2nd MOMENT AREA THEOREM

2^nd MOMENT AREA THEOREM

Consider the simply supported beam AB subjected to the load W. Let C and D be the two points between the supports A and B in order to determine the deflection for elemental length. Let ∆ be the deflection between the two points C and D. Let X be the distance from D to the meeting point of tangent. Let ϴ_CD be the angle between the tangents drawn from points C and D.

From property of circles,

Referring to the figure

∆ = x (ϴ_CD)

From 1^st moment area theorem

W k t

ϴ_CD = _C∫^D   (M/ E I) (dx)

∆ = _C∫^D   (M/ E I) (x) (dx)

Therefore 2^nd  theorem of moment area states that 

“Deflection at a point in a beam in the direction perpendicular to its original straight line position measured from tangent to elastic curve at another point is given by moment of M/EI diagram about the point where deflection is required.