BFC 20903 (Mechanics of Materials)
Chapter 7: Statically Determinate
Plane Trusses
Shahrul Niza Mokhatar
shahruln@uthm.edu.my
Chapter Learning Outcome
1. Determine the type of trusses and its
application in construction
2. Analyse the trusses members using related
methods.
BFC 20903 (Mechanics of Materials)
Shahrul Niza Mokhatar (shahrul@uthm.edu.my
Introduction
• A truss is defined as a structure composed of slender elements
joined together at their end points. The members commonly used
in construction consist of wooden struts, metal bars, angles or
channels.
• If all the members of a truss and the applied loads lie in a single
plane, the truss is called a plane truss.
• Plane or planar truss composed of members that lie in the same
plane and frequently used for bridge and roof support.
• Loads that cause the entire truss to bend are converted into tensile
and compressive forces in the members.
Loading causes bending of truss,
which is develops compression in
top members, tension in bottom
members.
Application
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Two or more trusses are connected at their joints by beams,
termed as purlins, to form a 3-D framework.
The roof is attached to the purlins, which
transmit the roof load (weight of the roof plus
any other load) as well as their own weight to the supporting
trusses at the joints.
Because of this applied loading acts on each truss in its own plane, the trusses can be
treated as plane trusses.
The roof truss along with its supporting columns called as a bent.
To keep the bent rigid and capable of resisting horizontal wind forces, knee braces are
sometimes used at the supporting columns.
The space between adjacent bents is called a bay. Bays are
often tied together using diagonal bracing to maintain rigidity
of the structure.
The gusset plate is the connections which formed by bolting or
welding at the ends of the members to a common plate.
Type of roof truss
Assumptions in analysis
• The assumptions are necessary to determine the force developed in each
member when the truss is subjected to a given loading.
• The assumptions are;
– All members are connected at both ends by smooth frictionless pins.
– All loads are applied at joints (member weight is negligible).
• Because of these two assumptions, each truss acts as an axial force member and
the forces acting at the ends of the member must be directed along axis of the
member.
• If the force tends to elongate the member, it is tensile force (T)
• If the force tends to shorten the member, it is compressive force (C).
Stability and Determinacy
• Stability of truss is depend on the support condition and number
of internal member.
• To determine whether the truss is determinate or indeterminate
m+r = 2j ……just stiff (statically determinate)
m+r < 2j ……under stiff (form a mechanism)…unstable (it will collapse since there will
be an insufficient number of bars @ reactions to constraint all the joints).
m+r > 2j ……over stiff (statically indeterminate)
• To determine whether the truss is internally indeterminate or
externally indeterminate
m > 2j -3……statically internal indeterminate, r = 3
m > 2j -3……statically external indeterminate, r > 3
m = total number of members
j = total number of joints
r = number of reaction forces
Example 1
Method of to analyze member
forces
• Method of joint
– Method of Joints-the axial forces in the members of a statically determinate
truss are determined by considering the equilibrium of its joints.
– Tensile(T) axial member forceis indicated on the joint by an arrow pulling
away from the joint.
– Compressive(C) axial member forceis indicated by an arrow pushing toward
the joint.
– When analyzing plane trusses by the method of joints, only two of the three
equilibrium equations are needed due to the procedures involve concurrent
forces at each joint.
Method of to analyze member
forces
• Method of Sections
– This method involves cutting the truss into two portions (free body
diagrams, FBD) by passing an imaginary section through the members
whose forces are desired.
– Desired member forces are determined by considering equilibrium of
one of the two FBD of the truss.
– This method can be used to determine three unknown member forces
per FBD since all three equilibrium equations can be used.
Method of to analyze member
forces
• Alternative Computation using Joint Equilibrium Method
– An alternative method can be applied to determine the
member forces.
– The purpose is to reduce the time for calculation.
• Zero Force Members
– If only two non collinear members are connected to a joint that has
no external loads or reactions applied to it, then the force in both
members is zero.
– If three members, two of which are collinear, are connected to a
joint that has no external loads or reactions applied to it, then the
force in the member that is not collinear is zero.
Example 2
Calculate all member forces by
using method of joints.
Example 2: Solution
Example 3
Calculate all member forces by
using method of joints.