Write the differential equation of a beam subjected to uniformly distributed vertical load when one end is hinged the other is built-in.
Bending stiffness of the beam is EI.
Derive the deflection in the function of p and L.
(Neglect shear deformations.)
Solve Problem
Derive the deflection function.Solve
Check expression
Do you need help?
Steps
Step 2. Write the boundary conditions. Express the constants. The boundary conditions are: At the left support At the right support From the above conditions C3 and C4 can be expressed as: Step 3. Substitute the constants and give the deflection function.Step by step
Step 1. Write the differential equation of the bent beam and give the general solution.
Check differential equation
Check general solution
Check constants
Check result
Results
The general solution has the following form The boundary conditions are: At the left support At the right support From the above conditions C3 and C4 can be expressed as: Substituting the constants the deflection function results inWorked out solution
The differential equation of the bent beam is