NRI INSTITUTE OF TECHNOLOGY
MECHANICS OF SOLIODS
UNIT-5
ANALYSIS OF PIN-JOINTED PLANE FRAMES
1. Explain about different types of frames and analysis of frames?
Ans:
The Different types of frames are:
(i)
Perfect frame
(ii)
Imperfect frame
Imperfect frame may be deficient or a redundant frame.
Perfect Frame: The frame which is composed of such members, which are just sufficient to keep the
frame in equilibrium, when the frame is supporting an external load, is known as perfect frame.
Example:
(a)
(b)
(c)
Suppose we add a set of two members and a joint again, we get a perfect frame as shown in
the above fig©.
Hence for a perfect frame, the number of joints and number of members are given by,
n = 2j – 3
Where, n = Number of members, and
j = Number of joints.
Imperfect frame: A frame in which number of members and number of joints are not given by,
n = 2j – 3 is known, an imperfect frame. This means that number of members in an imperfect frame
will be either more or less than (2j – 3).
(i) If the number of members in a frame are less than (2j – 3), then the frame is known as
deficient frame.
(ii) If the number of members in a frame are more than (2j – 3), then the frame is known as
redundant frame.
M.VENKANNABABU
NRI INSTITUTE OF TECHNOLOGY
MECHANICS OF SOLIODS
The assumptions made in finding out the forces in a frame are:
(i)
The frame is a perfect frame
(ii)
The frame carries load at the joints
(iii)
All the members are pin-joined.
Reactions of supports of a frame:
(i)
On roller support or
(ii)
On a hinged
Analysis of a frame consists of:
(i)
Determinations of the reactions at the supports and
(ii)
Determinations of the forces in the members of the frame.
A frame is analysed by the following methods:
(i) Method of joints,
(ii) Method of sections, and
(iii) Graphical method.
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2. Find the forces in the members AB, AC and BC of the truss as shown in the below figure?
Ans:
M.VENKANNABABU
NRI INSTITUTE OF TECHNOLOGY
MECHANICS OF SOLIODS
Now let us consider the equilibrium of the various joints.
Joint B:
Resolving the forces acting on the joint B, vertically
Joint C:
3. A truss of span 7.5m carries a point load of 1 KN at joint D as shown in the below figure. Find the
reactions and forces in the members of the truss?
Ans:
Moments about A,
&
M.VENKANNABABU
NRI INSTITUTE OF TECHNOLOGY
Now let us consider the equilibrium of the various joints.
Joint A:
Joint B:
M.VENKANNABABU
MECHANICS OF SOLIODS
NRI INSTITUTE OF TECHNOLOGY
MECHANICS OF SOLIODS
Joint D:
Let the direction of F3 is assumed as shown in the below figure.
4. Determine the forces in the truss shown in the below figure. Which is subjected to inclined loads?
Ans:
M.VENKANNABABU
NRI INSTITUTE OF TECHNOLOGY
Joint A:
Joint C:
Joint E:
M.VENKANNABABU
MECHANICS OF SOLIODS
NRI INSTITUTE OF TECHNOLOGY
MECHANICS OF SOLIODS
Joint F:
Joint B:
Joint G:
MEMBER
M.VENKANNABABU
FORCE IN THE MEMBER
NATURE OF FORCE
NRI INSTITUTE OF TECHNOLOGY
MECHANICS OF SOLIODS
5. Find the forces in the members AB and AC of the truss as shown in the below figure using method
of section?
Ans:
6. A truss of span 9m is loaded as shown in the below figure. Find the reactions and foreces in the
members marked 1, 2 and 3.
Ans:
M.VENKANNABABU
NRI INSTITUTE OF TECHNOLOGY
MECHANICS OF SOLIODS
Now draw a section line (1-1), cutting the members 1, 2 and 3 in which forces are to be
determined.
Consider the equilibrium of the left part of the truss because it is smaller than the right part.
Moments about D:
Moments about G:
Moments about C:
M.VENKANNABABU