Simply Supported Beam Calculator
Analyze simply supported beams with point loads, uniform distributed loads (UDL), and applied couples. Calculate support reactions, peak midspan moment, and maximum elastic deflection.
M_max = (w·L²)/8, δ_max = (5w·L⁴)/(384EI)
Beam Master handles any combination of point loads, uniform distributed loads (UDL), varying loads (UVL), and applied moments with instant SFD, BMD, and deflection curves.
Standard Load Cases & Closed-Form Solutions
For standard symmetric configurations, the reactions are equal (R_A = R_B = wL/2 or P/2). The shear diagram is linear or step-wise, and the bending moment diagram forms a smooth symmetric parabola.
Engineering Formulas & Governing Equations
Maximum Bending Moment (Uniform Distributed Load w)
Equation 01Occurs exactly at midspan (x = L/2) where the shear force crosses zero.
Maximum Midspan Deflection (Uniform Load w)
Equation 02The standard theoretical formula for central downward displacement under uniform loading.
Maximum Bending Moment (Center Point Load P)
Equation 03Peak sagging moment directly beneath a concentrated load placed at x = L/2.
Maximum Midspan Deflection (Center Point Load P)
Equation 04Maximum elastic deflection for a midspan concentrated force.
Calculation Details & Clarifications
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