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Chapter 6: Analysis of Structures
Some of the most common structures we see around us are buildings & bridges. In addition to these,
one can also classify a lot of other objects as "structures."
The space station
Chassis of your car
Your chair, table, bookshelf etc. etc.
For instance:
Almost everything has an internal structure and can be thought of as a "structure".
The objective of this chapter is to figure out the forces being carried by these structures so that as an
engineer, you can decide whether the structure can sustain these forces or not.
Note: this includes "reaction" forces from the supports as well.
External forces: "Loads" acting on your structure.
of the structure together.
Internal forces: Forces that develop within every structure that keep the different parts
Recall:
Trusses
Frames
Machines
In this chapter, we will find the internal forces in the following types of structures :
Monday, October 26, 2009
10:08 AM
6.2-6.3 Trusses
Trusses are used commonly in Steel buildings and bridges.
All straight members
connected together with pin joints
connected only at the ends of the members
and all external forces (loads & reactions) must be applied only at the joints.
Definition: A truss is a structure that consists of
Every member of a truss is a 2 force member.
Trusses are assumed to be of negligible weight (compared to the loads they carry)
Note:
Types of Trusses
Simple Trusses: constructed from a "base"
triangle by adding two members at a time.
simple
simple
NOT
simple
Note: For Simple Trusses (and in general statically determinate trusses)
m: members
r: reactions
n: joints
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10:11 AM
Exercise 6.
Similarly, solve joints C, F and B in that order and calculate the rest of the unknowns.
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2:50 PM
6.5 Joints under special loading conditions: Zero force members
Many times, in trusses, there may be joints that connect
members that are "aligned" along the same line.
Exercise 6.
Identify the zero-force members.
Similarly, from joint E: DE=EF and AE=
Friday, October 30, 2009
7:40 AM
Similarly find the 3 unknowns F BD
, F
BC
and B Y
at joint B.
6.7 Analysis of Trusses: Method of Sections
The method of joints is good if we have to find the internal forces in all the truss members.
In situations where we need to find the internal forces only in a few specific members of a truss, the method of sections
is more appropriate.
For example, find the force in member EF:
Read Examples 6.2 and 6.3 from the book.
Find forces in the members EH and GI.
Exercise 6.
Imagine a cut through the members of interest
Try to cut the least number of members (preferably 3).
Draw FBD of the 2 different parts of the truss
Enforce Equilibrium to find the forces in the 3 members that are cut.
Method of sections:
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8:53 AM
6.8 Compound Trusses; Determinate vs. Indeterminate Trusses.
Trusses made by joining two or more simple trusses rigidly are called Compound Trusses.
Externally: Completely / Partially /Improperly constrained
Internally: Determinate / Indeterminate. (if completely constrained)
Exercise 6.69 Classify the trusses as:
Partially constrained
Overly constrained,
Indeterminate
Determinate
Monday, November 02, 2009
8:53 AM
6.9 - 6.11 Frames
i.e. atleast one member that has 3 or more forces acting on it at different points.
Frames are structures with at least one multi-force member,
(i) External Reactions
Frame analysis involves determining:
(ii) Internal forces at the joints
Follow Newton's 3rd Law
Note:
Frames that are not internally Rigid
When a frame is not internally rigid, it has to be provided with
additional external supports to make it rigid.
The support reactions for such frames cannot be simply
determined by external equilibrium.
One has to draw the FBD of all the component parts to find out
whether the frame is determinate or indeterminate.
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11:29 AM
(a)
(b)
6.12 Machines
Machines are structures designed to transmit and modify forces.
Their main purpose is to transform input forces into output forces.
Machines are usually non-rigid internally. So we use the components
of the machine as a free-body.
- Given the magnitude of P , determine the magnitude of Q.
Exercise 6.
Wednesday, November 11, 2009
11:35 AM
Examples:
