Unit IIDesign of Structures - II

Tension Members

Three ways a tie can fail — and the lowest one governs.

≈ 40 min + worked example

Tension is the kindest load on steel — the whole cross-section works at once, and there is no buckling to worry about. But a bolted tension member can fail three different ways, and design means finding all three and taking the lowest: ductile gross-section yielding, brittle net-section rupture at the holes, and block shear, where a chunk of metal tears clean out of the bolt group.

Learning objectives

By the end of this lesson, you will be able to — mapped to the course outcomes for Design of Structures I:

CO2 · Understand

Identify the types and sections used as tension members and where they occur.

CO2 · Apply

Compute the gross-yielding, net-rupture and block-shear strengths and take the minimum as the design tension.

CO2 · Analyse

Find the net area with bolt holes and the staggered-hole s²/4g rule, and account for shear lag in a single angle.

CO6 · Apply

Design a plate or angle tension member and check its slenderness limit.

Ties & sections

Where tension lives, and in what

Ties, bracing and truss bottom chords carry pure tension, in rods, angles, channels, plates and built-up members. Even a tie has a slenderness limit to control sag and vibration.^{[1, 3]}

DiagramA single angle connected to a gusset by one leg; the connected leg carries the load while the outstanding leg lags, needing the beta reduction

Ties, bracing, chords

Tension members carry pure axial tension: truss bottom (tension) chords and web ties, X/diagonal bracing, sag rods and tie rods, hangers and suspension elements. Tension is the most efficient way to use steel — the whole section works at once.^[3]

The lowest governs

Three modes of failure

Gross yielding (Ag·fy/γm0) is ductile and preferred; net rupture (0.9·An·fu/γm1) and block shear are brittle. Net area deducts the holes, with the s²/4g add-back for staggered holes.^[1]

DiagramThree failure modes of a bolted tension member: gross yielding stretching the bar, net rupture across the holes, and block shear tearing a block from the bolt group

DiagramA plate with staggered bolt holes showing the zig-zag failure path and the s squared over four g chain-rule add-back

Gross-section yielding (cl. 6.2)

The whole gross cross-section reaches the yield stress and stretches — a ductile, deformation-tolerant failure. Tdg = Ag·fy / γm0, with γm0 = 1.10. Designers PREFER this mode to govern because it gives visible warning.^[1]

Drive the numbers

Tension-member calculator

Enter the plate size and the bolt holes; the tool returns the yielding and rupture strengths and flags which governs. A 200×10 plate with two M20 holes is yielding-governed at about 455 kN.^[1]

Tension member · plate (IS 800 cl. 6)

Plate width b200 mmPlate thickness t10 mmBolt holes at section2 no.Bolt diameter

Hole = bolt + 2 mm. Yielding Tdg = Ag·fy/γm0; rupture Tdn = 0.9·An·fu/γm1. Design tension = the lower. Fe410.

0.0 kN

Design tension Td (yielding governs)

0 mm²

Gross area Ag

0 mm²

Net area An

Block shear (not shown) must also be checked — it often governs short end connections.

The contrasts

At a glance

Aspect	One	The other
Stress used	Yielding: fy on gross area, γm0 = 1.10	Rupture: fu on net area, γm1 = 1.25, ×0.9
Failure character	Yielding: ductile, gradual, warns	Rupture/block shear: brittle, sudden
Area	Gross (full section)	Net (holes deducted)
Plate vs single angle	Plate: no shear lag — 0.9·An·fu/γm1	Angle one-leg: shear lag — β on outstanding leg
Which governs	Take the MINIMUM of the three	Block shear often governs short connections

PhotoA steel roof truss — its bottom chord and web ties work in tension while the top chord is in compression.w_lemay · CC BY-SA 2.0 · via Wikimedia Commons

Vocabulary

Key terms

Gross area (Ag)

Full cross-sectional area, no hole deductions — used for yielding.

Net area (An)

Gross area minus bolt holes (with the s²/4g add-back for stagger) — used for rupture.

Gross-section yielding

Ductile failure when the whole section reaches fy: Tdg = Ag·fy/γm0.

Net-section rupture

Brittle fracture at the holes reaching fu: Tdn = 0.9·An·fu/γm1.

Block shear

A block of metal tears out of the bolt group along shear + tension planes (cl. 6.4).

Shear lag

Stress lag in the unconnected (outstanding) leg of a one-leg-connected member; the β reduction.

Gauge (g) / pitch (s)

Transverse spacing between bolt lines (g) and longitudinal stagger spacing (s).

Design tension

The LOWEST of yielding, rupture and block-shear strengths.

Apply it

Worked example

A 200×10 plate, Fe410, with two 22 mm holes: Ag = 2000 mm², An = (200 − 2×22)×10 = 1560 mm². Yielding Tdg = 2000×250/1.10 = 454.5 kN; rupture Tdn = 0.9×1560×410/1.25 = 460.5 kN. The lower — 454.5 kN, yielding — is the design tension. Then confirm block shear does not undercut it.

Check your understanding

Self-assessment

1. The design tension capacity of a member is —

2. Gross-section yielding uses the partial safety factor —

3. In the staggered-hole net-area chain rule, the term added back for the diagonal path is —

In a nutshell

Recap

A tension member is checked for three modes — gross yielding, net rupture and block shear — and the LOWEST governs.

Yielding (Ag·fy/γm0) is ductile and preferred; rupture (0.9·An·fu/γm1) and block shear are brittle.

Net area deducts the holes; the staggered-hole rule adds back Σ(s²/4g); a one-leg-connected angle loses capacity to shear lag (β).

Even a tie has a slenderness limit (≤ 400, or ≤ 350 with reversal) to control sag and vibration.

The evidence

References & further reading

[1]IS 800:2007 — General Construction in Steel, Code of Practice (Section 6: tension members; cl. 6.1–6.4; Tables 3, 5). Bureau of Indian Standards.
[2]SP 6 (Part 1) — ISI Handbook for Structural Engineers: Structural Steel Sections. Bureau of Indian Standards.
[3]N. Subramanian, Design of Steel Structures (2nd ed.). Oxford University Press, 2016.
[4]S.K. Duggal, Limit State Design of Steel Structures (2nd ed.). McGraw-Hill Education, 2014.