CIVL 3121 Trusses - Introduction 1/8
Analysis of Truss Structures Analysis of Truss Structures
We will discuss the determinacy, stability, and
analysis of three forms of statically determinate
trusses: simple, compound, and complex.
Analysis of Truss Structures Analysis of Truss Structures
Analysis of Truss Structures Analysis of Truss Structures
CIVL 3121 Trusses - Introduction 2/8
Analysis of Truss Structures Analysis of Truss Structures
Examples of gusset plates.
Definition of a Truss
A truss is a structure composed of slender
members joined together at their end points.
Planar trusses lie in a single plane.
Typically, the joint connections are formed by
bolting or welding the end members together to a
common plate, called a gusset plate.
Analysis of Truss Structures Analysis of Truss Structures
Common Types of Trusses Common Roof Trusses
Roof trusses - in general, the roof load is transmitted to the truss
by a series of purlins. The roof truss along with its supporting
columns is termed a bent. The space between bents is called a
bay.
Analysis of Truss Structures Analysis of Truss Structures
Common Roof Trusses Common Types of Trusses
Pratt Truss – This truss was patented in 1844 by two Boston
railway engineers; Caleb Pratt and his son Thomas Willis Pratt.
The design uses vertical beams for compression and horizontal
beams to respond to tension.
What is remarkable about this style is that it remained popular
even as wood gave way to iron, and even still as iron gave way
to steel.
CIVL 3121 Trusses - Introduction 3/8
Analysis of Truss Structures Analysis of Truss Structures
Common Types of Trusses Common Types of Trusses
Howe Truss -The relatively rare Howe truss, patented in 1840 Warren Truss -The Warren truss was patented in 1848 by its
by Massachusetts millwright William Howe. designers James Warren and Willoughby Theobald Monzani.
It includes vertical members and diagonals that slope up towards This truss and consists of longitudinal members joined only by
the center, the opposite of the Pratt truss. angled cross-members, forming alternately inverted equilateral
In contrast to the Pratt Truss, the diagonal web members are in triangle-shaped spaces along its length, ensuring that no
compression and the vertical web members are in tension. individual strut, beam, or tie is subject to bending or torsional
straining forces, but only to tension or compression.
Analysis of Truss Structures Analysis of Truss Structures
Common Types of Trusses Common Bridge Truss
Bridge trusses - the load is transmitted by the deck to
a series of stringers and then to a set of floor beams.
The floor beams are supported by two parallel trusses.
The supporting trusses are connected top and bottom
by lateral bracing.
Additional stability may be provided by portal and sway
bracing
Analysis of Truss Structures Analysis of Truss Structures
Common Bridge Truss Common Bridge Truss
CIVL 3121 Trusses - Introduction 4/8
Analysis of Truss Structures Analysis of Truss Structures
Common Bridge Truss Assumptions for Truss Design
To design both the members and connections of a truss,
the force in each member for a given loading must be
determined.
Two important assumptions are made in truss analysis:
Truss members are connected by smooth pins
All loading is applied at the joints of the truss
Analysis of Truss Structures Analysis of Truss Structures
Truss members are connected by smooth pins. All loading is applied at the joints of the truss.
Since the weight of each members is small compared to
The stress produced in these elements is called the
the member force, the member weight is often neglected.
primary stress.
However, when the member weight is considered, it is
The pin assumption is valid for bolted or welded applied at the end of each member.
connections if the members are concurrent. Because of these two assumptions, each truss member is
However, since the connection does provide some a two-force member with either a compressive (C) or a
rigidity, the bending introduced in the members is called tensile (T) axial force.
secondary stress. In general, compression members are bigger to help with
Secondary stress analysis is not commonly performed instability due to buckling.
Classification of Coplanar Trusses Classification of Coplanar Trusses
Simple Truss Simple Truss
The simplest framework that is rigid or stable is a triangle.
Therefore, a simple truss is constructed starting with a
basic triangular element and connecting two members to
form additional elements.
As each additional element of two members is placed on
a truss, the number of joints is increased by one.
CIVL 3121 Trusses - Introduction 5/8
Classification of Coplanar Trusses Classification of Coplanar Trusses
Simple Truss Compound Truss
This truss is formed by connecting two or more
simple trusses together.
This type of truss is often used for large spans.
Classification of Coplanar Trusses Classification of Coplanar Trusses
Compound Truss Compound Truss
There are three ways in which simple trusses 2. Trusses may be joined by three bars.
may be connected to form a compound truss:
1. Trusses may be connected by a common joint and bar.
Classification of Coplanar Trusses Classification of Coplanar Trusses
Compound Truss Compound Truss
3. Trusses may be joined where bars of a large simple truss, called 3. Trusses may be joined where bars of a large simple truss, called
the main truss, have been substituted by simple trusses, called the main truss, have been substituted by simple trusses, called
secondary trusses secondary trusses
Secondary Secondary
simple truss simple truss
CIVL 3121 Trusses - Introduction 6/8
Classification of Coplanar Trusses Classification of Coplanar Trusses
Complex Truss Types of Trusses
This is a truss that cannot be classified as being either
simple or compound.
Simple truss Compound truss
Complex truss
Determinacy of Coplanar Trusses Determinacy of Coplanar Trusses
Since all the elements of a truss are two-force members, r=3
the moment equilibrium is automatically satisfied.
b=5 r+b=2j determinate
Therefore there are two equations of equilibrium for each j=4
joint, j, in a truss. If r is the number of reactions and b is
the number of bar members in the truss, determinacy is
obtained by
b + r = 2j Determinate r=4
b = 18 r+b=2j determinate
b + r > 2j Indeterminate j = 11
Determinacy of Coplanar Trusses Determinacy of Coplanar Trusses
r=4 r=4
b = 10 r+b=2j determinate b = 14 r+b>2j indeterminate
j=7 j=8
r=4 r=3
b = 10 r+b=2j determinate b = 21 r+b>2j indeterminate
j=7 j = 10
CIVL 3121 Trusses - Introduction 7/8
Stability of Coplanar Trusses Stability of Coplanar Trusses
If b + r < 2j, a truss will be unstable, which means the r=3
structure will collapse since there are not enough reactions b=6 r+b<2j unstable
to constrain all the joints.
j=5
A truss may also be unstable if b + r 2j. In this case,
stability will be determined by inspection
b + r < 2j Unstable
r=3
b + r 2j Unstable if reactions are b=9 r+b=2j unstable
concurrent, parallel, or j=6
collapsible mechanics Section ABC is supported
by three parallel links
Stability of Coplanar Trusses Stability of Coplanar Trusses
External stability - a structure (truss) is externally unstable External stability - a structure (truss) is externally unstable
if its reactions are concurrent or parallel. if its reactions are concurrent or parallel.
Externally Concurrent Externally Parallel
Unstable Reactions Unstable Reactions
Stability of Coplanar Trusses Stability of Coplanar Trusses
Internal stability - may be determined by inspection of the Internal stability
arrangement of the truss members.
A simple truss will always be internally stable
The stability of a compound truss is determined by examining how
the simple trusses are connected
The stability of a complex truss can often be difficult to determine by
inspection.
In general, the stability of any truss may be checked by performing a Externally stable Internally stable
complete analysis of the structure. If a unique solution can be found
for the set of equilibrium equations, then the truss is stable
CIVL 3121 Trusses - Introduction 8/8
Stability of Coplanar Trusses Stability of Coplanar Trusses
Internal stability Internal stability
Collapsible mechanism Collapsible mechanism
Externally stable Internally unstable Externally stable Internally unstable
End of Trusses - Part 1
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