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Calculate elastic and plastic section modulus for beams under bending loads
S = I / c (where I = moment of inertia, c = distance to extreme fiber)
Rectangular beams are common in wood construction. Simple to calculate but less efficient than I-beams for the same material volume.
| Designation | Depth (in) | Width (in) | Area (in²) | Sx (in³) | Zx (in³) |
|---|---|---|---|---|---|
| W4x13 | 4.16 | 4.06 | 3.83 | 5.46 | 6.28 |
| W5x16 | 5.01 | 5 | 4.71 | 7.51 | 8.68 |
| W6x16 | 6.01 | 6.02 | 4.71 | 9.72 | 11.17 |
| W6x25 | 6.38 | 6.08 | 7.34 | 16.7 | 19.32 |
| W8x18 | 8.07 | 5.25 | 5.28 | 15.2 | 17.4 |
| W8x35 | 8.12 | 8.02 | 10.3 | 42.6 | 48 |
| W10x49 | 10 | 8 | 14.4 | 54.6 | 60.4 |
| W12x65 | 12.12 | 8.08 | 19.1 | 87.9 | 96.8 |
| W14x90 | 14.02 | 8.04 | 26.5 | 127 | 141 |
| W16x100 | 16.97 | 10.42 | 29.4 | 175 | 194 |
Used for elastic design. Assumes linear stress distribution. Critical for steel beams designed to limit permanent deformation.
Used for plastic design. Allows material to yield. Approximately 10-30% higher than S. Critical for collapse analysis.
Ratio of plastic to elastic modulus. Rectangle: 1.5, I-Beam: 1.1-1.15, Circle: 1.27, Triangle: 2.0
Steel I-beams for floor systems and roof support
High-capacity beams designed for heavy live loads
Overhead cranes and support structures
Laminated beams for floor and roof support
Section modulus (S or Z) is a geometric property that measures a beam's ability to resist bending stress. It depends on the cross-sectional shape and dimensions. A larger section modulus means the beam can support greater bending moments without excessive stress.
Elastic section modulus (S) is used when stresses remain below the yield point, assuming linear stress distribution. Plastic section modulus (Z) accounts for the entire cross-section yielding and is typically 10-30% larger than S. Engineers use S for service-level design and Z for ultimate strength analysis.
Consider strength-to-weight ratio, material availability, cost, and construction requirements. I-beams offer excellent strength with minimal weight. Hollow sections are efficient but may be harder to fabricate. Solid rectangles are simple but less efficient. For a given strength requirement, I-beams use the least material.
Allowable stresses vary by material and code. Steel AISC typically allows about 55% of yield strength for simple bending (36 ksi steel: ~20 ksi allowable). Wood varies by species and grade. Always refer to applicable building codes (IBC, AISC, ACI, NDS) and local jurisdictional requirements for your project location.
Shape factor is the ratio Z/S. It represents how much reserve strength a beam has before yielding. A higher shape factor means more material can yield before failure. Rectangles have SF of 1.5, I-beams 1.1-1.15, circles 1.27, triangles 2.0. Values closer to 1.0 indicate more efficient shapes.
Yes, often deflection governs design more than stress. Typical limits are L/360 for floors and L/240 for roofs. Deflection depends on moment of inertia (I), not section modulus (S). A stiff, light beam requires large flange areas; a strong beam requires large section modulus. Both considerations matter.
Section modulus is purely geometric and doesn't change with temperature. However, material properties change: steel strength decreases with heat, wood weakens when wet. At elevated temperatures, you must reduce allowable stresses. This calculator assumes room temperature conditions—consult code tables for special cases.
Always consult a licensed structural engineer for buildings, bridges, or critical structures. This calculator is educational. Professional design requires accounting for shear, torsion, lateral loads, connections, material grades, and local building codes. Never use calculations alone for engineering decisions.
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This calculator is for educational and preliminary design purposes only. It does not account for all factors affecting real-world beam design (lateral bracing, shear, torsion, connections, fatigue, etc.). Always consult with a licensed structural engineer and follow applicable building codes for all projects. The designer is responsible for the accuracy and appropriateness of results.