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Beam Four Supports Three Concentrated Loads Calculator

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Beam Four Supports with Three Concentrated Loads Applied Supports, Moments, Shear and Reactions Equations and Calculator.

Continuous beam of three equal spans - concentrated load, P, at center of each span Calculator.

Figure 1 Continuous beam of three equal spans Shear and Moment Diagrams

Preview: Beam Three Support Two Loads Calculator

Reactions:

Eq. 1
R₁ = (7/20) P

Eq. 2
R₂ = (23/20) P

Eq. 3
R₃ = (23/20) P

Eq. 4
R₄ = (7/20) P

Shear forces:

Eq. 5
V₁ = (7/20) P

Eq. 6
V₂ = -(13/20) P

Eq. 7
V₃ = (13/20) P

Eq. 8
V₄ = -(7/20) P

Eq. 9
V₅ = P/2

Eq. 10
V₆ = -P/2

Bending moments:

Eq. 11
M_max = (7/40) P · L

Eq. 12
M₁ = -(3/20) P · L

Eq. 13
M₂ = 1/10

Where

P = Concentrated load, lbf/in (N/m)
L = beam length, in, (m)
a = distance, in (m)
b = distance, in (m)
R_{1, 2, 3, 4} = 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