CELE Steel & Timber Design — Steel Compression MembersConcept Map

Concept

Elastic Buckling Stress

Sub Concepts

• Euler formula: Fe = π²E / (KL/r)²
• Effective length factor K
• Radius of gyration r
• Young's modulus E

Relationship To Central

Governs slender columns; derived from Euler theory

Concept

Critical Stress Fcr

Sub Concepts

• Inelastic buckling (stocky columns)
• Elastic buckling (slender columns)
• Transition slenderness ratio
• Imperfection reduction factor 0.877

Relationship To Central

Central design parameter; depends on slenderness ratio

Concept

Slenderness Classification

Sub Concepts

• Inelastic range: KL/r ≤ 4.71√(E/Fy)
• Elastic range: KL/r > 4.71√(E/Fy)
• Transition condition: Fy/Fe = 2.25
• Board-exam slenderness limit: KL/r ≤ 200

Relationship To Central

Determines which Fcr equation to use

Concept

Design Strength

Sub Concepts

• LRFD: φc·Pn = 0.90·Fcr·Ag
• ASD: Pn / Ωc = Fcr·Ag / 1.67
• Gross cross-sectional area Ag
• Resistance factors and safety

Relationship To Central

Capacity of compression member for LRFD and ASD

Concept

Buckling Modes

Sub Concepts

• Flexural (Euler) buckling
• Local buckling of slender elements
• Torsional buckling (open sections)
• Flexural-torsional buckling (singly symmetric)

Relationship To Central

Different failure modes for different cross-section types

Concept

Effective Length Factor K

Sub Concepts

• K = 0.5 (fixed–fixed, idealized)
• K = 0.7 (fixed–pinned)
• K = 1.0 (pinned–pinned)
• K = 2.0 (fixed–free cantilever)

Relationship To Central

Accounts for end-condition restraint; multiplier on unbraced length

Concept

NSCP 2015 & AISC 360 Standards

Sub Concepts

• Chapter F: Flexural Members
• Chapter E: Members subject to compression
• Limit states and load factors
• Quality control requirements

Relationship To Central

Design code references for Philippine engineering practice

Concept

Common Board-Exam Pitfalls

Sub Concepts

• Using wrong axis (smallest r governs)
• Confusing 0.658 base in inelastic equation
• Missing transition slenderness check
• Wrong resistance factor (0.90, not 0.65–0.75)

Relationship To Central

Critical errors to avoid in licensure examination

To

Critical Stress Fcr

From

Elastic Buckling Stress (Fe)

Strength

strong

Relationship

Fe is the baseline for calculating Fcr in both inelastic and elastic ranges; Fcr = 0.658^(Fy/Fe)·Fy (inelastic) or Fcr = 0.877·Fe (elastic)

To

Critical Stress Fcr

From

Slenderness Ratio KL/r

Strength

strong

Relationship

KL/r directly determines which Fcr formula applies and the magnitude of Fcr; larger KL/r yields smaller Fcr

To

Slenderness Classification

From

Transition Slenderness 4.71√(E/Fy)

Strength

strong

Relationship

Acts as the boundary between inelastic and elastic regimes; divides columns into stocky and slender categories

To

Design Strength Pn

From

Critical Stress Fcr

Strength

strong

Relationship

Design strength is directly proportional to Fcr; Pn = Fcr·Ag, then φc·Pn = 0.90·Fcr·Ag for LRFD

To

Slenderness Ratio KL/r

From

Effective Length Factor K

Strength

strong

Relationship

K is the multiplier in KL/r; different end conditions yield different K values (0.5 to 2.0), directly affecting slenderness

To

Transition Slenderness 4.71√(E/Fy)

From

Material Properties (Fy, E)

Strength

strong

Relationship

Both Fy and E are parameters in the transition formula; higher Fy or lower E shifts the transition point, changing inelastic/elastic boundary

To

Critical Stress Fcr

From

Buckling Modes

Strength

moderate

Relationship

Different buckling modes (flexural, torsional, flexural-torsional) have different governing stress equations; flexural is most common for symmetric sections

To

Design Strength Pn

From

Local Buckling

Strength

moderate

Relationship

If local buckling occurs before global buckling, a Q-factor reduction is applied to Fcr, reducing design strength

To

Design Strength Formula Pn = Fcr·Ag

From

NSCP 2015 / AISC 360

Strength

strong

Relationship

Code standards specify the critical stress formula, resistance factor φc = 0.90, and load factor methodology for design

To

Slenderness Ratio KL/r

From

Radius of Gyration r

Strength

strong

Relationship

r appears in the denominator of KL/r; smaller r (weak axis) yields larger KL/r and governs design

To

Design Strength Pn

From

Gross Area Ag

Strength

strong

Relationship

Pn is directly proportional to Ag; larger cross-section increases capacity but adds weight and material cost

To

Stocky Columns KL/r ≤ 4.71√(E/Fy)

From

Inelastic Buckling Formula

Strength

strong

Relationship

The parabolic equation Fcr = 0.658^(Fy/Fe)·Fy is used only in the inelastic range; applies to short, rigid members

To

Slender Columns KL/r > 4.71√(E/Fy)

From

Elastic Buckling Formula Fcr = 0.877·Fe

Strength

strong

Relationship

The 0.877 factor accounts for initial imperfections; applied only to slender columns in elastic regime

To

Serviceability & Constructability

From

Practical Limit KL/r ≤ 200

Strength

moderate

Relationship

Columns with KL/r > 200 are impractical, difficult to fabricate, sensitive to construction errors, and prone to excessive deflection

To

Design Strength Calculation

From

LRFD Method φc = 0.90

Strength

strong

Relationship

Resistance factor 0.90 reflects the reliability and variability of compression member behavior; directly multiplies Fcr·Ag to obtain design strength

To

Allowable Stress Calculation

From

ASD Method Ωc = 1.67

Strength

moderate

Relationship

Safety factor 1.67 divides nominal stress Fcr·Ag to obtain allowable load; inverse relationship to LRFD resistance factor

To

Correct Problem-Solving Strategy

From

Board-Exam Pitfalls

Strength

moderate

Relationship

Understanding common errors guides systematic checks: verify weak axis, confirm transition point, select correct Fcr formula, apply φc = 0.90, check KL/r ≤ 200