Design of Tension Members

Introduction

A tension member is a structural component subjected primarily to axial tensile force. Typical examples include tie rods, hangers, bracing members, truss diagonals, suspenders, and members of industrial frames. Although tension members do not normally suffer from overall buckling, their design is not automatically simple. Strength may be governed by gross-section yielding, net-section rupture, block shear, connection failure, or excessive deformation. In addition, the connection may reduce the effective strength of an otherwise adequate member.

This chapter presents a limit-state approach suitable for structural steel design. Numerical values and resistance factors vary among design standards; therefore, the governing national code must always be consulted. The equations below use a commonly adopted factored-resistance format similar to those used in modern steel specifications.

Learning Objectives

After completing this chapter, the student should be able to:

• identify rods, plates, angles, channels, and built-up tension members;
• distinguish gross area, net area, and effective net area;
• check yielding, rupture, block shear, and connection requirements;
• account for bolt holes, staggered holes, shear lag, and eccentricity;
• select suitable sections and connections for practical construction;
• interpret a complete tension-member design and communicate assumptions clearly.

1. Structural Behaviour of Tension Members

An ideal tension member carries a concentric axial force and develops nearly uniform tensile stress over its cross-section. The nominal average stress is

where P is axial force and A is the area normal to the force. The equation is an average-stress relationship, not a complete strength equation. Real members contain holes, threads, welds, changes in geometry, residual stresses, and connection eccentricities.

A tension member may reach one of several limit states:

1. Gross-section yielding: the full cross-section yields before fracture.
2. Net-section rupture: the reduced section through holes or other discontinuities fractures.
3. Block shear: a block of material tears out through combined tension and shear planes near a connection.
4. Connection failure: bolts, welds, gusset plates, or connected elements fail.
5. Excessive elongation or vibration: serviceability becomes unacceptable even when strength is adequate.

The design resistance is the smallest resistance associated with all applicable limit states.

Gross and Net Areas

The gross area, A_g, is the total cross-sectional area before deducting holes. The net area, A_n, is the gross area less the area removed by holes along a potential fracture path. For a plate of thickness t and width b, with one transverse line of bolt holes of diameter d_h,

where n is the number of holes on the section. The hole diameter used in design is the code-specified design hole diameter, which may exceed the nominal bolt diameter to allow for clearance and fabrication tolerances.

For staggered holes, the net width along a failure path is commonly calculated as

where s is the longitudinal stagger pitch and g is the transverse gauge. The summation extends over the holes crossed by the fracture path. The stagger term increases the net width because the fracture path is inclined rather than straight. The formula applies to standard bolted patterns under the assumptions of thin-plane geometry and the code’s prescribed hole arrangement.

The effective net area, A_e, accounts for nonuniform force transfer caused by shear lag:

where U is the shear-lag factor, with 0 < U ≤ 1. The factor is determined from the design standard based on member type, connection length, connected elements, and weld or bolt arrangement.

2. Design Philosophy and Limit States

For factored-load design, the basic requirement is

where P_u is the factored axial tension, R_n is nominal resistance, and φ is the resistance factor. In a partial-factor format, the equivalent requirement is R_d ≥ P_d, where R_d is design resistance and P_d is design action. The designer must not mix factors from different standards.

For a conventional steel tension member, the principal member resistances are:

2.1 Gross-Section Yielding

Thus, the factored yielding resistance is

where F_y is specified yield stress. This limit state controls ductility and prevents excessive overall yielding. It is based on the gross area because yielding begins across the complete section away from holes.

2.2 Net-Section Rupture

and

where F_u is specified ultimate tensile stress. The effective area must reflect the actual force-transfer mechanism. Using A_n without shear-lag adjustment can overestimate strength when only part of a section is directly connected.

2.3 Block Shear

Block shear is a combined failure involving tension on one plane and shear on one or more planes around a connection. A commonly used nominal-resistance model is

where A_nv is net shear area, A_nt is net tension area, and A_gv is gross shear area. The exact equation and resistance factor are code-dependent. The first expression represents fracture on the shear and tension planes; the second represents yielding on the gross shear planes combined with tension fracture. The relevant failure path must be identified geometrically rather than selected mechanically.

3. Member Types and Their Design Considerations

Rods and Bars

Round rods are efficient for small tensile forces and are commonly used in bracing and hangers. Threaded portions have a reduced tensile area. For a threaded rod, design should use the code-defined tensile-stress area, not the gross shank area, when rupture through the threaded portion is possible. Connections may use clevises, turnbuckles, nuts, or welded end details. Nuts and washers must be compatible with the rod grade and thread system.

