The main disadvantage of force method is its complexity increases as the degree of indeterminacy for our target structure is high. We may avoid this problem by using displacement method instead.
One of the approaches under displacement method is slope-deflection equations. To solve a beam using slope-deflection equation, the beam is first segmentized span by span, then they are classified based on the support conditions and presence of end moments. Suitable slope-deflection equation is then adopted for each of the unknown end moment, as our first step to solve for them.
Readily available fixed end moment (FEM) formula is used to determine the unknown FEM in the slope-deflection equation. Then, span end displacement is identified based on support uplift or settlement. Node rotation on the other hand, is dependent of the support condition.
After all the parameters are determined, we construct equilibrium equations containing all unknowns. We can calculate the unknowns by solving these simultaneous equations. After solving for internal moments, we can proceed with determining span end shear force using them. Following to this, support reactions can be determined at any time.
The following introduces the solution of continuous beam using slope-deflection equation. Watch the video above for full details.
Beam overview
Slope deflection equations based on span type
Implementation of slope deflection equation in the example
Fixed end moment formula
Application of FEM in the example
Elimination of span end displacement parameter
Simplification of equations based on boundary condition
Solution for simultaneous equations
Solution for internal moment
Calculation for span ends shear force
Solution for beam support reactions
0 Comments