Final answer:
The question pertains to the calculation of rotation and vertical deflection in a structural system using various engineering methods, including static equilibrium equations, the energy method, the virtual work method, and solving a system of linear equations.
a) By utilizing the moment equilibrium equation
Step-by-step explanation:
The student's question is focused on calculating the rotation at a point (B) and the vertical deflection at another point (D) in a mechanical or structural system. There are multiple methods proposed for finding the solution: moment equilibrium equations, the energy method, the virtual work method, and the solution of a system of linear equations.
Step-by-step Approach Using Moment Equilibrium
- Determine the system of interest.
- Draw a free body diagram to identify all external forces and moments acting on the system.
- Apply the condition that the sum of moments (torques) about any point must be zero for static equilibrium (net T = 0).
- Solve for the unknowns using the equations obtained from the static equilibrium conditions.
Energy Method
- Identify all forces on the body.
- Calculate the work done by these forces during the body's deflection.
- Equate the total work done to the change in the system's potential and kinetic energy to find the deflection.
Virtual Work Method
- Apply a virtual displacement at point D.
- Calculate the work done by all forces through this virtual displacement.
- Equate the total virtual work to zero to solve for the deflection.
System of Linear Equations
- Write down the equilibrium conditions for the system.
- Formulate a system of linear equations based on the conditions of equilibrium.
- Solve the linear system to find the rotation at B and deflection at D.
a) By utilizing the moment equilibrium equation