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Concentrated Load Between Two Supports Equations and Calculator

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Beam Three Supports Concentrated Load between two supports, Moments, Shear and Reactions Equations and Calculator.

Continuous beam of two equal spans - concentrated load, P, at center of one span Calculator.

Figure 1 Continuous beam of two equal spans Indeterminate Beam

Preview: Beam Three Support Two Loads Calculator

Reactions:

Eq. 1
R₁ = (13/32) P L

Eq. 2
R₂ = (11/16) P L

Eq. 3
R₃ = -(3/32) P L

Shear forces:

Eq. 4
V₁ = (13/32) P L

Eq. 5
V₂ = -(19/32) P L

Eq. 6
V₃ = (3/32) P L

Bending moments:

Eq. 7
M_max = (13/64) P L , at point of load

Eq. 8
M_R -(3/32) P L , at support of load

Eq. 9
δ = ( 0.96 P L³ ) / ( 64 E I ) at Eq. 9a
Eq. 9a
x = 0.48 L

Where

P = Concentrated load, lbf/in (N/m)
L = beam length, in, (m)
x = location, in (m)
R_{1, 2, 3} = reaction at support , lbf (N)
V_{1, 2, 3} = shear forces lbf, (N)
M_{R, max} = bending moments, lb-in, (N-m)
δ = deflection, in, (m)
E = modulus of elasticity, psi, (Pa)
I = area moment of inertia in⁴, (m⁴)

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Source

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