Question

7. The simple beam AB shown in the figure supports two equal concentrated loads P, one acting downward and the other upward. Determine the angle of rotation $\theta_B$ at the left-hand end, the deflection $\delta_1$ under the downward load, and the deflection $\delta_2$ at the mid point. $\theta_B = \frac{P}{6EIL}(3La^2 - 2a^3 - aL^2)$, $\delta_1 = -\frac{Pa^2}{6EIL}(L - 2a^2)$, $\delta_2 = 0$

          7. The simple beam AB shown in the figure supports two equal concentrated loads P, one acting downward and the other upward. Determine the angle of rotation $\theta_B$ at the left-hand end, the deflection $\delta_1$ under the downward load, and the deflection $\delta_2$ at the mid point.
$\theta_B = \frac{P}{6EIL}(3La^2 - 2a^3 - aL^2)$, $\delta_1 = -\frac{Pa^2}{6EIL}(L - 2a^2)$, $\delta_2 = 0$

7. The simple beam AB shown in the figure supports two equal concentrated loads P, one acting downward and the other upward. Determine the angle of rotation at the left-hand end, the deflection δ1 under the downward load, and the deflection δ2 at the mid point.
= (P)/(6EIL)(3La^2 - 2a^3 - aL^2), δ1 = -(Pa^2)/(6EIL)(L - 2a^2), δ2 = 0

Added by Robert V.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Penny Riley

01/09/2023

Step 1

Step 1: The angle of rotation at the left-hand end, $θ_B$, is given by the formula: $$θ_B = \frac{P}{6EIL}(3La^2 - 2a^3 - aL^2)$$ where: * P is the load * E is the modulus of elasticity * I is the moment of inertia * L is the length of the beam * a is the distance Show more…

Show all steps

Thanks for your feedback!

7. The simple beam AB shown in the figure supports two equal concentrated loads P, one acting downward and the other upward. Determine the angle of rotation $θ_B$ at the left-hand end, the deflection $δ_1$ under the downward load, and the deflection $δ_2$ at the mid point. a P B PA B a $$θ_B = \frac{P}{6EIL}(3La^2 - 2a^3 - aL^2), δ_1 = -\frac{Pa^2}{6EIL}(L - 2a)^2, δ_2 = 0$$