CELE Steel & Timber Design — Steel Beams: Flexure and ShearConcept Map

Concept

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

Concept

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

Concept

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

Concept

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

Concept

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

Concept

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

To

Section Compactness

From

Plastic Moment Capacity

Strength

strong

Relationship

Plastic moment Mn = Mp × Fy × Zx is only achieved if the section is compact and can develop full inelastic strains without local buckling

To

Unbraced Length Limits

From

Lateral-Torsional Buckling

Strength

strong

Relationship

LTB occurs when unbraced length exceeds Lp; limit lengths Lp and Lr define the transition between full plasticity, inelastic, and elastic buckling

To

Lateral Bracing

From

Unbraced Length Limits

Strength

strong

Relationship

Braces placed at spacing ≤ Lp prevent LTB and allow full plastic moment; spacing must be calculated based on section properties and steel grade

To

Lateral-Torsional Buckling

From

Moment Gradient Factor

Strength

moderate

Relationship

Cb factor increases flexural strength when moment distribution is non-uniform; maximum value is capped at Mp to avoid unconservative results

To

Shear Strength

From

Web Shear Area

Strength

strong

Relationship

Shear capacity Vn = 0.6 × Fy × Aw; web area Aw = d × tw is the primary geometric parameter in shear resistance

To

Shear Strength

From

Web Slenderness

Strength

strong

Relationship

Web slenderness ratio h/tw determines the shear coefficient Cv; stocky webs (Cv = 1.0) are simpler; slender webs require iterative calculation

To

Plastic Moment Capacity

From

Material Properties

Strength

strong

Relationship

Yield strength Fy directly multiplies plastic modulus Zx; higher steel grade increases moment capacity proportionally

To

Unbraced Length Limits

From

Material Properties

Strength

strong

Relationship

Lp = 1.76 × ry × √(E/Fy) depends on yield strength, modulus, and section geometry; higher Fy increases LTB vulnerability

To

Flexural Strength

From

Resistance Factors

Strength

moderate

Relationship

Design strength φb × Mn (LRFD) or Mn/Ωb (ASD) applies safety factors per AISC 360 and NSCP 2015; φb = 0.90 for most cases

To

Shear Strength

From

Resistance Factors

Strength

moderate

Relationship

Design shear strength φv × Vn applies resistance factor; φv = 1.0 for rolled I-shapes, 0.90 for others

To

Flexural Strength

From

Section Classification

Strength

strong

Relationship

Compact sections reach Mp; non-compact sections have reduced capacity; slender sections may be governed by local buckling rather than flexure

To

Local Buckling

From

Flange Compactness

Strength

strong

Relationship

Flange width-to-thickness ratio λ = b/2tf; if λ > λp, flange may buckle locally, limiting stress to less than Fy

To

Local Buckling

From

Web Compactness

Strength

strong

Relationship

Web slenderness λ = h/tw; if λ > λp, web may buckle locally; if λ > λr, strength is significantly reduced

To

Shear Strength

From

Plastic Moment Capacity

Strength

weak

Relationship

In combined bending and shear, both limit states must be checked; shear rarely governs for rolled sections but becomes important near supports

To

Design Equations & Factors

From

AISC 360

Strength

strong

Relationship

AISC 360-16 (or latest) provides standard equations, resistance factors, and procedures for calculating flexural and shear strength of steel members

To

Design Equations & Factors

From

NSCP 2015

Strength

strong

Relationship

NSCP 2015 adopts AISC specifications for Philippine civil engineering practice; provides local design methodology and load factors