1635176170366_a_MECH_101_3_(Frames).pptx

frames

1. 3. Pin jointed Frames NB: Student required to be familiar with the concepts of FORCE, TURNING MOMENT, POLYGON OF FORCES and REACTIONS. These should be studied before work on pinned frames.

2. Common applications Roof trusses. Electric Pylons. Cranes. Bridges

3. Pinned joints (plane trusses)

4. Pin joint : Allows the joined members to swivel as opposed to a rigid joint that does not. Rigid joint : Are welded but a pin joint may be a bolt, a rivet or any form of swivel pin. • The connected members are free to rotate. • The force in the member can only pull (tie ) or push ( strut ) along the line of the member.

5. Elements of pinned frames Strut: Tie:

6. Key Considerations Key design considerations Length of compression members is minimized. For tension members, length is irrelevant to load-carrying capacity. Loads are applied at nodes only joints are pinned and assumed to be frictionless. Members are subject to axial compression or tension . There is no bending or shear on members.

7. Perfect frames Perfect Frame: Is composed of such members, which are just sufficient to keep the frame in equilibrium, when the frame is supporting an external load. n = 2j – 3 where n=members j=joints 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

8. Frame analysis 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. (iii)A frame is analysed by method of joints,

9. STRUTS AND TIES A pin joint can only push or pull on the joint along the direction of its length. A member in tension is called a TIE and is shown with arrows pointing inwards at each end. A member in compression is called a strut and is shown with arrows pointing outwards at each end.

10. Note Internal forces are shown as forces exerted by members on pin joints Away from pins (acting inwards) for a TIE in tension Towards pin (outwards) for a STRUT under compression Frames involve statics problem in equilibrium for forces and moments Start resolving for reaction and joints with a maximum of two unknowns can be solved

11. Recap !! You learned earlier that a strut is a member in compression and a tie is a member in tension. They are drawn with the internal forces shown as follows.

12. Example1 A strut is held vertical as shown by two guy ropes. The maximum allowable compressive force in the strut is 20 kN. Calculate the forces in each rope. Note that ropes can only be in tension and exert a pull. They cannot push.

13. Solution 1

14. Example 2

15. Example 3 Find the forces in the members AB, AC and BC of the truss as shown in the below figure?

16. Now let us consider the equilibrium of the various joints. Joint B: Resolving the forces acting on the joint B, vertically

17. Joint C:

18. Example 4 Solve the forces and the reactions for the frame shown R1 = 150 N. R2 = 50

19. Example 5 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?

20. Determine the forces in the truss shown in the below figure. Which is subjected to inclined loads? Example 6

21. Thank You