# 5.7 Practice Problems

- What are the assumptions of the Bernoulli-Euler beam theorem?
- Determine the slope $\theta(x)$ and deflection $\Delta(x)$ equations for the beam below using the direct integration method. Assume $EI$ is constant.

- Determine the slope $\theta(x)$ and deflection $\Delta(x)$ equations for the beam below using the direct integration method. Assume $EI$ is constant.

- For the beam shown below, determine the slope at midspan ($\theta_{mid}$), slope at point B ($\theta_B$), deflection at midspan ($\Delta_{mid}$) and deflection at point B ($\Delta_B$) using the moment area theorems.

- For the beam shown below, determine the slope to the left of the hinge at point B ($\theta_{B,left}$), slope to the right of the hinge at point B ($\theta_{B,right}$), deflection at point B ($\Delta_{B}$) and deflection at point D ($\Delta_D$) using the moment area theorems.

- For the beam shown below, determine the location and value of the maximum deflection using the moment area theorems. You must find and compare all potential local maxima and minima.

- For the beam shown below, determine the location and value of the maximum deflection using the moment area theorems. You must find and compare all potential local maxima and minima.

- Repeat problem 5 using the conjugate beam method.
- For the beam shown below, determine the slope and deflection at Point B ($\theta_B$, $\Delta_B$) and at point D ($\theta_D$, $\Delta_D$) using the conjugate beam method.

- For the beam shown below, determine the slope and deflection at Point B ($\theta_B$, $\Delta_B$) and at point C ($\theta_C$, $\Delta_C$) using the conjugate beam method.

- For the beam shown below, determine the minimum moment of inertia ($I$) such that its deflection does not exceed $\frac{L}{360}$.

- For the beam shown below, determine the minimum moment of inertia ($I$) such that its deflection does not exceed $\frac{L}{360}$. Use the length of each span (AB and BC) to calculate the maximum deflection for each.

- For the beam shown below, determine the deflection at point C ($\Delta_C$) using the virtual work method.

- For the beam shown below, determine the rotation at point A ($\theta_A$) and the deflection at point D ($\Delta_D$) using the virtual work method.

- For the beam shown below, use virtual work to determine the minimum moment of inertia ($I$) such that its deflection does not exceed $\frac{L}{360}$.

- For the beam shown below, use virtual work to determine the minimum moment of inertia ($I$) such that its deflection does not exceed $\frac{L}{360}$.

- For the frame shown below, determine the vertical deflection at point C ($\Delta_C$) using the virtual work method.

- For the frame shown below, determine the rotation and vertical deflection at point A ($\theta_A$, $\Delta_A$) using the virtual work method.

- For the frame shown below, determine the rotation at point D ($\theta_D$) and the horizontal deflection at point E ($\Delta_E$) using the virtual work method.

- For the truss shown below, determine the vertical deflection at point B ($\Delta_B$) and the horizontal deflection at point H ($\Delta_H$) using the virtual work method.

- For the truss shown below, determine the vertical deflection at point C ($\Delta_C$) and the vertical deflection at point F ($\Delta_F$) using the virtual work method.

- For the truss shown below, use virtual work to determine the minimum cross-sectional area ($A$) such that the horizontal deflection at point H ($\Delta_H$) does not exceed $\SI{20}{mm}$.

- For the truss shown below, use virtual work to determine the minimum cross-sectional area ($A$) such that the vertical deflection at point C ($\Delta_C$) does not exceed $\SI{35}{mm}$.

- For the truss from problem 20 but with no external loads, determine the horizontal deflection at point F ($\Delta_F$) if members AE, AB, BC and CG experience a temperature increase of $\SI{50}{\celsius}$ and member BF experiences a temperature decrease of $\SI{20}{\celsius}$ ($\Delta T = \SI{-20}{\celsius}$). Assume that $\alpha=\SI{1.2E-5}{/ \celsius}$.
- For the truss from problem 21 but with no external loads, determine the vertical deflection at point B ($\Delta_B$) if members BD, DF and AD were each fabricated $\SI{10}{mm}$ too short and member DE was fabricated $\SI{5}{mm}$ too long.