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Beam Three Support Four Loads Equations and Calculator

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Beam Three Support four Loads, Moments, Shear and Reactions Equations and Calculator

Continuous beam of two equal spans - four concentrated loads, P, at third points of each span Calculator

Figure 1 Continuous beam of two equal spans

Preview: Beam Three Support Two Loads Calculator

Reactions:

Eq. 1
R₁ = (2/3) P

Eq. 2
R₂ = (8/3) P

Eq. 3
R₃ = (2/3) P

Shear forces:

Eq. 4
V₁ = (2/3) P

Eq. 5
V₂ = ±(4/3) P

Eq. 6
V₃ = - (2/3) P

Bending moments:

Eq. 7
M_max = -(1/3) P L , at R₂

Eq. 8
M₁ = (2/9) P L, at point of load

Eq. 9
M₂ = (1/9) P L, at point of load

Where

P = concentrated load, lbf (N)
L = beam length, in, (m)
R_{1, 2, 3} = reaction at support , lbf (N)
V_{1, 2, 3} = shear forces lbf, (N)
M_{1, 2, max} = bending moments, lb-in, (N-m)

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Source

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