For the loading shown determine a the equation of the elasti

For the loading shown, determine (a) the equation of the elastic curve for the cantilever beam AB o)the equation of the elastie curve for the cantilever beam 4B. (b) the deflection at the free end, (c) the slope at the free end

Solution

Data Given

Overturning couple acting at free end of antilever beam = Mo

Length of the beam = L

Assumptions

Modulus of eleasticity of the beam material = E

Moment of inertia of the beam material = I

a) Elastic curve

0<=x<=L

EI(d^2 y/d*^2) = Mo

EI (dy/dx) = Mox + C1 ( by doing intergration)

Elastic curve - EI * y = 1/2(Mo * x^2) + C1 + C2 (by doing integration)

b) Deflection at the free end of the cantilever beam = (Mo * L^2)/(2EI)

c) Slope at free end = (Mo * L)/EI