Plates and Flat Bars

Plates are simple and economical for tension, but bolt holes can substantially reduce net area. Slender plates may distort, vibrate, or buckle out of plane under accidental compression or load reversal. Edge distances, pitch, tear-out, and connection eccentricity are important.

Angles

Single angles are frequently used in trusses and bracing. Their centroid is offset from one leg, so a connection through one leg generally introduces eccentricity. The connected leg carries load directly while the outstanding leg transfers force through shear. Shear lag may therefore be significant. Double angles can improve symmetry and reduce eccentricity.

Channels, Tees, and I-Shapes

These sections are useful when a larger area or greater connection width is needed. If only one flange or web is connected, the effective-net-area factor must reflect incomplete force transfer. Connection detailing should avoid unnecessary eccentricity and local distortion.

Built-Up Tension Members

Built-up members may consist of two angles, plates, channels, or latticed components. Components must be connected sufficiently to act together and to prevent independent movement. Bolted or welded battens, tie plates, or lacing may be required. The design must consider the force in individual components, load sharing, splice forces, and the possibility of load reversal.

4. Connection Design Requirements

A tension-member design is incomplete until its connection is designed. The connection must transfer the required force without failure of the fasteners, connected material, or connecting element.

Bolted Connections

Important checks include:

• bolt shear;
• bolt tension, when applicable;
• bearing and tear-out of connected material;
• net-section rupture;
• block shear;
• slip resistance where a slip-critical connection is specified;
• adequate pitch, gauge, end distance, and edge distance.

The design hole diameter must be used in net-area calculations. Minimum spacing and edge distances are governed by the applicable steel code and fabrication requirements. Excessively small edge distance can cause tear-out; excessive spacing can permit local distortion and reduce connection effectiveness.

Welded Connections

Welded tension connections require checks for weld-metal strength, base-metal strength, effective throat, weld length, and stress distribution. Fillet-weld resistance depends on effective throat, weld length, and the design strength of the weld metal or connected material, as specified by the code. Long welds may produce nonuniform force transfer and shear lag. Intermittent welds are generally unsuitable where continuity, corrosion protection, or fatigue resistance requires a continuous connection.

Eccentricity

If the line of action of the member force does not pass through the centroid of the connected section, the connection carries axial force plus moment. For an eccentricity e, the additional moment is

This moment may increase bolt-force variation, weld stress, and local bending. Symmetrical connection layouts are therefore preferred whenever practical.

5. Shear Lag and Effective Net Area

Shear lag occurs when force is introduced into only part of a cross-section. The connected portion begins carrying force directly, while the remaining portion is engaged through shear along the connection. Stress is consequently nonuniform near the connection.

The effective-net-area approach replaces the actual nonuniform distribution by an equivalent uniformly stressed area:

Typical code provisions assign higher U values to long, symmetrical connections and lower values to short, eccentric, or partially connected details. The value should not be guessed. It should be obtained from the applicable code provisions or a justified analytical method. The connection length, measured in the direction of force, is often a governing parameter.

Shear lag is especially important for single angles connected through one leg, tees connected through a flange or web, and plates connected over only part of their width. A larger gross area does not necessarily produce a larger design resistance if the connection is inefficient.

6. Design Procedure

A systematic design procedure is as follows:

1. Establish the factored tensile force and service-load requirements.
2. Select a preliminary member based on required gross area and constructability.
3. Determine material properties F_y and F_u.
4. Select a connection type and layout.
5. Calculate gross area, net area, and effective net area.
6. Check gross-section yielding.
7. Check net-section rupture, including shear lag.
8. Check block shear where a bolted or otherwise discontinuous connection exists.
9. Design bolts, welds, gusset plates, washers, end fittings, and splice details.
10. Check serviceability, corrosion protection, fatigue, handling, erection, and possible load reversal.
11. Confirm that the smallest factored resistance exceeds the factored demand.

A useful design table is:

7. Worked Example: Bolted Plate Tension Member

Problem

Design-check a 100 mm × 10 mm steel plate connected by two lines of bolts. Assume a factored tension P_u = 300 kN, F_y = 250 MPa, F_u = 400 MPa, design hole diameter d_h = 22 mm, and shear-lag factor U = 0.90. Use illustrative resistance factors φ_y = 0.90 and φ_u = 0.75. Check gross yielding and net rupture. Block shear and the bolts must also be checked separately.

Solution

Gross area:

Gross-yielding resistance:

Therefore, gross yielding does not resist the required 300 kN.

Assume the critical transverse section crosses two holes. Net area:

Effective net area:

Net-rupture resistance:

The plate fails both checks for the specified demand, and rupture is the smaller resistance. Increasing the plate width or thickness, reducing the number of holes on the critical path, improving the connection arrangement, or selecting a stronger material may be considered. However, improving U alone cannot overcome the inadequate gross area in this example. A complete redesign must also check block shear, bolt strength, bearing, edge distances, and the gusset plate.

