Problem on Deflection of a SSB Carrying a
Problem on : Deflection of a SSB Carrying a Point Load at the Center Dr R Vaikunta Rao Mechanics of Solids Mechanical Engineering REC 1
Problem on : Deflection of a SSB Carrying a Point Load at the Center Dr R Vaikunta Rao Mechanics of Solids Mechanical Engineering REC 2
Problem on : Deflection of a SSB Carrying a Point Load at the Center Dr R Vaikunta Rao Mechanics of Solids Mechanical Engineering REC 3
Problem on : Deflection of a SSB Carrying a Point Load at the Center Dr R Vaikunta Rao Mechanics of Solids Mechanical Engineering REC 4
Exercise Problems Dr R Vaikunta Rao Mechanics of Solids Mechanical Engineering REC 5
Exercise Problems Dr R Vaikunta Rao Mechanics of Solids Mechanical Engineering REC 6
Assignmant Question : A Circular Beam of 50 mm dia made of steel having E= 200000 N/mm^2. Find Slope at end and Deflection at center if the beam is subjected to a point load of 1000 KN at the center. Take Length of Beam is 10 m. Dr R Vaikunta Rao Mechanics of Solids Mechanical Engineering REC 7
MOMENT AREA METHOD Dr R Vaikunta Rao Mechanics of Solids Mechanical Engineering REC 8
MOMENT AREA METHOD Dr R Vaikunta Rao Mechanics of Solids Mechanical Engineering REC 9
MOMENT AREA METHOD Dr R Vaikunta Rao Mechanics of Solids Mechanical Engineering REC 10
MOMENT AREA METHOD Dr R Vaikunta Rao Mechanics of Solids Mechanical Engineering REC 11
MOHR’S THEOREM These two equations slope and deflection are known as Mohr's Theorem. They are state as following: 1. The change of slope between any two points is equal to the net area of the B. M. diagram between these points divided by EI. 2. The total deflection between any two points is equal to the moment of the area of B. M. diagram between the two points about the last point (i. e. , B) divided by EI. Dr R Vaikunta Rao Mechanics of Solids Mechanical Engineering REC 12
MOHR’S THEOREM These two equations slope and deflection are known as Mohr's Theorem. They are state as following: 1. The change of slope between any two points is equal to the net area of the B. M. diagram between these points divided by EI. 2. The total deflection between any two points is equal to the moment of the area of B. M. diagram between the two points about the last point (i. e. , B) divided by EI. The Mohr`s theorem is conveniently used for following cases: 1. Problems on cantilevers (Zero slope at fixed end). 2. Simply supported beams carrying symmetrically loading (zero slope at the centres). 3. Beams fixed at both ends (Zero slope at each end). Dr R Vaikunta Rao Mechanics of Solids Mechanical Engineering REC 13
MOHR’S THEOREM Dr R Vaikunta Rao Mechanics of Solids Mechanical Engineering REC 14
Slope and Deflection of a SSB carrying a point load at the center by Mohr’s Theorem Let take • Simply Supported Beam AB • W Point load • Beam Distance L Dr R Vaikunta Rao Mechanics of Solids Mechanical Engineering REC 15
Problem on : Deflection of a SSB Carrying a Point Load at the Center Dr R Vaikunta Rao Mechanics of Solids Mechanical Engineering REC 16
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