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INPUT   DATA

♥ EXAMPLE Of Input/Output

Title

Distance between supports, L		ft
Length of overhang, a		ft
Modulus of elasticity, E		106lb/in2
Area moment of inertia, I		in4
Force applied, F		lb

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OUTPUT   VARIABLES   &   GRAPHS

Variables	Values	Units
♦  Maximum Shear force, Vmax		lb	Graphs:  Shear force Vs Distance    Bending moment Vs Distance    Deflection Vs Distance
♦  Maximum Bending moment, Mmax		ft.lb
♦  Maximum Deflection, Dmax		in
♦  Distance of point of Dmax		ft
♦  Max upward Deflection, Du		in
♦  Location of Du		ft
♦  Reaction force, R1		lb
♦  Reaction force, R2		lb
♦  Slope angle, θ1		°
♦  Slope angle, θ2		°

Bending Of A Straight Elastic Prismatic Beam

Consider a simply-supported slender bar, having a double overhang and concentrated forces acting vertically and located at the each of the two free ends of the beam. The following equations describe the distribution of shear force, bending moment and deformation:

where
     F = applied force at the tip of each overhang
     L = distance between supports
     a = length of each overhang
     x = distance from left end of beam
     E = modulus of elasticity of beam material
     I = area moment of inertia of cross-sectional area about axis through centroid
     V = shear force
     M = bending moment
     D = deflection
     R₁ = vertical reaction at left support
     R₂ = vertical reaction at right support
     θ₁ = angle of slope at left support
     θ₂ = angle of slope at right tip

Tips

    ◊ Use link EXAMPLE Of Input/Output  to demo data entry expectations and results; you may edit & use it as starting point

BIBLIOGRAPHY

• Brown TH; Marks' Calculations for Machine Design; McGraw Hill, New York, 2005, Chapter 2.
• Hicks TG; Mechanical Engineering Formulas, Pocket Guide; McGraw Hill, New York, 2003, Section 3.
• Young WC & Budynas RG; Roark's Formulas for Stress and Strain; 7th Edition, McGraw Hill, New York, 2002, Chapter 8.
• Gieck K & Geick R; Engineering Formulas, 7th Edition, McGraw Hill, New York, 1997, Section P.