Design Interpretation

The example demonstrates that a member can have a substantial gross area yet possess a much smaller effective net area. It also shows why member selection and connection design must proceed together. If the plate thickness is increased to 16 mm while retaining the same width and hole pattern, the gross-yielding resistance becomes

and the net-rupture resistance becomes

Thus, the revised plate still fails the 300 kN rupture requirement. A wider plate, fewer holes, a different connection arrangement, or a larger effective connection is needed. This illustrates an important design principle: solving one limit state does not guarantee that the governing limit state has been solved.

8. Illustrative Case Study: Bracing Connection in a Construction Hall

Background

A steel construction hall uses diagonal bracing to resist wind actions. An initial design specifies a single angle connected through one leg to a gusset plate with a short row of bolts.

Problem

The gross-area calculation indicates adequate yielding resistance, but the connection is eccentric and only one angle leg is directly connected. The engineer must determine whether the proposed member is adequate.

Analysis and Approach

The design team calculates the net area through the bolt holes and applies the code shear-lag provision for a single angle. Block shear is checked around the bolt group, while bolt shear, bearing, and gusset-plate yielding are also evaluated. The team then compares the single-angle detail with two alternatives: a double-angle connection and a welded end connection.

Solution and Outcome

The single angle has adequate gross yielding resistance but inadequate effective-net-section rupture resistance because its U factor is low. Block shear is also close to the factored demand because the end distance is short. The selected solution uses two angles connected on opposite sides of the gusset, a longer bolt group, and increased end distance. The symmetric detail improves force distribution and reduces eccentricity. The final design satisfies member, connection, and constructability requirements.

Learning Points

• Gross area alone is not a sufficient design measure.
• Connection geometry directly affects member resistance.
• Symmetry reduces eccentricity and can improve effective force transfer.
• A code-compliant design must include the gusset and fasteners, not only the principal member.
• Constructability, inspection access, corrosion protection, and erection sequence influence the final detail.

9. Serviceability, Durability, and Professional Practice

Tension members may experience noticeable elongation. Elastic elongation of a prismatic member is approximated by

where ∆ is elongation, L is member length, E is Young’s modulus, and the force and area are consistent. The equation assumes elastic, uniform axial behaviour and neglects connection deformation. Excessive movement can damage cladding, affect alignment, or produce vibration.

Fatigue is important where tension members experience repeated or fluctuating stress, such as crane-support systems, bridges, towers, and vibrating industrial structures. Weld details, bolt holes, abrupt section changes, and thread run-outs can act as stress concentrations. The relevant fatigue provisions must be used rather than relying only on static resistance.

Durability requires suitable coatings, drainage, galvanizing, compatible materials, and inspection access. Water trapped between plates can cause concealed corrosion. Threads, crevices, and interfaces between built-up components require particular attention.

The engineer has a professional duty to state the governing design standard, material grade, load combinations, assumptions, connection details, and inspection requirements. Computer software can calculate areas and capacities, but it cannot independently judge whether the selected failure path, shear-lag factor, erection condition, or load path is appropriate. Engineering judgment remains essential.

Challenges and Limitations

The simplified equations in this chapter represent idealized limit states. They may not fully capture local bending, prying action, residual stress, weld discontinuities, corrosion loss, fatigue, fire exposure, or complex three-dimensional connection behaviour. Where the connection is highly irregular, experimental evidence, finite-element analysis, or specialist guidance may be necessary. Such methods should supplement, not replace, code-based checks and sound detailing.

Best-Practice Checklist

• Use the governing edition of the applicable steel design code.
• Use specified design-hole dimensions, not merely nominal bolt diameters.
• Identify every plausible net-section and block-shear path.
• Obtain shear-lag factors from code provisions.
• Design the connection and connected plate or gusset simultaneously.
• Prefer direct and symmetrical load transfer.
• Check serviceability, fatigue, corrosion, erection, and inspection.
• Document units, material properties, resistance factors, and assumptions.
• Review the final detail for constructability and safe load transfer.

Chapter Summary

Tension-member design requires more than calculating gross area. Gross-section yielding, net-section rupture, block shear, shear lag, bolt or weld resistance, bearing, tear-out, eccentricity, and serviceability must be considered together. Gross area controls yielding, whereas net and effective net areas control rupture. The effective-net-area relation A_e = U A_n accounts for incomplete force transfer. Block shear combines shear and tension failure around a connection and must be evaluated using the actual geometry. Rods, plates, angles, and built-up members each present distinctive detailing issues. A reliable design compares factored demand with the smallest factored resistance, then verifies durability, constructability, inspection, and possible fatigue effects.

