ME101-Basic Mechanical Engineering
(STATICS)
Structural Analysis
Textbook: Engineering MechanicsSTATICS and DYNAMICS
11th Ed., R. C. Hibbeler and A. Gupta
Course Instructor: Miss Saman Shahid
Simple Truss
• A truss is a structure composed of slender
members joined together at their end points.
• The joints connections are usually formed by
bolting or welding the ends of the members to
a common plate, called a gusset plate.
Examples of Trusses
Gusset plate
Joints are often bolted, riveted, or
welded. Gusset plates are also often
included to tie the members together.
However, the members are designed to
support axial loads so assuming that
the joints act as if they are pinned is a
good approximation.
Photo - Pin-jointed connection of the approach
span to the San Francisco-Oakland Bay Bridge
6-3
Simple Trusses
• A rigid truss will not collapse under the
application of a load.
• A simple truss is constructed by
successively adding two members and one
connection to the basic triangular truss.
• In a simple truss, m = 2n - 3 where m
is the total number of members and n
is the number of joints.
Example of Truss: The use of the metal gusset plates in the
construction of these Warren trusses is clearly evident.
Planar Trusses
• Planar trusses lie in a single plane and are often used to support roofs
and bridges. The truss.
• The truss ABCDE shown is an example of a typical roof-supporting truss.
• The analysis of the forces developed in the truss members is twodimensional.
• In case of a bridge, the load on the deck is first transmitted to stringers,
then to floor beams and finally to the joints B,C and D of the two
supporting trusses.
• When bridge or roof trusses extend over large distances, a rocker or
roller is commonly used for supporting one end, e.g., joint E. this type of
support allows freedom for expansion or contraction of the members
due to temperature or application of loads.
Examples
The roof truss shown is formed by two
planar trusses connected by a series of
purlins.
Members of a truss are slender
and not capable of supporting
large lateral loads. Loads must be
applied at the joints.
Types of a Truss
Examples of Trusses
Roof trusses – Safeco Field in Seattle
Examples of Trusses
Photo - Because roof trusses, such as those shown, require support only at their ends,
it is possible to construct buildings with large unobstructed floor areas.
Design of a Truss
• All loadings are applied at the joints.
• Most structures are made of several trusses joined
together to form a space framework. Each truss carries
those loads which act in its plane and may be treated as
a two-dimensional structure.
• Bolted or welded connections are assumed to be pinned
together. This assumption is satisfactory provided the
center lines of the joining members are concurrent.
• Forces acting at the member ends reduce to a single force
and no couple. Only two-force members are considered.
• When forces tend to pull the member apart, it is in
tension. When the forces tend to compress the
member, it is in compression.
Method of Joints
• Dismember the truss and create a freebody diagram
for each member and pin.
• The two forces exerted on each member are equal,
have the same line of action, and opposite sense.
• Forces exerted by a member on the pins or joints at
its ends are directed along the member and equal
and opposite.
• Because the truss members are all straight two-force
members lying in the same plane, the force system
acting at each joint is coplanar and concurrent.
Therefore, moment equilibrium is automatically
satisfied. At the joint (or pin).
• And it is only necessary to satisfy ΣFx=0=ΣFy , to
ensure equilibrium.
• Always assume the unknown member forces acting
on the joint’s free-body diagram to be in tension
(pulling) on the pin. If this is done, then numerical
solution of the equilibrium equations will yield
positive scalars for members in tension and
negative scalars for the members in compression.
Zero-Force Members
• Truss analysis using the method of joints is greatly simplified if we first
determine those members which support no loading.
• These zero-force members are used to increase the stability of the
truss during construction and to provide support if the applied loading
is changed.
• The zero-force members of a truss can generally be determined by the
inspection of each of its joints.
• As a general rule, if only two members form a truss joint and no
external load or support reaction is applied to the joint, the members
must be zero-force members.
• If three members form a truss joint for which two of the members are
collinear, the third member is a zero-force member provided no
external force or support reaction is applied to the joint.
Example: Zero-Force Member
Space Trusses
• An elementary space truss consists of 6 members
connected at 4 joints to form a tetrahedron.
• A simple space truss is formed and can be extended
when 3 new members and 1 joint are added at the
same time.
• In a simple space truss, m = 3n - 6 where m is the
number of members and n is the number of joints.
• Conditions of equilibrium for the joints provide 3n
equations. For a simple truss, 3n = m + 6 and the
equations can be solved for m member forces and 6
support reactions.
• Equilibrium for the entire truss provides 6 additional
equations which are not independent of the joint
equations.
Space Trusses
Photo – Three-dimensional or
space trusses are used for
broadcast and power
transmission line towers, roof
framing, and spacecraft
applications, such as components
of the International Space
Station.
Frames and Machines
• Frames and Machines are two types of
structures which are often composed
of pin-connected multiforce members,
that is, members that are subjected to
more than two forces.
• Frames are generally stationary and are
used to support loads, whereas
machines contain moving parts and are
designed to transmit and alter the
effect of forces.
• The forces acting at the joints and
supports can be determined by
applying the equations of equilibrium
to each member.
• Examples 6.9, 6.10, 6.11, 6.12 and 6.13
Frames Which Cease To Be Rigid When
Detached From Their Supports
• Some frames may collapse if removed from their
supports. Such frames can not be treated as rigid
bodies.
• A free-body diagram of the complete frame indicates
four unknown force components which can not be
determined from the three equilibrium conditions.
• The frame must be considered as two distinct, but
related, rigid bodies.
• With equal and opposite reactions at the contact point
between members, the two free-body diagrams
indicate 6 unknown force components.
• Equilibrium requirements for the two rigid bodies
yield 6 independent equations.
Equations of Equilibrium
(frame or machine)
• Provided the structure is properly supported and
contains no more supports or members than are
necessary to prevent its collapse, then then the
unknown forces at the supports and connections
can be determined from the equations of
equilibrium.
• If the structure lies in the x-y plane, then for each
free-body diagram drawn the loading must satisfy
ΣFx=0=ΣFy and ΣMo=0
Machines
• Machines are structures designed to transmit and
modify forces. Their main purpose is to transform
input forces into output forces.
• Given the magnitude of P, determine the
magnitude of Q.
• Create a free-body diagram of the complete
machine, including the reaction that the wire
exerts.
• The machine is a nonrigid structure. Use one of
the components as a free-body.
• Taking moments about A,
 M A  0  aP  bQ
Q
a
P
b
References:
• Engineering Mechanics- STATICS and DYNAMICS,
11th Ed., R. C. Hibbeler and A. Gupta, Prentice Hall.
• Vector Mechanics for Engineers, Statics, 7th Ed.,
Ferdinand P. Beer, E. Russell Johnson, Jr.,McGrawHill , Lecture notes by J. Walt Oler (Texas Tech
University)