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Beam Three Support Two Loads Reactions Equations and Calculator

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

Continuous beam of two equal spans equal concentrated loads, P, at center of each span Calculator

Figure 1 Continuous beam of two equal spans

Preview: Beam Three Support Two Loads Calculator

Reactions:

Eq. 1
R₁ = (5/16) P

Eq. 2
R₃ = (5/16) P

Eq. 3
R₂ = 1.375 P

Shear forces:

Eq. 4
V₁ = (5/16) P

Eq. 5
V₃ = - (5/16) P

Eq. 6
V₂ = ±(11/16) P

Bending moments:

Eq. 7
M_max = -(6/32) P L , at R₂

Eq. 8
M_P = (5/32) 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_{P, max} = bending moments, lb-in, (N-m)

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Source

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