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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👉Doubly reinforcement beam section
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.
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| A Cantilever beam carries point load of W KN at its free end |
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| A cantilever beam carries, UDL of W kN/m |
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| A cantilever beam carries a clock wise couple at its free end |
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| A simply supported beam carries point load at its center |
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| beam subjected to uniformly varying load |
