Pin joint frames

PIN - JOINT FRAMES BY ANALYTICAL METHOD AND GRAPHICAL METHOD

1. PIN – JOINT FRAMES ANALYTICAL METHOD GRAPHICAL METHOD 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 CONTENT:

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. Introduction:

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. Frames / Truss:

5. Classification of Frames: 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)

6. If a frame can be analyzed completely by using the three equilibrium equation Σ V=0, Σ H=0, Σ M=0 then the frame can be defined as the determinate frames. Example : All perfect frames have not more than two supports. Determinate Frames:

7. If a frame cannot be analyzed by using the three equilibrium equations Σ V=0, Σ H=0, Σ M=0 then the frame can be defined as Indeterminate Frames Example : frames having more than two supports and frames with both ends fixed. Indeterminate Frames:

8. 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 Perfect Frames:

9. (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!

10. 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 Imperfect Frames:

11. 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 Deficient Frames:

12. (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!

13. 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 Redundant Frames:

14. (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!

15. Formulation of Perfect Frames: 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.

16. Common Types of Trussess :

17. Support Conditions: Simple Support Roller Support Hinged Support Fixed Support

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

19. 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 Roller Support:

20. There will be only rotation and no lateral displacement. In this support there will be vertical and horizontal reaction. Hinged Support:

21. 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. Fixed Support:

22. Depending upon the Joints Depending upon the Space Diagrams Designation of Force: Analytical method Graphical method Method of Analysis:

23. When a truss is subjected to external force then in each member an opposite force is induced. Compression Force Tensile Force Nature of Force in a Frame:

24. 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. Compressive Force:

25. 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. Tensile Force:

26. 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 Assumption:

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