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Six Concentrated Loads Applied Equations and Calculator

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

Continuous beam of three equal spans - concentrated load, P, at third points of each span.

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

Preview: Beam Three Support Two Loads Calculator

Reactions:

Eq. 1
R₁ = (11/15) P

Eq. 2
R₂ = (34/15) P

Eq. 3
R₃ = (34/15) P

Eq. 4
R₄ = (11/15) P

Shear forces:

Eq. 5
V₁ = (11/15) P

Eq. 6
V₂ = -(19/15) P

Eq. 7
V₃ = (19/15) P

Eq. 8
V₄ = -(11/15) P

Eq. 9
V₅ = P

Eq. 10
V₆ = -P

Bending moments:

Eq. 11
M_max = -(12/45) P · L

Eq. 12
M₁ = (11/45) P · L

Eq. 13
M₂ = (7/45) P · L

Eq. 14
M₃ = (3/45) P · L

Where

P = Concentrated load, lbf/in (N/m)
L = beam length, in, (m)
R_... = reaction at support , lbf (N)
V_... = shear forces lbf, (N)
M_... = bending moments, lb-in, (N-m)

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Source

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