shear Transfer in Square Knees
8.30.4 Intersection of a Column and a Beam
8.30.5 Diagonal Stiffeners
8.31 Bolts Subjected to Eccentric Shear
8.32 Welded Brackets
8.33 Crane Loading
8.34 Design for Structural Integrity
Objectives:
Upon completion of this chapter, the graduate students will be able to:
1. Provide an overview of the importance of connections in structural design.
2. Explain the role of connections in transferring forces and ensuring stability and
safety in buildings and structures.
3. Introduce different methods of connecting structural elements, such as welding,
bolting, and riveting.
4. Classify connections based on the types of forces they need to withstand,
including tension, compression, and shear.
5. Describe specific joint configurations used in connecting structural members,
such as butt joints, lap joints, tee joints, corner joints, and edge joints.
6. Explain the various types of connections used in truss structures and their
significance in supporting loads and maintaining stability.
7. Detail the design considerations for moment connections and simple
connections in building frames and beams.
8. Discuss the use of splices to connect and extend structural members in cases
where longer lengths are required.
9. Explain the role of brackets in providing additional support and stability to
structural connections.
10. Describe the design of bearing joints for compression members to ensure
proper load transfer and structural integrity.
11. Explore the practical application of bolted and welded connections in various
structural scenarios.
12. Introduce different welding techniques commonly used in structural
connections, such as gas welding and electric arc welding.
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13. Highlight the benefits of using welding in structural connections.
14. Explain different types of welds, including groove welds, fillet welds, slot welds,
and plug welds, along with their applications and symbols.
15. Discuss the stresses involved in fillet welds and the design considerations for
their proper sizing.
16. Explain the factors affecting the strength of weld material and its relevance to
connection design.
17. Discuss the importance of using compatible weld metals to ensure the integrity
of welded connections.
18. Provide guidelines for determining the dimensions and thickness of gusset
plates in truss connections.
19. Outline the step-by-step procedure for designing welded truss connections.
20. Explain the design considerations for riveted and bolted truss connections.
21. Describe the different types of stresses that fasteners experience in
connections.
22. Discuss the design of bearing-type connections to ensure proper load transfer.
23. Explain the concept of effective bearing area in connection design.
24. Provide guidelines for determining the values of rivets and bolts in connection
design.
25. Specify the required clearances for fasteners in connections.
26. Provide recommendations for the proper placement of welds and fasteners in
connections.
27. Discuss the minimum strength requirements for structural connections.
28. Explain the considerations for selecting the appropriate diameter of fasteners
in connection design.
29. Describe the design considerations for anchor bolts and their embedment in
concrete.
30. Highlight the advantages of using bolts over rivets in certain connection
scenarios.
31. Outline the step-by-step procedure for designing riveted truss connections.
32. Explain the design considerations for truss joints subjected to various loading
conditions.
33. Provide guidelines for designing simple and shear connections in both riveted
and welded scenarios.
34. Discuss the design of moment connections, including various components and
considerations.
35. Explain the design considerations for bolts subjected to eccentric shear.
36. Discuss the design of welded brackets in structural connections.
37. Explain the design considerations for connections subjected to crane loading.
38. Emphasize the importance of designing connections to ensure overall
structural integrity.
8.1 Introduction
- Connections are the devices used to join elements of a structure together at a
point such that forces can be transferred between them safely. Connection design
is more critical than the design of members because a failure of connection
usually means collapse of a greater part or whole of the structure. In general,
relatively more factor of safety is provided in the design of connections. The rigid
connection should provide sufficient strength and ductility. The ductility is very
useful for redistribution of stresses and dissipation of extra energy in case of
earthquakes, etc. according to AISC J1.1, where the gravity axes of intersecting
axially loaded members do not intersect at one point, the effects of eccentricity
must be considered. The types of connections depending on means of connecting
and type of forces to be transferred are explained in the following paragraphs.
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8.2 Types of Connections
8.2.1 Based on Means of Connection
 Welded connections
 Riveted connections
 Bolted connections
8.2.2 Based on Forces to Be Transferred
 The forces to be transferred affect the behavior and use of a particular type
of connection. Following are the common types, the details of which are
provided in the coming paragraph:
A. Truss connections
B. Moment connection
B.1 Fully restrained (FR)
B.2 Semi-rigid connections or partially restrained (PR)
C. Simple / shear connection
D. Splices
E. Brackets
F. Bearings
8.2.3 Types of Joints Based on Placement of Parts to Be Joined
 The types of joints depend on factors such as the size and shape of the
members coming into the joint, the type of loading, the amount of joint area
available for welding, and the relative costs for various types of welds.
8.2.3.1 Butt Joints
o The butt joint is used mainly to join the ends of flat plates of the
same or nearly the same thickness. A gab or groove is left between
abutting members, which is later on filled with weld (Figure 8.1). The
principal advantage of this type of joint is to eliminate the eccentricity
developed in a single lap joint.
8.2.3.2 Lap Joints
o The members are either overlapped with each other or with some
connecting plates like gusset plates, splices plates, etc., as shown
in Figure 8.2. Eccentricity of load and hence moment may be
produced in these joints. In welded lap joints, the minimum amount
of lap is to be five times the thickness of the thinner part joined, but
not less than 25 mm.
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o Advantages
a. The plates of different thickness can easily be joined such as in a
truss connection (Figures 8.3 and 8.4).
b. Ease of Filling: Pieces being joined do not require the preciseness
in fabrication, as do the other types of joints. The pieces can be
slightly shifted to accommodate minor errors in fabrication or to
make adjustments in length.
c. Ease of Joining: The edges of the pieces being joined do not need
special preparation and are usually sheared or flame cut.
Occasionally the pieces are positioned by a small number of
erection bolts, which may be either left in place or removed after
the welding is completed.
8.2.3.3 Tee Joints
o In a tee joint, one member meets the other member at right angles
as shown in Figure 8.5.
8.2.3.4 Corner Joints
o A typical example of corner joint is shown in Figure 8.6.
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Problem Set:
Final Problem Set No. 2 (FPS-02)
1. Design a welded square knee connection to join a W610x125 section beam to a
W 360x134 section column. The factored moment to be carried through the joint
is 570 kN-m. Shear at the end of beam is 300 kN while the axial force is 80 kN.
Use A36 steel and E70 electrodes with SMAW.
2. Design a riveted truss connection for 2Ls 76x51x7.9 section member to 10 mm
thick gusset plate. The member is 2.5 m long and carries a factored compressive
force of 150 kN. Show complete design on a neat sketch.
3. Design the welded bracket shown in the Figure. The bracket plate is 10mm thick
and the flange of the W-section column is 12 mm thick.
4. Find the required diameter of the rivets for the following eccentricity loaded
connection.
5. Find the required rivet diameter for the shown bracket.
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6. Find the required rivet diameter.
References:
1. Steel Design, 6th Edition, by William T. Segui, 2018
2. Structural Steel Design, 3rd Edition, by Abi Aghayere, Jason Vigil, 2020
3. Steel Structures Design and Behavior, 5th Edition, Charles G. Salmon, John E.
Johnson, Faris A. Malhas, 2009
4. Unified Design Steel Structures, 3rd Editon, by Louis F. Geeschwindner, Judy Liu
Charles J. Carter, 2017
5. Structural Steel Design, 5th Edition by Jack C. McCormac, Stephen F. Csernak,
Manojkumar V. Chitawadagi, 2012
6. Steel Structures, 4th Edition, by Zahid Amad Siddiqi, 2017
7. Structural Steel Design and its Applications, 1st Edition, by Ahmed Mohamed
Sayed Elngaoy, 2020