1. Supports and Reactions
CIV THEORY OF STRUCTURES (1) - A
Giza Higher Institute for Eng. & Tech. - Dr. M Abdel-Kader
Supports and Reactions
Structural elements carry their loading to other elements through connections.
Structures carry their loading to the ground through supports.
Reactions are the forces that can be resisted at supports.

2. Supports and Reactions
CIV THEORY OF STRUCTURES (1) - A
Giza Higher Institute for Eng. & Tech. - Dr. M Abdel-Kader
Supports and Reactions
Types of supports
There are three common types of supports that can be found in plane structures:
Roller support
Hinged support
Fixed support
There is no single accepted graphical icon to represent each of these support types.
Link support (Link member)
Intermediate hinge

3. Supports and Reactions
CIV THEORY OF STRUCTURES (1) - A
Giza Higher Institute for Eng. & Tech. - Dr. M Abdel-Kader
Supports and Reactions
Roller support
Free to translate (move) only parallel to the supporting surface.
Free to rotate.
Resulting reaction is always perpendicular to the surface.
Can take the form of rubber bearing.

4. Supports and Reactions
CIV THEORY OF STRUCTURES (1) - A
Giza Higher Institute for Eng. & Tech. - Dr. M Abdel-Kader
Supports and Reactions
Hinged support
Not move to any direction.
Free to rotate.
Resulting reaction has horizontal and vertical components Ax and Ay .
Resulting reaction RA and its inclination  to the horizontal can be obtained from:

5. Supports and Reactions
CIV THEORY OF STRUCTURES (1) - A
Giza Higher Institute for Eng. & Tech. - Dr. M Abdel-Kader
Supports and Reactions
Fixed support
Not move to any direction.
Not rotate.
Resulting reaction has moment, horizontal and vertical components MA , Ax and Ay .
Reaction RA (which is the resultant of Ax and Ay only, not moment MA) and its inclination  can be obtained from:

6. Supports and Reactions
CIV THEORY OF STRUCTURES (1) - A
Giza Higher Institute for Eng. & Tech. - Dr. M Abdel-Kader
Supports and Reactions
Link support
It has the same action as the roller support.
It can resist forces along its axis only. So, the resultant reaction will be along the link axis.
Here, the link member supports the lower part with the upper part.

7. Supports and Reactions
CIV THEORY OF STRUCTURES (1) - A
Giza Higher Institute for Eng. & Tech. - Dr. M Abdel-Kader
Supports and Reactions
Intermediate hinge
It transmits horizontal and vertical forces from one part of the structure to the other.
It is free to rotate. So, it cannot transmit moment from one part to the other or vice versa.
The algebraic sum of the moments about the intermediate hinge of all the forces (including reactions) acting on one part of the structure must be equal zero, so:

8. Supports and Reactions
CIV THEORY OF STRUCTURES (1) - A
Giza Higher Institute for Eng. & Tech. - Dr. M Abdel-Kader
Supports and Reactions
Equilibrium
In general, for three-dimensional (space) structures, the force and moment equations of equilibrium must be satisfied.
Equilibrium of forces:
Equilibrium of moments:
For planar structures

9. O.K. Supports and Reactions CIV 111 - THEORY OF STRUCTURES (1) - A
Giza Higher Institute for Eng. & Tech. - Dr. M Abdel-Kader
Supports and Reactions
Example:
Determine the reactions at the supports A and B of the simple beam loaded as shown.
Solution:
Ax = 0
Ay (12) – 300 (5) = 0 +
Ay = 125 kN
300 (7) – By (12) = 0
By = 175 kN +
Check
O.K.
Ay – By = 125 – =

10. Thank You CIV 111 - THEORY OF STRUCTURES (1) - A
Giza Higher Institute for Eng. & Tech. - Dr. M Abdel-Kader
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