# Find shear and moment for simply-supported beam

Jonathan Ochshorn

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Directions: Enter values for loads and their positions along the beam, using any consistent units. To eliminate a load, set its magnitude to zero. Refer to the diagram for variable names. For example, use ft for distances; use either lb/ft and lb units, or kips/ft and kip units for loads; the reactions will be in either lb or kips; the shear will be in either lb or kips; and the moment will be in either ft-lb or ft-kips, depending on your choice. Loads are assumed to act in a downward direction, with reactions acting in an upward direction. Upward-acting loads should be entered as negative numbers; a negative reaction indicates that its direction is actually downward-acting rather than upward-acting. Positive moments are those corresponding to tension at the bottom of the beam; negative to tension at the top. Positive shear corresponds to a downward-acting force on the right side of a free-body diagram cut where the shear force is being measured; negative to an upward-acting force.

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More detailed explanations and examples can be found in my text.

Fig. 1. Beam geometry (lengths) and magnitude of loads

 Positions of loads and reactions (ft) Reaction positions Length Uniform load position Point load positions A B C D E F G H Loads (use kips/ft and kips or lb/ft and lb) w P1 P2 P3 Reaction at "a" Reaction at "b" Max pos. moment "" Max neg. moment Checks: sum Max pos. shear A=0 A=0 D0 H>0 G>F H>G F<>A & B G<>A & B H<>A & B