Structural Beam
A structural beam is a horizontal or inclined load-bearing member that resists transverse loads primarily through bending and shear, transferring forces from the loaded surface to the supports at its ends or along its length. Beams develop internal bending moments and shear forces that determine the distribution of tensile and compressive stresses across the cross-section, with the neutral axis experiencing zero direct stress. Beams are among the most fundamental structural elements and are constructed from steel, reinforced concrete, prestressed concrete, timber, or aluminium depending on the application.
Key Formula
Bending stress = (Bending moment × distance from neutral axis) / Second moment of area
LaTeX: \sigma = \frac{M \cdot y}{I}
| Symbol | Meaning | Unit |
|---|---|---|
| \sigma | Bending (flexural) stress at a point | MPa (N/mm²) |
| M | Bending moment at the cross-section | kN·m |
| y | Distance from neutral axis to the point of interest | mm |
| I | Second moment of area of the cross-section about the neutral axis | mm⁴ |
Worked Example
Problem
A simply supported rectangular timber beam (width b = 100 mm, depth d = 200 mm) carries a central point load of 10 kN over a span of 4 m. Calculate the maximum bending stress.
Solution
Step 1: Maximum bending moment (mid-span) = PL/4 = (10 × 4)/4 = 10 kN·m = 10 × 10⁶ N·mm. Step 2: Second moment of area: I = bd³/12 = (100 × 200³)/12 = 66.67 × 10⁶ mm⁴. Step 3: Distance to extreme fibre: y = d/2 = 100 mm. Step 4: Bending stress σ = My/I = (10 × 10⁶ × 100) / (66.67 × 10⁶) = 15 N/mm² = 15 MPa.
Answer
Maximum bending stress = 15 MPa (at the top and bottom fibres at mid-span)
Common Beam Cross-Section Types and Their Typical Applications
| Cross-Section | Material | Typical Span (m) | Key Advantage | Common Use |
|---|---|---|---|---|
| Rectangular solid | Timber / concrete | 2–8 | Simple to fabricate | Residential floors |
| I-section (ISMB) | Structural steel | 5–20 | High I/weight ratio | Industrial buildings |
| T-beam | Reinforced concrete | 4–12 | Slab acts as flange | Monolithic floor systems |
| Box section | Steel / concrete | 15–40 | High torsional stiffness | Bridges, cantilevers |
| Pre-stressed I-girder | Pre-stressed concrete | 20–50 | Eliminates tension cracks | Highway bridges |
| Hollow rectangular (RHS) | Steel | 4–15 | Clean aesthetic | Architectural frames |
Interactive Tools
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Related Terms
Structural Load
A structural load is any force or collection of forces that acts on a structure, causing internal stresses, deformations, or displacements within the members. Loads are classified by their nature (static or dynamic), their source (gravity, wind, seismic), and their duration (permanent or transient). Accurate load estimation is the foundation of structural design, ensuring that every member can safely resist the demands placed on it throughout the life of the structure.
Truss (structure)
A truss is a structural framework composed of straight members connected at their ends by joints (nodes), forming a series of triangular units that collectively carry loads by developing only axial tension or compression in each member, with no bending. The triangular geometry makes the truss one of the most efficient structural forms because it converts bending into purely axial forces, allowing slender members to span large distances with minimal material. Trusses are widely used in roof structures, bridges, transmission towers, and space frames in both steel and timber construction.
Structural Column
A structural column is a vertical compression member that transmits axial compressive loads from beams, slabs, and other upper-structure elements down to the foundation, and may also resist bending moments arising from lateral loads or eccentric loading. Columns are classified by their slenderness ratio (effective length divided by radius of gyration) into short columns, which fail by material crushing, and long (slender) columns, which fail by elastic or inelastic buckling before the material reaches its yield stress. In reinforced concrete design to IS 456, columns are also classified as axially loaded, uniaxially bent, or biaxially bent based on the combination of forces they carry.
The word "beam" comes from Old English "bēam" meaning a tree or piece of timber, reflecting the original use of timber logs as horizontal structural members. The modern engineering sense, expanded to include steel and concrete members, developed through the Industrial Revolution as iron and steel replaced timber in large-span structures.