Calculate the deflection v at the free end, B, for the beams shown below. Both beams have the same rectangular cross section. Give your solution in terms of P,L,E and I.
To calculate the deflection v at the free end B of the beams shown, we can use the standard formula for the deflection of a simply supported beam with a point load at the center:
v = (P * L^3) / (48 * E * I)
Where:
- v is the deflection at the free end B
- P is the point load applied at the center of the beam
- L is the length of the beam
- E is the modulus of elasticity of the material
- I is the moment of inertia of the cross-sectional area of the beam
Since both beams have the same rectangular cross section, their moment of inertia I would be the same.
So the final solution for the deflection v at the free end B is:
v = (P * L^3) / (48 * E * I)
To calculate the deflection at the free end B for the beams shown, we can use the equation for deflection of a simply supported beam under a point load applied at its midspan. The equation is given by:
v = (P * L^3) / (48 * E * I)
Where:
- v is the deflection at point B
- P is the applied load
- L is the length of the beam
- E is the modulus of elasticity of the material
- I is the moment of inertia of the beam's cross-section
In this case, both beams have the same rectangular cross-section, so they have the same moment of inertia, denoted by I. Therefore, the deflection at the free end B for both beams will be the same.
Make sure you have the values of P, L, E, and I. Then, plug in these values into the formula and perform the calculation to get the deflection at point B in terms of P, L, E, and I.