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 SANS 10162-1, by hand and in 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, net and effective net areas, including staggered holes and shear lag;
find the factored tensile resistance Tr from gross yield, net fracture and block shear;
choose between a bolted and a welded end detail;
check a tie in the STATIX steel member calculator.
Your own copy of SANS 10162-1 is useful; this lesson gives clause numbers only.
A pocket calculator and about 45 minutes.
3. Where tension members are
Where tension members are. In a roof truss under gravity load the bottom chord is pulled apart; 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. Along its length the whole gross section yields and the member stretches, which gives warning. At a bolted end the holes leave less steel, and the member can tear through them at the ultimate strength. The design checks both.Why two strengths. Steel yields at Fy and then stretches a long way before it reaches its ultimate strength Fu and breaks. Yielding of the whole member is a safe, visible failure; reaching Fu at a hole is not, hence the lower φu. For S355 to SANS, STATIX uses Fy = 355 MPa (up to 40 mm thick) and Fu = 480 MPa.
5. Net area
Net area. Across a line of holes the steel is the gross area less the holes. The code counts each hole a little wider than it is drilled or punched, because the edges are damaged.Staggered holes. When holes are staggered, a zigzag tearing path may be weaker than a straight one. For each diagonal step the code adds s²/4g back to the net width, where s is the pitch along the member and g the gauge across it; the smallest net area governs.
An = Ag − Σ(hole width × t) + Σ(s²/4g × t) for the weakest path
6. Shear lag and the effective net area
Shear lag in angles (SANS 10162-1, 12.3.3.2). When an angle is bolted through one leg only, the outstanding leg does not carry its full share at the connection. The code reduces the effective net area, more when there are few bolts. STATIX needs this ratio typed for an angle; without it the net fracture check is NOT CHECKED.End details decide the net area. A member welded all round keeps its whole section, so the net area equals the gross area. Bolt holes take steel away exactly where the force is concentrated. In STATIX this is the net-area ratio Ane/Ag (default 0.85): type 1.0 for a welded end.
7. The tensile resistance (SANS 10162-1, 13.2)
The tension resistance (SANS 10162-1, 13.2 and 13.11) is the smallest of three. Yield uses φ = 0.9 on the gross area; fracture and block shear use φu = 0.75 on the ultimate strength, because a fracture gives no warning.
gross yield: Tr = φ Ag Fy, φ = 0.9
net fracture: Tr = φu Ane Fu, φu = 0.75
block shear: Tr = φu [Ut Ant Fu + 0.6 Agv (Fy + Fu)/2] (13.11)
Ut = 0.6 for an angle connected by one leg; 1.0 for a symmetrical block
Tr = the smallest; Tf ≤ Tr
Block shear (SANS 10162-1, 13.11). The bolts can drag out a whole block of the leg: shear along the bolt line and tension across to the edge. For an angle connected by one leg the tension area counts only partly: Ut = 0.6. STATIX takes the gross shear area Agv and the net tension area Ant you enter, in cm², and uses Ut = 0.6 for a single angle connected by one leg.Slenderness of ties. A tie does not buckle, so strength does not need a stiff section. But a very slender tie sags, vibrates and is easily damaged in handling. Designers keep L/r (length over radius of gyration) modest; 300 is a common limit.
8. In STATIX
The tension route in the STATIX steel member calculator: pick the section and grade, enter N as a negative number, fill in the tension check under More inputs, and read Tr and the utilisation (with the clause on the calc sheet).
9. Example A: an angle tie bolted through one leg
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10. Example B: a welded hanger
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11. Do it in STATIX
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12. Common mistakes
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13. Exercises
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14. Self-check quiz
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15. Lesson 1 on one page
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Next: Lesson 2, compression members and columnsFrom pulling to pushing: buckling, slenderness and the column resistance Cr. Go to lesson 2
A worked example for learning, not a design. Check every value against the current code and your own project, and have the design checked and signed by a registered professional engineer.
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