M = maximum bending moment, in.-lbs. P = total concentrated load, lbs. R = reaction load at bearing point, lbs. V = shear force, lbs. W = total uniform load, lbs. w = load per unit length, lbs./in. Δ = deflection or deformation, in. x = horizontal distance from reaction to point on beam, in. List of Figures
Fixed End Moments . Title: Microsoft Word - Document4 Author: ayhan Created Date: 3/22/2006 10:08:57 AM
Beams –SFD and BMD: Example (1) • Draw the SFD and BMD. • Determine reactions at supports. • Cut beam at C and consider member AC, V P 2 M Px 2 • Cut beam at E and consider member EB, V P 2 M P L x 2 • For a beam subjected to concentrated loads, shear is constant between loading points and moment varies linearly Maximum BM occurs The beam is supported at each end, and the load is distributed along its length. A simply supported beam cannot have any translational displacements at its support points, but no restriction is placed on rotations at the supports. Fig:1 Formulas for Design of Simply Supported Beam having Uniformly Distributed Load are shown at the right
Fixed End Moments . Title: Microsoft Word - Document4 Author: ayhan Created Date: 3/22/2006 10:08:57 AM From simple physics, this means that the sum of the forces in the y direction equals zero (i.e. the total downward forces equal the total upward forces). A second formula to remember is that the sum of the moments about any given point is equal to zero. This is because the beam is static and therefore not rotating. Beam Deflection and Stress Formula and Calculators Engineering Calculators . Area Moment of Inertia Equations & Calculators . Structural Beam Deflection, Stress, Bending Equations and calculator for Beam Supported on Both Ends Loaded at any Location. Points of zero shear (V = 0) — for moment diagrams only. Important features to remember when drawing the diagram: Concentrated forces cause an instant jump in shear. Concentrated moments cause an instant jump in moment. Order increases from load to shear to moment (that is, 1st order load diagram, 2nd order shear, 3rd order moment).