CIV-35

Steel bending fb = M/S

fb = M / S. Allowable-stress snapshot; compare fb to 0.66 Fy (AISC ASD vintage).

Reading speed

Steelfb = M/S

Governing equation

f_b=M/S

$M \in \left[5, 800\right]$

where

M: Moment (kN·m)
S: Section modulus (cm^3)
f_b: Bending stress (MPa)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

f_b=M/S

$M \in \left[5, 800\right]$

$M = 5$ $f_b = 6250$

Along the curve

②

Domain of the variable — blue

M_{\min} = 5,\quad M_{\max} = 800

$M \in \left[5, 800\right]$

$M = 5$ $M = 5$

Along the curve

③

Response curve — green

f_b=M/S

$M \in \left[5, 800\right]$

$M = 5$ $f_b = 6250$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}f_b}{\mathrm{d}M}

$M \in \left[5, 800\right]$

$M = 10$ $f_b^{\prime} = 1250$

Along the curve

Lecture brief

Historical brief

From Euler’s 1744 elastica and Navier’s beam theory to Mohr’s circle and transformed-section RC, structural mechanics grew as a closed-form craft before finite elements. The lab keeps those governing lines for buckling, flexure, joints and influence. This sheet (CIV-35 — Steel bending fb = M/S) is the form associated with fb = M/S. Working symbols: $M$ , $S$ $\rightarrow$ $f_b$ . Elastic section modulus converts moment to extreme-fibre stress. Compact I-shapes stay elastic to Fy.

Purpose

Purpose: compute

f_b

from

M

S

in Structural & civil via

f_b=M/S

fb = M / S. Allowable-stress snapshot; compare fb to 0.66 Fy (AISC ASD vintage). Use it when a real structural & civil question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

M = 120.000\,\mathrm{kN·m}

S = 800.000\,\mathrm{cm^3}

, the governing relation

f_b=M/S

yields

f_b = 150000.00\,\mathrm{MPa}

. A steel I, a moment, a fibre stress. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Moment M120 kN·mSection modulus S800 cm^3

Outputs

Bending stress f_b150000.00 MPa

Reading speed

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Narration of this film

A steel I, a moment, a fibre stress.

Elastic section modulus converts moment to extreme-fibre stress. Compact I-shapes stay elastic to Fy.

Reading speed

Watch on YouTube