The equation method is one type of the procedures in determining the shear and moment of beams. Although longer than the other method, the equation method can identify the point of inflection (point of zero V) along the beam.
HOW TO WORK WITH EQUATION METHOD
- With a given beam of certain loading, solve for the support reactions using the equilibrium equations.
- The equation method requires to place a cutting plane at every segment of load change.
- After a cutting plane has been located, decide if the left of the right side of the beam is to be analyzed. Usually the length of the cut segment is designated as x.
- Place the shear, V and moment, M at the cut. Most of the cases assume positive shear and positive moment.
- Apply equilibrium equations to determine the equation for shear, V, of a segment and its bending moment, M.
- Draw the shear and moment diagram with these equations.
HOW TO DRAW THE SHEAR AND MOMENT DIAGRAM
The shear diagram will be drawn similar with the moment diagram. That is by planting the x-values for the equations derived. In cases where there are no x-values, that would imply constant shear. The values from the equations are used as coordinates to draw the diagrams. Connect these coordinates to come up with the shear diagram.
Moments on the other hand usually are drawn with curves.
Moments on the other hand usually are drawn with curves.
EXAMPLE 4.4.3. EQUATION METHOD: BEAM WITH RECTANGULAR LOADS AND CONCENTRATED LOADS
EXAMPLE 4.4.5. EQUATION METHOD: BEAM WITH TRIANGULAR AND RECTANGULAR LOADS
EXAMPLE 4.4.6. EQUATION METHOD: BEAM WITH TRIANGULAR, RECTANGULAR AND POINT LOADS
EXAMPLE 4.4.7. EQUATION METHOD: BEAM WITH TRAPEZOIDAL LOADS
EXAMPLE 4.4.8. EQUATION METHOD: BEAM WITH COMBINED LOADS
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