A B F C b a l x y R1 R2
Loaded Beam - Simple Support Ends [see Budynas p. 1015 and Machinery's Handbook 29th Ed. p. 257]:


\Delta_{b} = \frac{Fa^{2}b^{2}}{3EIl} \sigma_{a} = \frac{Faby}{Il} fos = \frac{\sigma_{yield}}{\sigma_{a}} 

R_{1} = \frac{Fb}{l} R_{2} = \frac{Fa}{l}

Length (l): Distance to load from A (a): Force (F):
Inches Inches Pounds
Material Properties: Table 1
Material Name Elastic Modulus (E) Yield Strength (\sigma_{yield})
ksi ksi
Beam Cross-Section Properties: (see also Table 3)
Beam Designation Area M. Inertia (I) Distance y, c or d
Inch4 Inch
Stress at point B: Deflection at B: Factor of Safety:
Psi Inches
Shear R1: Shear R2:
Pounds Pounds

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