Beam Elastic Stress vs Reviewed Allowable Calculator

How the beam elastic stress vs reviewed allowable calculator works

Axial stress magnitude in MPa is kN × 1,000 ÷ area in mm². Bending stress magnitude is kN·m × 1,000,000 ÷ section modulus in mm³. The conservative sum of these magnitudes estimates the largest combined extreme-fiber magnitude for the stated one-axis elastic comparison. Divide by the externally reviewed allowable for the displayed ratio.

This is not a code capacity check or safe beam-sizing tool. The user supplies compatible demands, area, correct-axis modulus and allowable; no code factors or material strengths are selected. Buckling, lateral stability, shear, fatigue, connections, support behavior and other limit states are excluded. A ratio below 100% is not structural approval, and there is no safe/pass badge.

Quantities use the stated units and finite bounded inputs. Whole purchases round up under the documented model; cost components round half-up to cents before totals are summed. Undefined ratios stay unavailable. π and logarithms use normal numeric precision. Display rounding does not alter the entered assumptions.

Worked example

10 kN over 1,000 mm² gives 10 MPa axial stress. A 10 kN·m moment over 100,000 mm³ gives 100 MPa bending stress. Their magnitude sum is 110 MPa, or about 73.333% of an illustrative reviewed 150 MPa allowable. At 20 kN·m, the sum becomes 210 MPa and the ratio 140%.

Sources and assumptions

The source material explains the underlying calculation or pricing structure. Entered prices, costs, schedules and scenario choices are your assumptions; this tool does not obtain supplier quotes or predict actual results.

• MIT OpenCourseWare: elementary linear-elastic beam stresses