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Design tools · Beams

Simply supported beam under uniformly distributed load

Instant results: deflection, bending moment and shear force. The formulas used are given below the calculator.

The calculator needs JavaScript. The formulas are given below.

Formulas

Maximum deflection
δmax=5 q L4384 E I\delta_{\mathrm{max}} = \frac{5\ q\ L^4}{384\ E\ I}
Minimum bending moment
Mmin=−q L28M_{\mathrm{min}} = -\frac{q\ L^2}{8}
Maximum shear force
Vmax=q L2V_{\mathrm{max}} = \frac{q\ L}{2}
Minimum shear force
Vmin=−q L2V_{\mathrm{min}} = -\frac{q\ L}{2}

Notations

  • EEmodulus of elasticity, in GPa
  • IIsecond moment of area of the cross-section, in cm⁴
  • LLeffective span, in cm
  • qquniformly distributed load, in kN/m