Steel Tension Members Design

Concept

Structural steel tension members are components (such as tie rods, truss members, or cables) that are subjected to outward pulling forces along their longitudinal axis. Because tension tends to keep the member straight, tension members are not susceptible to buckling, which makes them highly efficient. The design of a tension member involves ensuring it does not fail by either elongating excessively (yielding) or tearing apart entirely (fracture). Standard structural codes, such as AISC (American Institute of Steel Construction), require checking two primary limit states: tensile yielding in the gross section and tensile rupture (fracture) in the net section (where holes are drilled for bolts).

Formula & Method

Using Load and Resistance Factor Design (LRFD), the required tensile strength ($P_u$) from factored loads must be less than or equal to the design tensile strength ($\phi P_n$).

1. Tensile Yielding in the Gross Section: Failure occurs if the entire cross-section yields. $\phi_y P_{ny} = \phi_y F_y A_g$ Where $\phi_y = 0.90$.

2. Tensile Rupture in the Net Section: Failure occurs if the member fractures across the smaller area where bolt holes have been removed. $\phi_t P_{nt} = \phi_t F_u A_e$ Where $\phi_t = 0.75$. The effective net area ($A_e$) is the net area ($A_n$) multiplied by a shear lag factor ($U$), which accounts for uneven stress distribution if not all elements of the cross-section are connected: $A_e = A_n U$

The controlling design strength is the smaller of $\phi_y P_{ny}$ and $\phi_t P_{nt}$.

Variables & Units

• $P_u$ = Required tensile strength (factored load), in Newtons (N) or kips.
• $F_y$ = Specified minimum yield stress of the steel, in MPa or ksi.
• $F_u$ = Specified minimum tensile (ultimate) stress of the steel, in MPa or ksi.
• $A_g$ = Gross cross-sectional area, in mm$^2$ or in$^2$.
• $A_n$ = Net cross-sectional area (gross area minus bolt holes), in mm$^2$ or in$^2$.
• $A_e$ = Effective net area, in mm$^2$ or in$^2$.
• $U$ = Shear lag factor (dimensionless, $\le 1.0$).
• $\phi_y, \phi_t$ = Resistance factors for yielding and tension rupture, respectively.

Worked Example

A detailed interactive calculation example for steel tension members design can be found at Worked Example: Steel Tension Members Design.

Engineering Meaning

The two limit states reflect different physical failures. Yielding across the gross section causes massive elongation, rendering the structure unusable even if it hasn't snapped. Therefore, it is evaluated against the yield stress ($F_y$) with a higher confidence factor (0.90). Fracture across the bolt holes is a catastrophic, sudden separation, so it is evaluated against the ultimate stress ($F_u$) with a stricter penalty factor (0.75) to ensure sudden fracture is heavily discouraged in the design process.

Engineering Check

When calculating the net area ($A_n$), engineers must add an extra tolerance (typically $2 \text{ mm}$ or $1/16 \text{ in}$) to the actual bolt diameter to account for the clearance hole and the damage caused to the steel during drilling or punching. Never use the nominal bolt diameter to calculate the subtracted hole area.

Explicit Exclusions

This foundational article excludes the calculation of Block Shear rupture at the connection, which is a combined tension-and-shear failure mechanism. It also excludes the detailed calculation of the shear lag factor ($U$) for complex asymmetric profiles (like angles and channels) and threaded rod design.