Can I add two or more point loads?

Yes. Use the + Add load button to add as many P–a rows as you like. The calculator superposes each load and updates reactions, diagrams, deflection, slope, and stress.

How are reactions computed for multiple point loads?

Reactions are the sum of each load’s contribution: R1 = Σ P_i (L − a_i)/L and R2 = Σ P_i a_i/L. End slopes are also sums by superposition.

Where does maximum moment occur with multiple loads?

Peak moments typically occur under one of the loads or at support regions. The chart highlights the envelope; you can evaluate M(x) at any position with the calculator.

What sign convention do you use?

Shear and deflection are positive upward; bending moments are positive when top fibers are in compression.

Which units are supported?

Global Force, Length, Moment, Stress, Slope, Modulus, and Inertia units are selectable with automatic conversion. Deflection length (y) and fiber distance c each have independent unit pickers.

AmesWeb

Simply Supported Beam — Two Point Loads

Use this free simply supported beam calculator to analyze multiple point loads placed anywhere along the span L. It returns reactions, shear, bending moment, slope, deflection, and bending stress. For a single point load version, see Simply Supported Beam — Point Load at Position a. If your loading is continuous, try Simply Supported Beam — Uniform Distributed Load (UDL).

Global units

Length

Force

Moment

Stress

Slope

E (modulus)

I (inertia)

Deflection length (y)

These selections apply to all inputs and results. Choose Force/Length first; other unit groups update automatically.

Input parameters

Point loads (P at position a)

P lbf	a (from left) ft	Action
		Remove

+ Add load

Beam length L Unit: ft

Report position x Unit: ft

Elastic modulus E Unit: ksi

Distance to extreme fiber c

Unit for c:

Second moment of area I Unit: in⁴

Use dot “.” as decimal separator.
0 ≤ aᵢ ≤ L and 0 ≤ x ≤ L.
Sign convention: shear/deflection positive upward; moments positive when compressing top fibers.

Need I? Try Sectional Properties Calculators.

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 (\|y\|max)	--- inch
Bending Stress @ x (σₓ)	--- psi
Max Bending Stress (σmax)	--- psi

Charts

The plots update after calculation.

Need more than two loads or distributed loads?

For any number of point loads, applied moments, UDL segments, and varying (trapezoidal) loads, use the main calculator: