Tension Members

Tension Members

$Learning Objectives$

Distinguish gross-section yielding from effective-net-section rupture.
Calculate net area for straight and staggered bolt-hole paths using the applicable hole dimensions.
Apply shear lag only within the connection geometry and specification provisions for which it is valid.
Evaluate block shear from explicit gross/net shear and net tension areas.
Separate member strength checks from connection bearing/tear-out checks.
Treat the commonly cited $L/r=300$ value as a preferred serviceability/detailing recommendation rather than a tension-strength limit.

$Tension Member$

A structural member whose principal force is axial tension, such as a truss chord, hanger, tie, or brace. A member may still require connection, fatigue, fracture, serviceability, and construction checks in addition to axial strength.

Available Tensile Strength

Gross-section yielding

Nominal strength for yielding of the gross cross-section.

P_n=F_yA_g

Variables

Symbol	Description	Unit
$F_y$	Specified yield stress	ksi or MPa
$A_g$	Gross area	in² or mm²

$Gross yielding factors$

For the AISC tension-member format commonly taught here: LRFD $\phi_t=0.90$ and ASD $\Omega_t=1.67$ . Always verify the adopted specification edition for project work.

Effective-net-section rupture

Nominal strength for tensile rupture through the effective net area.

P_n=F_uA_e

A_e=UA_n

Variables

Symbol	Description	Unit
$F_u$	Specified tensile strength	ksi or MPa
$A_n$	Net area through the governing fracture path	in² or mm²
$U$	Applicable shear-lag factor	-
$A_e$	Effective net area	in² or mm²

$Net rupture factors$

For the AISC tension-member format commonly taught here: LRFD $\phi_t=0.75$ and ASD $\Omega_t=2.00$ .

Net Area and Hole Deductions

$Use the actual code-defined hole deduction$

Do not memorize “bolt diameter plus 1/8 in” as a universal rule. Determine the applicable hole size from the governing connection standard/specification, then apply the net-area deduction required by the adopted AISC provision. For common standard holes this often produces familiar values, but oversized and slotted holes require different dimensions.

Straight net path

Net area for a flat plate through holes on the same transverse failure path.

A_n=A_g-\sum d_h t

Variables

Symbol	Description	Unit
$d_h$	Code-defined hole deduction for the failure path	in or mm
$t$	Thickness	in or mm

Staggered-hole net width

Net-width expression for a candidate zigzag fracture path.

w_n=w_g-\sum d_h+\sum\frac{s^2}{4g}

Variables

Symbol	Description	Unit
$s$	Longitudinal spacing between staggered holes	in or mm
$g$	Transverse gage between the same holes	in or mm

$The governing path must be searched$

The fracture path with the smallest valid net area controls. For staggered layouts, compare every plausible straight and zigzag path rather than assuming the visually shortest line controls.

$Fracture-path visualizer$

Use this visualization to understand why multiple fracture paths must be considered. Treat it as a path-exploration aid; final design uses the actual connection geometry and the adopted specification's hole deductions.

Interactive Net Area Calculator

Click on the bolt holes to simulate a potential fracture path. The calculator will automatically apply Cochrane's rule ( $s^2/4g$ ) for staggered bolts.

Assume 3/4" bolts. Hole diameter = 3/4" + 1/8" = 0.875".
Select a valid logical path (e.g., A-B is invalid for tension rupture as it's a vertical tear, choose A-C-D instead).

Path Calculation

Select holes on the plate to generate a fracture path.

Governing Path

In actual design, you must calculate the Net Area ( $A_n$ ) for all possible paths and select the smallest value to determine the governing design capacity for tension rupture.

Shear Lag

$Why shear lag occurs$

If only part of a cross-section is connected, stress is not transferred uniformly into every element at the connection. The effective net area is reduced by a shear-lag factor $U$ prescribed by the specification for the relevant connection configuration.

General shear-lag form used for applicable cases

Connection eccentricity and length influence load-transfer efficiency.

U=1-\frac{\bar{x}}{L}

$Do not use one U equation for every connection$

The general $1-\bar{x}/L$ relationship is not a universal replacement for the specification table/case requirements. W-shapes, tees, angles, plates, welded connections, and bolted connections can have specific limits and prescribed values. Identify the applicable case first.

Block Shear

Block shear nominal strength

Combined shear and tension failure along an explicit connection block.

