# Design of Tension Members in Trusses

**SYMBOLS**

**A _{g} :** Cross-section area without loss

**A _{e} :** Effective net cross-sectional area

**A _{n} :** Net cross-section area

**A _{gv} :** Area without loss under shear stress

**A _{nv} :** Net area under shear stress

**A _{nt} :** Net area under tensile stress

**F _{y} :** Structural steel characteristic yield stress

**F _{u} :** Structural steel characteristic tensile strength

**K** : Twisting length coefficient

**L:** Element length between supported points

**i:** Radius of inertia

**U:** Stress irregularity effect coefficient

**U _{bs} :** A coefficient considering the spread of tensile stresses

**T _{n} :** Design tensile strength

### Tensile Strength of Elements

Tension members are structural elements that transmit the axial tensile forces. If tension elements are used together with bolted connections, yield stress will be reached earlier in the areas where bolt holes are located. This situation will affect the strength determined by using the load-displacement curve.

In bolted and welded connections of tension members, the cross-sectional area operating in load transfer is not equal to the entire cross-section area, as a result of the uneven distribution of the loads.

Since the L and U sections are used especially in the corners that are not connected with bolts or welds, a certain region is called an effective area in the load distribution. The consequence of this partial connection is that the connected element becomes overloaded and the unconnected part is not fully stressed. Due to this phenomenon called the 'Shear Lag' effect, an effective net area is used in the design.

3 different areas are used in the strength calculation in tension members:

Gross Area (A

_{g})Net Area (A

_{n})Effective Net Area (A

_{e})

### Design with AISC 360-16

There are 3 different collapse conditions in the elements affected by the tensile force: Yielding Limit State, Rupture Limit State and Block Shear Limit State

The design tensile strength is taken as the minimum strength to be calculated according to the yield limit state, rupture limit state and block shear limit state of the element under axial tensile force. Block shear limit state is an additional check for joints.

The tension element slenderness ratio should be controlled. In accordance with article

**D1**of the regulation, the slenderness ratio should be less than 300.

#### Yielding Limit State

The design tensile strength, φ

_{t}P_{n}, and the allowable tensile strength, P_{n}/Ω_{t,}of tension members, for yielding limit state in tensile members is calculated determined by equation D2-1.

#### Rupture Limit State

The characteristic tensile strength, P

_{n}, for rupture limit state in tensile members is determined by equation D2-2 using the effective net cross-sectional area.

#### Block Shear Conditions

The characteristic block shear strength is calculated by equation 13.19, based on the yielding and rupture limit states along R

_{n}shear surface or surfaces and the rupture limit states along the vertical tensile surface.