PIN - JOINT FRAMES BY ANALYTICAL METHOD AND GRAPHICAL METHOD

1. ENGINEERING MECHANICS

2.  Introduction
 Frames / Trusses
 Classification of Frames
 Formulation of perfect Frames
 Common types of Trusses
 Support Conditions
 Nature of Forces in Frames
 Analysis of Frames

3.  The built-up structure made up of several members
such as angles, channels, pipes, etc. to resist the
external loads are known as Frames.
 They are jointed together at their ends either by
riveting or by welding.
 If the frames are used in the place of roofs they are
called Roof Truss.
 The place where the members are jointed are known
as nodes and all loads act at the nodal points.
 The members are subjected to only axial forces and
not subjected to bending moment or shear force.

4.  If all the members of the rigid frame are
constructed by frictionless pins to form
triangles, then it is known as Trusses.
 Triangle is the simple geometric figure which
is rigid and stable for external load.

6. PIN – JOINT FRAMES
Determinates Frames Indeterminate Frames
Perfect Frames
(m = 2j - 3)
Imperfect Frames
(m ≠ 2j - 3)
Deficient Frames
(m ≺ 2j - 3)
Redundant Frames
(m ≻ 2j - 3)

7.  If a frame can be analyzed completely by
using the three equilibrium equation ΣV=0,
ΣH=0, ΣM=0 then the frame can be defined
as the determinate frames.
 Example : All perfect frames have not more
than two supports.

8.  If a frame cannot be analyzed by using the
three equilibrium equations ΣV=0, ΣH=0,
ΣM=0 then the frame can be defined as
Indeterminate Frames
 Example : frames having more than two
supports and frames with both ends fixed.

9.  If the number of frames are just sufficient to
keep it in equilibrium without changes in its
shape under the action of external load, then
it is known as Perfect Frames.
 The perfect frame satisfy the following
equation
◦(m = 2j - 3)
 m – Number of members
 j – Number of joints

10. ◦(m = 2j - 3)
 Number of members - m = 7
 Number of joints - j = 5
7 = (2 x 5) – 3
7 = 7
 Number of members - m = ?
 Number of joints - j = ?
Guess what type of Frame???
It is a Perfect Frame!

11.  If the number of member of a frames are not
sufficient to keep it in equilibrium under
action of external loads, then it is called as
Imperfect Frames.
 (m ≠ 2j - 3)
 m – Number of members
 j – Number of joints
 It is again classified into
◦ Deficient Frames
◦ Redundant Frames

12.  If the number of members are less than that
is required to keep it in equilibrium is known
as Deficient Frames
◦(m ≺ 2j - 3)
 m – Number of members
 j – Number of joints

13. ◦(m ≺ 2j - 3)
 Number of members - m = 8
 Number of joints - j = 6
8 = (2 x 6) – 3
8 ≺ 9
 Number of members - m = ?
 Number of joints - j = ?
Guess what type of Frame???
It is a Deficient Frame!

14.  If the number of a frame are more than that is
required to keep it in equilibrium is known as
Redundant Frames
◦(m ≻ 2j - 3)
 m – Number of members
 j – Number of joints

15. ◦(m ≻ 2j - 3)
 Number of members - m = 6
 Number of joints - j = 4
6 = (2 x 4) – 3
6 ≻ 5
 Number of members - m = ?
 Number of joints - j = ?
Guess what type of Frame???
It is a Redundant Frame!

16.  A perfect frames should be made up of
minimum of 3 members
 All the members should be connected to each
other with pin joints at their ends
 The members should not intersects each
other at their joints
 The frames should be a combinations of
continuous triangles
 If the frames are constructed as a simple
supported frames, then one support should
be of roller support and the other should be
of hinged one.

21.  Simple Support
 Roller Support
 Hinged Support
 Fixed Support

22.  If trusses simply rests over the supports is
known as Simple Support.
 There will be only vertical reaction in the
supports.

23.  If the trusses rests on the rollers over the
supports then there will be rotation and
lateral displacement
 There will be a vertical reaction perpendicular

24.  There will be only rotation and no lateral
displacement.
 In this support there will be vertical and
horizontal reaction.

25.  If the trusses are rigidly fixed to the support
there will not be any rotation, lateral
displacement or vertical displacement
 There will be a vertical, horizontal reaction
and a moment.

26.  Depending upon the Joints
 Depending upon the Space Diagrams
 Analytical method
 Graphical method

27.  When a truss is subjected to external force
then in each member an opposite force is
induced.
◦ Compression Force
◦ Tensile Force

28.  If the compressive force acting on a member,
then there will be an equal & opposite force
induced in the member
 The opposite compressive force produced in
the member can be expressed by an arrow
directing outwards.

29.  If tensile force is acting on a member then
there will be an equal an opposite force
induced in the member
 The opposite tensile force produced in the
member can be expressed by an arrow
directing inwards.

32.  All frames are perfect and statically determinate
 All joints are frictionless pinned joints
 Loads are applied only at the joints or nodes
 Self weight of the members are not taken into
account
 The deflection due to external loads are
considered to be minimum and hence can be
neglected
 All the members lie in one plane
 The effect of temporary variation can be ignored

35. Life isn’t about finding Yourself……
Life is about Creating Yourself!!!!........
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