Deflection in Beams

 Deflection in Beams

In this we discuss the various methods to find deflection in beams

A beam is subjected to varying B.M. from support to center such that the max. B.M.

will occur at center due to which member is subjected to deflection & slope.

Slope & deflection in a beam can be determined by using 4 methods:

1). moment area method

2). stain energy method

3). double integration method

4). Conjugate beam method

Moment Area Method

In this method, slope & deflecting can be determined by using two theorems of Mohr’s

1). Mohr’s 1st theorem

This theorem states that slope b/w tangents to the deflection curve are the area under

𝑀 /𝐸𝐼 diagram. 

or

Slope at a point in a beam is the area under 𝑀/ 𝐸𝐼 diagram towards approaching max. B.M 

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2). Mohr’s 2nd theorem

The deflection at a point from the tangent from the deflection curve is the area under

moment of area under 𝑀 /𝐸𝐼 diagram. 

or

Deflection at a point is the first moment of 𝑀/ 𝐸𝐼 diagram from that point at which slope  is determined.

A Cantilever beam carries point load of W KN at its free end

 A cantilever beam carries, UDL of W kN/m

A cantilever beam carries a clock wise couple at its free end

A simply supported beam carries point load at its center

beam subjected to uniformly varying load