CORE PRINCIPLES
What to establish first
- Load and support conditions establish shear-force and bending-moment diagrams.
- Bending stress depends on moment and section modulus.
- Deflection depends on stiffness EI and grows rapidly with span.
Beams & Structural Mechanics
Bending, shear, deflection, section properties and structural response.
MODULE OVERVIEW
Beams & Structural Mechanics in practical engineering work.
Beam calculations relate loads, reactions, shear, moment, stress and deflection. A member may satisfy stress limits but still be unsuitable because of deflection, buckling or connection behaviour.
DESIGN CONCEPTS
Terms worth checking
- Section modulus
- Second moment of area
- Boundary condition
Common applications: Machine bases · Support frames · Shafts and structural members
KEY RELATIONSHIP
Elastic bending stress
σ = M/Z
- M — bending moment, N·mm
- Z — elastic section modulus, mm³
- σ — nominal stress, MPa
Use the correct critical moment, section axis and material limit; this equation does not check instability.
WORKED EXAMPLE
Known values → substitution → interpretation
- Known values
- M = 25 kN·m; Z = 250,000 mm³
- Method
- Convert M to 25 × 10⁶ N·mm, then divide by Z
- Interpretation
- The nominal bending stress is 100 MPa.
KEY DESIGN CHECKS
Confirm the conditions behind the number
- Define the governing load case, duty cycle and required design life before using a simplified relation.
- Use compatible units and material data for the actual condition, temperature and manufacturing state.
- Compare the result with strength, stiffness, fatigue, safety, serviceability and applicable-code requirements.
COMMON ENGINEERING MISTAKES
Keep the model within its scope
- Applying elastic bending stress outside the assumptions shown on this page.
- Using a nominal condition while a peak, alternating, transient or environmental case governs the design.
- Treating a calculated value as a final component selection without checking interfaces, tolerances and the current governing standard.
AVAILABLE CALCULATORS
Select a calculator
RELATED RESOURCE
Open Beam Bending Stress Calculator
Check nominal stress with a live beam diagram and units.
Open related resource →REFERENCES & LIMITATIONS
Use this content as a transparent starting point
ReferenceS. Timoshenko and D. H. Young, Elements of Strength of Materials; applicable structural code controls design.ScopeRelationships are presented for the assumptions stated on this page and linked tool.Design reviewCheck material condition, loads, environment and the applicable current code.SafetyResults are educational/preliminary and do not certify safety or compliance.
RELATED ENGINEERING