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Support reactions
The document discusses the mechanics of solids, particularly focusing on support reactions relevant to beams in structural engineering. It covers various types of beams, loads, and supports, detailing how they interact and the methods available for calculating support reactions. The introduction highlights the importance of understanding these concepts for effective building design and includes examples and analytical methods for determining support reactions.
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Support reactions
- 1. GUJARAT TECHNOLOGICAL UNIVERSITY Subject :Mechanics Of Solids (2130003) Sem-3 (Chemical) Aug - 2016 Topic : Support Reactions
- 3. Contents: Introduction Types of Beam Typesof Loads acting on beam Types of Supports Instrument used for finding “Support Reactions” How to find “Support Reactions”
- 4. “Support Reactions” • Support:- A support prevents translation of a body in a given direction, a force is developed on the body in that direction. • Reactions:- The forces and moments exerted on an object by its supports are called reactions.
- 5. Introduction • When designingbuildings, frames, beams it is important to know the magnitude and direction of the load that resides within a support. • All of these supports can be located anywhere along a structural element. They are found at the ends, at midpoints, or at any other intermediate points. The type of support connection determines the type of load that the support can resist. The support type also has a great effect on the load bearing capacity of each element.
- 6. Types of Beam Beam:- A beam is a structural element that is capable of withstanding load primarily by resisting bending.
- 7. In engineering, beamsare of several types: 1. Simply supported Beam – A beam supported on the ends which are free to rotate and have no moment resistance. 2.Fixed beam -a beam supported on both ends and restrained from rotation.
- 8. 3) Cantilever :-it has one end fixed and other end free.
- 9. 4) Over hanging:– A simple beam extending beyond its support on one end.
- 10. 5) Continuous Beam- Abeam extending over more than two supports.
- 11.
- 12. Types of Loadsacting on Beams 1) Point load(concentrated load)- w1 and w2 are point loads. the load concentrated at one point is called point load. Unit of point load is n or kn. eg. 20 kn,100kn,60n,etc w1 w2
- 13. 2) Uniformly Distributed Load(U.D.L)-Load uniformly distributed on certain length of beam is called uniformly distributed load. it is written as u.d.l unit of u.d.l is kn/m or n/m.
- 14. 3) Uniformly VaryingLoad (U.V.L)- this type of load is gradually increase Or decrease on the length of the beam. it is also called triangular load.
- 15.
- 16. Types of supports 1)Simple support :- In this type of support,beam is simply supported on the support. There is no connection between beam and support. At this type of support,only vertical reaction will be produced.
- 17. 2) Fix endsupport :- Beam is completely fixed at end in the wall or support. Beam cannot rotate at end. Reactions may be vertical,horizontal,inclined and moment.
- 18. 3) Roller support:- Inthis type of support,rollers are placed below beam and beam can slide over the rollers. Reaction will be perpendicular to the surface on which rollers are supported. This type of support is normally provided at the end of a bridge. Due to breaking forces of vehicles and temperature forces,bridge slab can slide over the roller support and damage to bridge pier can be avoided.
- 19. 4) hinge support:- Beamand support are connected by a hinge. Beam can rotate about the hinge. Reactions may be vertical,horizontal or inclined.
- 20. Methods to calculate SupportReactions Analytical Method Graphical Method
- 21. Q- Determine thesupport reactions of the following examples ? Taking moment @ A :- vb X 7+ 6x2 = 8x3x5.5 ∴ Vb = 17.14 kN ∴ va + Vb = (8 x 3 - 6) ∴ Va = 0.86 kN ∴ Ha = 12 cos30⁰ = 10.39 kN
- 22. Q- Determine thesupport reactions of the following examples ? Taking moment @ A :- vb x6 = (12x2x1)+ (30x3)+30+(22.52x5) ∴ Vb = 42.76 kN ∴ va + Vb = 24+30+22.5 ∴ Va = 33.76 kN ∴ Ha = 22 cos 60⁰ = 10.39 kN
- 23. Q- Determine thesupport reactions of the following examples ? Taking moment @ A :- Vf = (5.1x2.2x10)+ (25x2)-30+(20x0.8) ∴ Vb = 148.2 kN ∴ Va = (10x2.2)+20+25 ∴ Va = 67 kN ∴ Ha = 0 kN
- 24. Q- Determine thesupport reactions of the following examples ? tanӨ =15/8 ∴ Ө = 61.92⁰ Taking moment @ A :- vb x 2.5 = 150x2.8 ∴ Vb = 168 kN ∴ va + Vb = 150 ∴ Va = - 18 kN ∴ Ha = 170 cos61.92⁰ = 80 kN
- 25. Q- If supportreactions of the following example is equal then find load P ? Taking moment @ A :- vb x 6 = (16x4x2)+(px7) ∴ Vb x 6 = 128 + 7p ………( a) ∴ va + Vb = 16 x 4 + p ……………..(b) and va = vb On comparing (a)&(b) we get , ∴ Vb = 32 + 0.5 P ∴ P = 16 kN
- 26.
- 27. Instrument used forfinding “Support Reactions”
- 28. References:- • Wikipedia • EngineeringMechanics by Beer and Johnson • Mechanics of solids by R.P.Rethaliya ,by M.N.Patel , N.K. Arora • By Slideshare and Youtube videos • Researching in google and many more…