Where is the maximum deflection for a simply supported beam with a point load?

The maximum deflection occurs at x = a when the point load is not at midspan, and at midspan when a = L/2. The calculator reports |y|max and its location.

What sign convention do you use?

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

What 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.

Do boundary conditions match a simple support?

Yes. End deflections are zero; end rotations are generally nonzero and reported as θ1 and θ2.

AmesWeb

Simply Supported Beam — Point Load at Position a

Downward point load P applied at distance a from the left support on a simply supported beam of length L. Shear/deflection are positive upward; moments are positive when top fibers are in compression.

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 load P * Unit: lbf

Beam length L Unit: ft

Load position a (from left) 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 ≤ a ≤ 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

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

Need multiple loads or more load types?

This page solves a single point load case. For multiple point loads, applied moments, UDL segments, and varying (trapezoidal) loads, use the main calculator: