Simply supported beam with a linear load patch.

Model a partial triangular or trapezoidal line load at any position on a simply supported span and see the resulting reactions, peak moment, and elastic movement.

transparent load model

Move the resultant, not just the load label.

The line load varies linearly from q₁ to q₂ over the loaded length b, beginning a metres from the left support. This covers the common triangular and trapezoidal patch cases without creating a separate page for every orientation.

Equations used

RESULTANTW = (q₁ + q₂)b/2

RESULTANT LOCATIONx̄ = a + b(q₁ + 2q₂)/(3(q₁ + q₂))

Support reactions follow from vertical equilibrium and moments about the supports: R_A = W(L - x̄)/L and R_B = Wx̄/L. The calculator then integrates the sectional moment curve to obtain the maximum positive moment and elastic deflection using EIv'' = M.

Assumptions and limits

One downward, non-negative triangular or trapezoidal patch on a prismatic simply supported beam.
Constant E and I, small deflection, Euler-Bernoulli bending, and no shear deformation.
No self-weight, load factors, support settlement, cracking, vibration, lateral stability, or code resistance checks.
Use the resulting actions as analysis inputs for a separate Eurocode or Hong Kong design check.

source trail

Classical beam response, declared clearly.

The load shapes and response conventions are informed by standard beam tables and the StructX beam-case index. CivilKits presents an original parameterized screen and does not reproduce source page text.