Key Terms

Gross area: Total cross-sectional area before deducting holes.

Net area: Cross-sectional area after deducting bolt holes along a failure path.

Effective net area: Net area reduced for shear-lag effects.

Shear lag: Nonuniform force transfer caused by connecting only part of a cross-section.

Tension member: Structural member carrying primarily axial tensile force.

Gross-section yielding: Yielding of the complete cross-section.

Net-section rupture: Fracture through a reduced or effective section.

Block shear: Combined tension and shear failure of a material block near a connection.

Factored demand: Design action obtained from the specified load combination.

Nominal resistance: Idealized resistance before application of a resistance factor.

Resistance factor: Code factor used to obtain design resistance from nominal resistance.

Design hole diameter: Hole dimension specified for strength calculations.

Gauge: Transverse distance between bolt lines.

Pitch: Longitudinal spacing between adjacent bolts.

Edge distance: Distance from a bolt centre to the connected element edge.

Eccentricity: Offset between the force line and the centroidal or connection line.

Gusset plate: Plate connecting bracing or truss members.

Built-up member: Member assembled from two or more structural components.

Serviceability: Performance relating to deformation, vibration, durability, or use.

Limit state: Condition beyond which a structural requirement is not satisfied.

Review Questions

Short Answer Questions

1. Distinguish gross area, net area, and effective net area.
2. Why can a single angle experience shear lag?
3. What is the purpose of a block-shear check?
4. State two important requirements for a bolted tension connection.
5. Why should the connection be designed together with the tension member?

Long Answer Questions

1. Explain the principal limit states governing a steel tension member and give the corresponding resistance expressions.
2. Describe how staggered bolt holes affect net area.
3. Explain shear lag and discuss factors affecting the value of U.
4. Compare rods, plates, single angles, and built-up members as tension members.
5. Present a complete design procedure for a bolted plate tension member.

Analytical / Application Questions

1. A 120 mm × 12 mm plate has two 22 mm design holes on a transverse section. Using F_y = 250 MPa, F_u = 400 MPa, and U = 0.85, calculate its gross area, net area, effective net area, and nominal rupture resistance.
2. A single angle has adequate gross-yielding resistance but fails the effective-net-section rupture check. Propose two changes to the member or connection and explain why each may improve the design.
3. For a bracing connection, identify the likely block-shear planes and list the information required to calculate the block-shear resistance.

Multiple Choice Questions with Answers

Question 1

Which area is used directly in the gross-section yielding check?

A. Gross area, A_g

B. Net area, A_n

C. Effective net area, A_e

D. Shear area only

Correct Answer: A. Gross area, A_g

Question 2

The effective net area is commonly expressed as:

A. A_e = A_g/U

B. A_e = U A_n

C. A_e = A_g + A_n

D. A_e = F_y A_g

Correct Answer: B. A_e = U A_n

Question 3

Which limit state involves combined tension and shear failure near a connection?

A. Local buckling

B. Gross yielding

C. Block shear

D. Elastic elongation

Correct Answer: C. Block shear

Question 4

For a plate with width 100 mm, thickness 10 mm, and two 22 mm design holes on a transverse section, the net area is:

A. 560 mm²

B. 780 mm²

C. 1000 mm²

D. 440 mm²

Correct Answer: A. 560 mm²

Question 5

If a force P acts with eccentricity e from the connection centroid, the additional moment is:

A. M = P/e

B. M = e/P

C. M = Pe

D. M = P + e

Correct Answer: C. M = Pe

Question 6

Which condition generally produces shear lag?

A. The entire section is connected symmetrically

B. Only part of the cross-section is directly connected

C. The member has no connection

D. The gross area is large

Correct Answer: B. Only part of the cross-section is directly connected

Question 7

For F_y = 250 MPa and A_g = 1000 mm², with φ_y = 0.90, the factored gross-yielding resistance is:

A. 225 kN

B. 250 kN

C. 277.8 kN

D. 90 kN

Correct Answer: A. 225 kN

Question 8

Which item is not normally a primary bolt-connection check?

A. Bolt shear

B. Bearing of connected material

C. Block shear

D. Young’s modulus of the paint coating

Correct Answer: D. Young’s modulus of the paint coating

Question 9

Elastic elongation of a uniform tension member is approximated by:

A. ∆ = AE/(PL)

B. ∆ = PL/(AE)

C. ∆ = PAE/L

D. ∆ = L/(PAE)

Correct Answer: B. ∆ = PL/(AE)

Question 10

Why is the smallest calculated resistance selected for design?

A. It represents the most critical applicable limit state

B. It always represents buckling

C. It eliminates the need to check connections

D. It is required only for rods

Correct Answer: A. It represents the most critical applicable limit state