Where does the distributed load act?

On the segment [a, a+b]. If a+b = L the load reaches the right support; otherwise it is an intermediate load.

What units should I use for w?

w is force per length (e.g., lbf/ft, N/m). The calculator converts units internally so inputs and results follow your selected units.

What sign convention is used?

Positive w acts downward (as drawn). Shear/deflection are positive upward. Moments are positive when the top fibers are in compression.

AmesWeb

Simply Supported Beam — Distributed Load (intermediate, linear wₐ→w_b)

The beam is simply supported at both ends. A distributed line load begins at position a and extends a length b, varying linearly from w_a at x=a to w_b at x=a+b. If a+b = L the load reaches the right support.

Simply supported beam with distributed load over [a, a+b], varying linearly from wₐ at x=a to w_b at x=a+b; reactions R1, R2 indicated.

Global units

Geometry length (L, a, b, x)

Force

Moment

Stress

Slope

E (modulus)

I (inertia)

Deflection length (y)

Extreme fiber distance (c)

Line load (w) Tip: For kN/m, enter as N/m or convert (1 kN/m = 1 N/mm).

These selections apply to all inputs and results on this page.

Input parameters

Distributed load at a (w_a) Unit: lbf/ft

Distributed load at end of segment (w_b at a+b) Unit: same as w_a

Beam length L Unit: ft

Start position of load a (from left support) Unit: ft

Length of loaded segment b Unit: ft

Report position x Unit: ft

Elastic modulus E Unit: ksi

Distance to extreme fiber c Unit: inch

Second moment of area I Unit: in⁴

Use dot “.” as decimal separator.
Positive w acts downward (as drawn).
Constraints: 0 ≤ a ≤ L, 0 ≤ b ≤ L, and a+b ≤ L.

Results

Parameter	Value
Reaction Force R₁	--- lbf
Reaction Force R₂	--- lbf
Shear @ x (Vₓ)	--- lbf
Max Shear (Vmax)	--- lbf
Moment @ x (Mₓ)	--- lbf·in
Max Moment (Mmax)	--- lbf·in
Slope @ x (θₓ)	--- radian
Max Slope (θmax)	--- radian
End Slope Left (θ₁)	--- radian
End Slope Right (θ₂)	--- radian
Deflection @ x (yₓ)	--- inch
Max Deflection (ymax)	--- inch
Bending Stress @ x (σₓ)	--- psi
Max Bending Stress (σmax)	--- psi

Charts

Moment, shear, slope, and deflection plots update after calculation.