Steel Beams: Flexure and Shear - Concept Map
Steel Beam Design: Flexural and Shear Strength
Related concepts
Flexural Strength (Bending Capacity)
Sub concepts
- Plastic Moment Capacity
- Lateral-Torsional Buckling
- Unbraced Length Limits
- Section Compactness
- Moment Gradient Factor
Relationship to central
Primary limit state; determines moment-carrying ability of beam
Shear Strength
Sub concepts
- Web Shear Area
- Web Slenderness
- Shear Stress Distribution
- Resistance Factor
Relationship to central
Secondary limit state; determines shear-carrying capacity of web
Section Classification
Sub concepts
- Compact Sections
- Non-Compact Sections
- Slender Sections
- Width-to-Thickness Ratios
Relationship to central
Governs which failure mode controls; affects design equations
Lateral Bracing
Sub concepts
- Limit Length Lp
- Limit Length Lr
- Bracing Spacing
- Brace Stiffness Requirements
Relationship to central
Critical design parameter; controls LTB and limits unbraced length
Material Properties
Sub concepts
- Yield Strength Fy
- Modulus of Elasticity E
- Radius of Gyration ry
- Steel Grade (ASTM A36, A992)
Relationship to central
Input parameters for all strength calculations
Design Equations & Factors
Sub concepts
- Resistance Factors
- Safety Factors (ASD)
- Effective Length Factor
- Moment Coefficient Cb
Relationship to central
Quantitative framework per AISC 360 and NSCP 2015
Concept connections
- Plastic Moment CapacitySection CompactnessPlastic moment Mn = Mp × Fy × Zx is only achieved if the section is compact and can develop full inelastic strains without local buckling
- Lateral-Torsional BucklingUnbraced Length LimitsLTB occurs when unbraced length exceeds Lp; limit lengths Lp and Lr define the transition between full plasticity, inelastic, and elastic buckling
- Unbraced Length LimitsLateral BracingBraces placed at spacing ≤ Lp prevent LTB and allow full plastic moment; spacing must be calculated based on section properties and steel grade
- Moment Gradient FactorLateral-Torsional BucklingCb factor increases flexural strength when moment distribution is non-uniform; maximum value is capped at Mp to avoid unconservative results
- Web Shear AreaShear StrengthShear capacity Vn = 0.6 × Fy × Aw; web area Aw = d × tw is the primary geometric parameter in shear resistance
- Web SlendernessShear StrengthWeb slenderness ratio h/tw determines the shear coefficient Cv; stocky webs (Cv = 1.0) are simpler; slender webs require iterative calculation
- Material PropertiesPlastic Moment CapacityYield strength Fy directly multiplies plastic modulus Zx; higher steel grade increases moment capacity proportionally
- Material PropertiesUnbraced Length LimitsLp = 1.76 × ry × √(E/Fy) depends on yield strength, modulus, and section geometry; higher Fy increases LTB vulnerability
- Resistance FactorsFlexural StrengthDesign strength φb × Mn (LRFD) or Mn/Ωb (ASD) applies safety factors per AISC 360 and NSCP 2015; φb = 0.90 for most cases
- Resistance FactorsShear StrengthDesign shear strength φv × Vn applies resistance factor; φv = 1.0 for rolled I-shapes, 0.90 for others
- Section ClassificationFlexural StrengthCompact sections reach Mp; non-compact sections have reduced capacity; slender sections may be governed by local buckling rather than flexure
- Flange CompactnessLocal BucklingFlange width-to-thickness ratio λ = b/2tf; if λ > λp, flange may buckle locally, limiting stress to less than Fy
- Web CompactnessLocal BucklingWeb slenderness λ = h/tw; if λ > λp, web may buckle locally; if λ > λr, strength is significantly reduced
- Plastic Moment CapacityShear StrengthIn combined bending and shear, both limit states must be checked; shear rarely governs for rolled sections but becomes important near supports
- AISC 360Design Equations & FactorsAISC 360-16 (or latest) provides standard equations, resistance factors, and procedures for calculating flexural and shear strength of steel members
- NSCP 2015Design Equations & FactorsNSCP 2015 adopts AISC specifications for Philippine civil engineering practice; provides local design methodology and load factors
Diagrams
Steel Beams: Flexure and Shear - Complete Concept Hierarchy
Complete hierarchical mind map showing all major concepts in steel beam design for flexure and shear, organized by topic area with sub-concepts at multiple levels. This represents the full knowledge structure for the chapter.
Flexural Strength Determination Process
Step-by-step flowchart for determining flexural strength, showing decision points for section compactness, unbraced length, and lateral-torsional buckling. Guides the engineer through the complete design process.
Shear Strength Determination Process
Systematic flowchart for shear strength calculation, determining web area, slenderness classification, and applying appropriate reduction factors per AISC 360.
Unbraced Length Limits (Lp and Lr) Determination
Detailed procedure for calculating limit lengths Lp and Lr, which are critical thresholds determining whether a beam reaches plastic moment or suffers lateral-torsional buckling.
Flexural Behavior States Based on Unbraced Length
State diagram showing the three fundamental behavioral states of a steel beam as unbraced length increases, illustrating transitions between fully yielding, inelastic buckling, and elastic buckling regimes.
Design Considerations Distribution
Approximate distribution of design effort and code provisions for steel beam design, highlighting that flexural strength is the primary concern, with LTB being a major consideration and shear typically secondary.
Section Compactness Classification
Hierarchical classification system for determining if a steel section is compact, non-compact, or slender based on element width-to-thickness ratios, which directly affects flexural strength calculation.