R_n=\min\left(0.60F_uA_{nv}+U_{bs}F_uA_{nt},\;0.60F_yA_{gv}+U_{bs}F_uA_{nt}\right)

Variables

Symbol	Description	Unit
$A_{gv}$	Gross shear area	in² or mm²
$A_{nv}$	Net shear area	in² or mm²
$A_{nt}$	Net tension area	in² or mm²
$U_{bs}$	Block-shear tension stress factor for the applicable stress distribution	-

$Block shear must come from geometry$

Do not allow a calculator to invent a generic block. Establish the actual shear and tension planes around the bolt/weld group, calculate their gross/net areas, and only then evaluate the limit state.

Bearing and Tear-Out Are Connection Checks

$Local bearing/tear-out$

A tension member connected with bolts may also be limited by bearing or tear-out of the connected material at individual holes. These checks use clear distance in the direction of force, connected-part thickness, material tensile strength, hole type, and the applicable deformation criterion. They are evaluated as connection limit states in addition to member yielding/rupture.

Slenderness and Serviceability

$L/r=300$

For ordinary tension members, AISC has historically recommended limiting $L/r$ to about 300 as a preferred serviceability/detailing practice to control excessive flexibility, sag, vibration, and handling concerns. It is not a strength-reduction equation comparable to column buckling. Rods and similar tension-only elements may be treated differently under the applicable provision.

$Built-up tension members$

Built-up members require adequate interconnection so individual components work together and remain properly positioned. Connector spacing and component behavior are detailing/serviceability issues in addition to the overall member-strength checks.

$Pin-connected members and eyebars$

Pin-connected plates and eyebars require special checks for net-section rupture, shear on the material beyond the pin, bearing, geometric proportions, and other connection-specific limit states. Do not apply the ordinary bolted-plate model without the provisions governing pin-connected members.

Interactive Strength Calculator

$What this calculator does$

The calculator evaluates gross yielding and effective-net rupture directly. Block shear appears only when you explicitly supply $A_{gv}$ , $A_{nv}$ , and $A_{nt}$ ; hidden/default connection geometry can no longer control the result.

ksi

in²

Shear lag U

Include block shear

Gross-section yielding97.2 kips

Effective-net-section rupture92.4 kips

Governing modeled design strength92.4 kips

Block shear is not inferred from arbitrary geometry. It is included only when the actual gross/net shear and net tension areas are supplied. Connection bearing, bolt strength, slenderness/serviceability, and other project-specific limit states remain separate checks.

$Tension-member workflow$

Determine required tensile strength from the adopted load combinations.
Identify material properties and gross area.
Enumerate valid hole/fracture paths and determine governing $A_n$ .
Determine the applicable shear-lag case and $U$ .
Check gross yielding and effective-net rupture.
Construct and check every applicable block-shear path.
Check bolt/weld bearing, tear-out, bolt/weld strength, and other connection limit states.
Review serviceability, fatigue/fracture, built-up-member detailing, and special pin/eyebar provisions where applicable.
Select the lowest applicable available strength; do not compare nominal capacities using inconsistent resistance factors.

Key Takeaways

Gross yielding and effective-net rupture are distinct limit states with different resistance/safety factors.
Net area comes from the actual code-defined hole deduction and the governing valid fracture path.
Shear lag depends on connection configuration; one generic $U$ equation does not cover every case.
Block shear must be based on explicit connection geometry.
The commonly cited $L/r\le300$ value is a preferred serviceability/detailing recommendation, not a tension-member strength equation.

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Learning Objectives

Tension Member

Available Tensile Strength

Gross-section yielding

Gross yielding factors

Effective-net-section rupture

Net rupture factors

Net Area and Hole Deductions

Use the actual code-defined hole deduction

Straight net path

Staggered-hole net width

The governing path must be searched

Fracture-path visualizer

Interactive Net Area Calculator

Path Calculation

Governing Path

Shear Lag

Why shear lag occurs

General shear-lag form used for applicable cases

Do not use one U equation for every connection

Block Shear

Block shear nominal strength

Block shear must come from geometry

Bearing and Tear-Out Are Connection Checks

Local bearing/tear-out

Slenderness and Serviceability

L/r=300L/r=300L/r=300 is not a tensile-strength limit

Built-up tension members

Pin-connected members and eyebars

Interactive Strength Calculator

What this calculator does

Tension-member workflow

$Learning Objectives$

$Tension Member$

$Gross yielding factors$

$Net rupture factors$

$Use the actual code-defined hole deduction$

$The governing path must be searched$

$Fracture-path visualizer$

$Why shear lag occurs$

$Do not use one U equation for every connection$

$Block shear must come from geometry$

$Local bearing/tear-out$

$L/r=300$

$Built-up tension members$

$Pin-connected members and eyebars$

$What this calculator does$

$Tension-member workflow$