CELE Steel & Timber Design — Steel Tension MembersConcept Map

Concept

Tensile Strength Limit States

Sub Concepts

• Tensile Yielding on Gross Section (Ductile)
• Tensile Rupture on Net Section (Sudden)
• Design Strength Comparison & Controlling Limit State

Relationship To Central

Core design checks that govern member capacity; two competing failure modes must both be verified

Concept

Net Area Computation

Sub Concepts

• Gross Area & Hole Diameter Allowance
• Simple Net Area (Straight Path)
• Staggered Holes & Zig-Zag Paths
• Effective Net Area & Shear-Lag Factor
• Shear-Lag Coefficient U

Relationship To Central

Essential for rupture limit state; accounts for bolt-hole reductions and staggered-hole geometry

Concept

Strength Calculation Framework (LRFD)

Sub Concepts

• Resistance Factors (phi) by Limit State
• Nominal Strength Formulas
• Design Strength vs. Factored Demand
• Comparison of Yield vs. Rupture Capacities

Relationship To Central

Load and resistance factor design methodology; governs design practice in NSCP 2015 / AISC 360

Concept

Member Geometry & Connections

Sub Concepts

• Bolt Hole Spacing & Patterns
• Connection Type & Load Transmission
• Cross-Sectional Elements & Attachment
• Pitch, Gage & Stagger Definitions

Relationship To Central

Physical details that determine net area, shear lag, and effective strength

Concept

Slenderness & Serviceability

Sub Concepts

• Slenderness Ratio L/r ≤ 300
• Least Radius of Gyration
• Tension Member Buckling (Not a Design Limit)
• Practical Application & Code Compliance

Relationship To Central

Recommended limits to control sag, vibration, and aesthetic concerns (non-mandatory for tension)

Concept

Block Shear & Connection Failures

Sub Concepts

• Block Shear Definition & Mechanics
• Shear & Tensile Rupture Paths
• Design for Block Shear Capacity
• Connection Adequacy Check

Relationship To Central

Additional rupture mode at the connection zone; critical for bolted end connections

Concept

NSCP 2015 & AISC 360 Code Requirements

Sub Concepts

• LRFD Method & Load Factors
• Material Properties (Fy, Fu)
• Resistance Factor Definitions
• Code Compliance & Verification

Relationship To Central

Regulatory framework and design standards applicable in the Philippines and internationally

Concept

Design & Sizing Procedures

Sub Concepts

• Member Selection by Trial & Iteration
• Verification of Both Limit States
• Effective Area Adjustments
• Final Capacity Confirmation

Relationship To Central

Step-by-step methodology to select adequate tension members for prescribed loads

To

Tensile Rupture on Net Section

From

Tensile Yielding on Gross Section

Strength

strong

Relationship

Both are mandatory limit states; the lower design strength (φPn) governs the member's capacity and controls sizing

To

Tensile Yielding on Gross Section

From

Gross Area Ag

Strength

strong

Relationship

Gross area is the input parameter for the yield limit state; full cross-section assumed active

To

Tensile Rupture on Net Section

From

Net Area An

Strength

strong

Relationship

Net area (reduced by bolt holes) is the input parameter for the rupture limit state; failure occurs at holes

To

Net Area Computation

From

Staggered Holes & Zig-Zag Paths

Strength

strong

Relationship

Staggered arrangement requires checking multiple failure paths and using the s²/4g recovery term for diagonal segments

To

Effective Net Area Ae

From

Shear-Lag Factor U

Strength

strong

Relationship

U is multiplied by An to get Ae; accounts for non-uniform stress distribution in partially connected members

To

Shear-Lag Factor U

From

Member Geometry & Connections

Strength

strong

Relationship

Connection type (all elements vs. one leg bolted) directly determines U value; geometry dictates load transmission

To

Tensile Yielding on Gross Section

From

Resistance Factor 0.90 (Yield)

Strength

strong

Relationship

φ = 0.90 is applied to the nominal yield strength Pn = Fy × Ag to get design strength

To

Tensile Rupture on Net Section

From

Resistance Factor 0.75 (Rupture)

Strength

strong

Relationship

φ = 0.75 (lower than yield) is applied to the nominal rupture strength Pn = Fu × Ae to account for higher variability

To

Resistance Factors (phi)

From

NSCP 2015 & AISC 360 Code Requirements

Strength

strong

Relationship

Code specifies the φ values (0.90 for yield, 0.75 for rupture) to achieve consistent reliability margins

To

Member Sizing

From

Design Strength Comparison & Controlling Limit State

Strength

strong

Relationship

The lower of the two design strengths determines what section size is required; the controlling mode drives selection

To

Tension Member Buckling (Not a Design Limit)

From

Slenderness Ratio L/r ≤ 300

Strength

moderate

Relationship

Slenderness is recommended but not mandatory for tension; no buckling failure occurs, but limits sag and vibration

To

Net Area Computation

From

Bolt Hole Spacing & Patterns

Strength

strong

Relationship

Spacing parameters (pitch, gage, stagger) define the bolt pattern and determine which failure path is most critical

To

Staggered Holes & Zig-Zag Paths

From

Pitch, Gage & Stagger Definitions

Strength

strong

Relationship

Pitch (s) and gage (g) are the geometric inputs required to calculate the s²/4g recovery term for staggered holes

To

Shear-Lag Coefficient U

From

Load Transmission Path

Strength

strong

Relationship

How force flows through the member and connection determines whether shear lag occurs; full connection → U=1.0, partial → U<1.0

To

Tensile Rupture on Net Section

From

Block Shear & Connection Failures

Strength

moderate

Relationship

Block shear is an additional rupture mode at the connection zone; both tensile rupture (net area) and block shear must be checked

To

Limit States & Strength

From

Material Properties (Fy, Fu)

Strength

strong

Relationship

Fy (yield stress) and Fu (ultimate stress) are the input material parameters for both yield and rupture calculations

To

Member Sizing by Trial & Iteration

From

Design Process

Strength

strong

Relationship

Systematic procedure: select trial section → check yield → check rupture → verify slenderness → adjust if needed

To

Design & Sizing Procedures

From

Verification of Both Limit States

Strength

strong

Relationship

Design methodology requires checking both yield and rupture; both must be satisfied before design is complete

To

Net Area Computation

From

Hole Diameter dh and Clearance Allowance

Strength

strong

Relationship

Hole diameter includes bolt diameter plus clearance (typically 2–3 mm); directly subtracted from gross width to get net width

To

Design Strength vs. Factored Demand

From

LRFD Method & Load Factors

Strength

strong

Relationship

LRFD requires φ·Pn ≥ Pu (factored load); resistance factors and nominal strengths apply this safety format