This document discusses engineering mechanics and frames/trusses. It defines frames as built structures made of members like angles and channels that resist external loads. Trusses are frames where all members form triangles connected by frictionless pins. Frames are classified as determinate or indeterminate based on whether equilibrium equations can analyze them. Trusses are also classified based on the number of members, including perfect, imperfect deficient and redundant frames. The document also covers support conditions, forces in frames, and methods of analyzing frames and trusses.

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

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