Tension members

The simplest steel member is a tie: it is only pulled. This lesson shows the ways a tie can fail, how bolt holes and connections reduce its strength, and how to design one to EN 1993-1-1 and EN 1993-1-8, by hand and on the Eurocode 3 route of the STATIX steel member calculator.

1. Learning outcomes

After this lesson you can:

recognise tension members and the two ways they fail;
work out the gross and net areas, including staggered holes;
find the design tension resistance N_t,Rd from the plastic resistance, the net section and block tearing;
apply the rules for angles bolted through one leg;
check a tie in the STATIX steel member calculator, and say which national choices it makes.

2. Before you start

The free STATIX steel member calculator, set to Eurocode 3 (EN 1993-1-1), open in a second tab.
Your own copy of EN 1993-1-1 and EN 1993-1-8 is useful; this lesson gives clause numbers only.
A pocket calculator and about 45 minutes.
The same lesson on the SA code: Steel Design 1, lesson 1 (SANS 10162-1).

3. Where tension members are

Where tension members are. In a roof truss under gravity load the bottom chord is pulled apart, and so are some of the diagonals. Hangers that carry a floor from above, and cross bracing, are other ties. They are the simplest steel members: no buckling, just a pull.

4. How a tie fails

The two ways a tie fails (EN 1993-1-1, 6.2.3). Along its length the whole gross section yields and the member stretches, which gives warning: the plastic resistance N_pl,Rd. At a bolted end the holes leave less steel, and the member can tear through them at the ultimate strength: N_u,Rd. The design checks both.

Why two strengths, and two partial factors. Steel yields at f_y and then stretches a long way before it reaches its ultimate strength f_u and breaks. Yielding of the whole member is a safe, visible failure and uses γ_M0; reaching f_u at a hole is not, so it uses the larger γ_M2. On the Eurocode route the calculator takes f_y by thickness (EN 10025-2) and f_u from EN 1993-1-1 Table 3.1.

What the steel member calculator’s Eurocode 3 route uses: the recommended partial factors γ_M0 = 1.0, γ_M1 = 1.0 and γ_M2 = 1.25 (EN 1993-1-1 6.1 and EN 1993-1-8 Table 2.1), with no national annex; E = 210 000 MPa; f_y by the thickest element of the section (EN 10025-2); f_u from EN 1993-1-1 Table 3.1, 490 MPa for S355 up to 40 mm. The SANS route of the same page uses other values.

5. Net area

Net area. Across a line of holes the steel is the gross area less the holes. EN 1993-1-1 deducts each hole at its own diameter d₀; for a bolt in a normal clearance hole that is the bolt size plus 2 mm (M20 in 22 mm), plus 3 mm from M27 up.

Staggered holes (6.2.2.2(4)). When holes are staggered, a zigzag tearing path may be weaker than a straight one. Each hole on the path is deducted, and for each diagonal step s²t/4p is given back, where s is the stagger along the member and p the spacing across it. The smallest net area governs.

A_net = A − Σ d₀ t + Σ s²t/4p for the weakest path (6.2.2.2)

6. Angles and end details

Angles bolted through one leg (EN 1993-1-8, 3.10.3). Only the bolted leg is gripped; the stress spreads into the other leg slowly (shear lag). The code reduces the net-section resistance with a factor β₂ or β₃ that depends on the number of bolts and their pitch, and gives its own rule for a single bolt.

β₂ = 0.4 at p₁ ≤ 2.5 d₀, rising to 0.7 at p₁ ≥ 5 d₀ (two bolts) β₃ = 0.5 at p₁ ≤ 2.5 d₀, rising to 0.7 at p₁ ≥ 5 d₀ (three or more) straight-line between the two (EN 1993-1-8 Table 3.8)

End details decide the net area. A member welded all round keeps its whole section, so only the plastic resistance applies. Bolt holes take steel away exactly where the force is concentrated. In STATIX the net area is the ratio A_net/A you type (default 0.85).

7. The design tension resistance (EN 1993-1-1, 6.2.3)

The design tension resistance N_t,Rd is the smallest of three. The calculator uses the recommended partial factors: γ_M0 = 1.0 for yield and γ_M2 = 1.25 for fracture. National annexes may choose other values; check yours.

plastic: N_pl,Rd = A f_y / γ_M0 (6.6) net section: N_u,Rd = 0.9 A_net f_u / γ_M2 (6.7) block tearing: V_eff,1,Rd = f_u A_nt / γ_M2 + f_y A_nv / (√3 γ_M0) (EN 1993-1-8 3.9) N_t,Rd = the smallest; N_Ed ≤ N_t,Rd

Block tearing (EN 1993-1-8, 3.10.2). The bolts can drag out a whole block: shear along the bolt line and tension across to the edge. Where the load is eccentric to the block, as in an angle bolted on one line, the tension term is halved. STATIX takes the net shear area A_nv and the net tension area A_nt you type, in cm²; for a single angle connected by one leg it uses the eccentric equation (3.10), otherwise (3.9).

Where a ductile failure is required, for example in capacity design for earthquakes, 6.2.3(3) also asks that the net section is stronger than the gross section yields (N_u,Rd ≥ N_pl,Rd). For ordinary ties the smallest value simply governs.

Slenderness of ties. A tie does not buckle, so its strength does not need a stiff section, and EN 1993-1-1 gives no slenderness limit for it. But a very slender tie sags, vibrates and is easily damaged in handling. Designers keep L/i (length over radius of gyration) modest; many offices use 300 to 400.

8. In STATIX

The tension route in the STATIX steel member calculator: set the design code to Eurocode 3, pick the grade and section, enter N as a negative number, fill in the tension check under More inputs, and read the tension resistance and the utilisation (with the clause on the calc sheet).