Mechanics of Materials (MindTap Co...
Solutions
Mechanics of Materials (MindTap Co...
The continuous frame ABC has a pin support at /l, roller supports at B and C, and a rigid corner connection at B (see figure). Members AB and BC each have flexural rigidity EI. A moment M0acts counterclockwise at B, Note: Disregard axial deformations in member AB and consider only the effects of bending.
- Find all reactions of the frame.
Find the required new length of member BC in terms of L., so that
(a)
All the reactions of the frame.
Given Information:
The following figure is given with all relevant information,
Calculation:
Consider the following free body diagram,
Take equilibrium of horizontal forces as,
Take equilibrium of vertical forces as,
Take equilibrium of moments about B as,
The bending moment at distance x from A along AB in part AB is given by,
Use second order deflection differential equation,
Integrate above equation to get rotation as,
Integrate above equation to get rotation as,
The bending moment at distance x from B along BC in part BC is given by,
Use second order deflection differential equation,
  
(b)
Rotations at joints A, B and C.
(c)
Length of BC.
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