FINAL TOOLBOX
01 // Chart Studio02 // Visual Solvers03 // Calculators04 // Formulas05 // Unicode & Symbols
03 // Bidirectional STEM Calculators // ENGINEERINGσ (MPa) = (F × L) / (4 × S)

Simply Supported Beam Bending Stress Calculator

For a simply supported beam of span L carrying a central point load F, the peak midspan bending moment M = FL/4 divided by the elastic section modulus S yields maximum outer-fiber flexural stress σ = (F × L) / (4 × S).

σ (MPa) = (F × L) / (4 × S)
Pick which value you want to calculate (or type into any field):Solving for: σ (MPa) — Peak Bending Stress (MPa)
Calculated

Maximum outer-fiber tensile/compressive stress in Megapascals

12,000.00
unit

Concentrated center load in Newtons

105,000,000.00

Distance between pin and roller supports in meters

0.150

Section modulus S = I / c in cm³ (1 cm³ = 10⁻⁶ m³)

0.5100,000.00
unit
Calculated Result · Peak Bending Stress (MPa) (σ (MPa))
125

Step-by-Step Calculation

01Canonical Law: σ (MPa) = (F × L) / (4 × S)
02Given Inputs (Base Units): F = 25,000 N, L = 4 m, S (cm³) = 200
03Solve for σ (MPa) (Peak Bending Stress (MPa)): σ (MPa) = 125

For a simply supported beam of span L carrying a central point load F, the peak midspan bending moment M = FL/4 divided by the elastic section modulus S yields maximum outer-fiber flexural stress σ = (F × L) / (4 × S).

Real-World Reference Values

ASTM A36 Yield Strength (F_y)250 MPa (Allowable ≈ 150 MPa)

ASD 0.60 F_y safety factor design limit

ASTM A992 Wide-Flange Steel345 MPa (Allowable ≈ 207 MPa)

Modern structural I-beam grade

6061-T6 Aluminum Yield276 MPa (Allowable ≈ 165 MPa)

Aerospace and marine structural alloy

20-Row Comparison Table

Peak Bending Stress (MPa) (σ (MPa)) · Midspan Point Load (F)

Simply Supported Beam Bending Stress Calculator — Midspan Point Load → Peak Bending Stress (MPa)
#Midspan Point Load (N)Peak Bending Stress (MPa) (σ (MPa))Δ %
0110 N0.05 -99.96%
0225,000.00 NCurrent125 0.00%
0375,008.80 N375.044 +200.04%
04112,508.20 N562.541 +350.03%
05150,007.61 N750.038 +500.03%
06187,507.01 N937.535 +650.03%
07225,006.41 N1,125.03 +800.03%
08262,505.81 N1,312.53 +950.02%
09300,005.21 N1,500.03 +1100.02%
10337,504.61 N1,687.52 +1250.02%
11375,004.01 N1,875.02 +1400.02%
12412,503.41 N2,062.52 +1550.01%
13450,002.82 N2,250.01 +1700.01%
14487,502.22 N2,437.51 +1850.01%
15525,001.62 N2,625.01 +2000.01%
16562,501.02 N2,812.51 +2150.00%
17600,000.42 N3,000.00 +2300.00%
18637,499.82 N3,187.50 +2450.00%
19674,999.22 N3,375.00 +2600.00%
20712,498.63 N3,562.49 +2749.99%
Was this tool helpful?

Frequently Asked Questions

How is Elastic Section Modulus S related to Moment of Inertia I?+

Section modulus equals S = I / c, where c is the vertical distance from the neutral axis to the extreme outer fiber (half the beam depth for symmetric I-beams).

How do I select a beam profile from an AISC steel table?+

Click SOLVE FOR on S (cm³), enter your design load F, span L, and allowable stress σ, then pick the lightest beam whose listed S_x exceeds the solved value.

Where does maximum bending stress occur on this beam?+

Peak bending moment M_max = FL/4 occurs directly under the midspan point load at the top (compression) and bottom (tension) flanges.