MOMENT AREA THEOREMS

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The moment area method is based on the following two theorems

Theorem 1   The change in the slope between two points on a straight member under flexure is equal to the area of M/EI diagram between those two points 

Where  M is the Bending Moment 

              E is the Young's Modulus

and           I is the Moment of Inertia

          Consider the beam AB(Figure 2.1(a)). Let C and D be any two points on this beam. The (M/EI) diagram is also shown in the figure. Figure 2.1(b) shows the elastic curve of the beam after loading. According to this throrem,thita CD which is the angle between the tangents at C and D is equal to the area of (M/EI) diagram between C and D (shaded portion). Thus

        

 

   

Theorem 2   Deflection at a point in a beam in the direction perpendicular to its original straight line position measured from the tangent to the elastic curve at another point is given by the moment of (M/EI) diagram about the point where the deflection is required 

    In figure 2.1(b),delta, the vertical (perpendicular to the horizontal position of AB) deflection at point D' from the tangent to the elastic curve at C' is given the moment of(M/EI) diagram between C and D about the point D. Thus,