Related Resources: calculators

Beam Three Supports Uniform Load Deflections Equations and Calculator

Civil Engineering Resources
Structural Design Engineering Resources

Beam Three Supports Uniform Load, Moments, Shear, Reactions and Deflections Equations and Calculator

Continuous beam of two equal spans - uniformly distributed load of w in load/unit length Calculator

Figure 1 Continuous beam of two equal spans

Preview: Beam Three Support Two Loads Calculator

Reactions:

Eq. 1
R₁ = (3/8) w L

Eq. 2
R₂ = 1.25 w L

Eq. 3
R₃ = (3/8) w L

Shear forces:

Eq. 4
V₁ = (3/8) w L

Eq. 5
V₂ = ±(5/8) w L

Eq. 6
V₃ = - (3/8) w L

Bending moments:

Eq. 7
M_max = -(1/8) w L²

Eq. 8
M₁ = (9/128) w L²

Eq. 9
Maximum deflection:
δ = 0.00541[ ( w L⁴ ) / ( E I ) ],
Eq. 9a
at x = 0.4215 L

Eq. 10
δ = ( w / ( 48 E I ) ) ( L³ x - 3 L x³ + 2 x⁴),
Eq. 10a
at 0 ≤ x ≤ = L

Where

w = uniformly distributed load, lbf/in (N/m)
L = beam length, in, (m)
x = location, in (m)
δ = deflection, in (m)
R_{1, 2, 3} = reaction at support , lbf (N)
V_{1, 2, 3} = shear forces lbf, (N)
M_{1, max} = bending moments, lb-in, (N-m)
E = Modulus of elasticity lbs/in², (N/m²)
I = area moment of inertia in⁴, (m⁴)

Related

• Beam Three Support Four Loads Equations and Calculator
• Beam Three Support Two Loads Reactions Equations and Calculator
• Engineering Statics Equations and Basics Equation and Calculator
• Flat Plates Stress, Deflection Design Equations and Calculators
• Engineering Analysis
• 2D Static's Load Modeler and Calculator Create 2D static's model and solve for reaction forces.
• Online Simple Loads Static's 2D Modeler Calculator Simple Loads and Reactions 2D Static's Modeler Calculator
• Strength of Materials Basics and Equations | Mechanics of Materials
• Beam Deflection Calculator Supported on Both Ends Uniform Loading Deflection and Stress Stress, Deflection Equation and Calculator using total applied load and line load.
• Cantilevered Beam Deflection Equations and Calculator Deflection and Stress Structural Beam Deflection, Stress, Equations and calculator for a Cantilevered Beam with Load at Location Between Support and Load.
• Beam Stress Equations and Calculator for a Beam supported One End, Cantilevered Single Load at End Deflection and Stress Equations and Calculator for a Beam supported One End, Cantilevered at Defined Location and Single Load at End
• Stress Deflection Strain Calculator Beam Supported Tapering Load Applied Stress Deflection Strain Equations and Calculator Beam Supported Tapering Load Applied
• Beam Stress Deflection Calculator with Partial Tapering Loading Beam Deflection Calculator and Stress Equations for a Beam Fixed at Both Ends with Partial Tapering Loading.
• Beam Deflection Calculator and Stress Deflection Equations / Continuous Beam, with Two Unequal Spans, Unequal, Uniform Loads Beam Deflection Calculator Beam Stress Equations and calculator for a Continuous Beam, with Two Unequal Spans, Unequal, Uniform Loads.
• Distributed Load on the Horizontal Member Elastic Frame Deflections Equations and Calculator
• Lifting Boom, Davits Application and Design Equations

Source

Civil Engineering Reference Manual, Fifteenth Edition, Michael R. Lindeburg, PE