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An overhanging beam ABC is loaded as shown in figure given below. Determine the deflection of the beam at point C in terms of E, I, W and L?
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An overhanging beam ABC is loaded as shown in figure given below. Dete...
Deflection of an Overhanging Beam
Given Information
- Beam: ABC
- Load: W
- Length of the beam: L
- Modulus of elasticity: E
- Moment of inertia: I
Calculating the Deflection at Point C
- Calculate the reaction forces at points A and B using the equations of equilibrium.
- Calculate the shear force (V) and bending moment (M) at point C using the equations of equilibrium.
- Calculate the deflection (δ) at point C using the equation:
δ = (W*L^3)/(48*E*I) + (M*L^2)/(2*E*I) - (V*L)/(2*E*I)
Explanation
When a beam is subjected to a load, it experiences bending which results in deflection. In this case, the beam is overhanging and loaded with a concentrated load W. The deflection at point C is calculated by first determining the reaction forces at points A and B. Once the reaction forces are determined, the shear force and bending moment at point C can be calculated. Finally, the deflection at point C can be calculated using the equation mentioned above.
Assumptions Made
- The beam is homogeneous and isotropic.
- The material is linearly elastic.
- The cross-section of the beam is constant along its length.
- The beam is loaded only by the applied load and its own weight is neglected.
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An overhanging beam ABC is loaded as shown in figure given below. Determine the deflection of the beam at point C in terms of E, I, W and L?
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