Point Load Analysis Calculator

Analyze beams with single or multiple point loads - reactions, moments, shear, and deflection.

Single Point Load at Center

M_max = PL/4 | R = P/2 | δ_max = PL³/48EI

Point Load (P)

Load Unit

Span (L)

Span Unit

E (psi) - Optional

I (in⁴) - Optional for deflection

Results

Maximum Moment

—

Reaction at Each Support (R) —

Max Shear (V) —

Max Deflection (δ) —

Deflection Ratio (L/δ) —

Deflection Limits:
Floor beams: L/360 (live) or L/240 (total)
Roof beams: L/180 to L/240
Cantilevers: L/180

Multiple Point Loads

Add multiple point loads at different positions along the beam.

Beam Span (ft)

Load (lb)

Position (ft from left)

No loads added yet

Results

Maximum Moment

—

Left Reaction (R_A) —

Right Reaction (R_B) —

Max Shear —

Moment Location —

Note: For multiple point loads, max moment typically occurs under one of the loads or between them. Check moment at each load location.

Off-Center Point Load

R_A = Pb/L | R_B = Pa/L | M_max = Pab/L

Point Load (P) - lbs

Total Span (L) - ft

Distance a (from left) - ft

E (psi)

I (in⁴)

Results

Maximum Moment (at load)

—

Left Reaction (R_A) —

Right Reaction (R_B) —

Distance b —

Max Deflection —

Deflection Location —

Note: For a ≤ L/2, max deflection occurs at x = √(L²-b²)/3 from the left support, not directly under the load.

Point Load + Uniform Load

Point Load (P) - lbs

Point Load Position (ft from left)

Uniform Load (w) - plf

Span (L) - ft

Results

Total Maximum Moment

—

Left Reaction (R_A) —

Right Reaction (R_B) —

Moment from Point Load —

Moment from Uniform Load —

Max Shear —

Superposition: Total effects = Point load effects + Uniform load effects. This works for linear elastic behavior.

Quick Reference - Simple Beam Formulas

Loading	Max Moment	Max Deflection	Location
Point @ Center	PL/4	PL³/48EI	Center
Point @ a from end	Pab/L	Pa(L²-a²)^1.5 / 9√3·EIL	Under load
Two Equal Points @ L/3	PL/3	23PL³/648EI	Center
Uniform Load	wL²/8	5wL⁴/384EI	Center
Triangular (max @ end)	wL²/12	0.01304wL⁴/EI	0.519L