# Example D.3 WT-shape tension member

The results of tensile yielding and recommended slenderness limit calculation according to SDC Verifier and Design Examples of AISC (official version 14.1) are compared. The goal is to test SDC Verifier and reach valid results according to Specification for Structural Steel Buildings (ANSI/AISC 360-10 chapter D).

The results are generated with SDC Verifier 3.6 and calculated with FEMAP v11.0.0

**Task:**

A WT6×20 ASTM A992 member has a lengtt of 30 ft and carries a dead load of 40 kips and a live load od 120 kips in tension. The end connection is fillet welded on each side for 16 in. Verify the member tensile strength by both LRFD and ASD. Assume that the gusset plate and the weld are satisfactory.

**Solution**

From AISC Manual Table 2-4, the material properties are as follows:

W6×20

ASTM A992

F_{y}=50 ksi

F_{u}=65 ksi

From AISC Manual Table 1-8, the geometric properties are as follows:

W6×20

A_{g} =5.84 in.^{2}

b_{ƒ} =8.01 in.

t_{ƒ} =0.515 in.

<r_{x} =1.57 in.

γ^{‾} =1.09 in.= χ^{‾} (in equation for U)

From Chapter 2 of ASCE/SEI 7, the required tensile strength is:

LRFD | ASD |
---|---|

P_{u} = 1.2(40 kips) + 1.6(120 kips)=240 kips | P_{a} = 40 kips + 120 kips= 160 kips |

*Tensile Yielding*

Check tensile yielding limit state using AISC Manual Table 5-3

*Check Recommended Slenderness Limit*

=229 < 300 from AISC *Specification* Section D1 **o.k.**

All units of measurement were chosen according to British metric system (lb, in, lb/in^3, lb/in^2).

Material used is A992 Steel with Yield Stress = 50000 and Tensile Strength = 65000

Moment of inertia W6×20 is modified manually from original Moment I2 or Iyy> 15.3 to 14.40, because section is modeled without fillets.

#### Example from AISC Design Examples

From AISC Manual Table 1-8, the geometric properties are as follows:

W6×20

A_{g} =5.84 in.^{2}

b_{ƒ} =8.01 in.

t_{ƒ} =0.515 in.

r_{x} =1.57 in.

γ^{‾} =1.09 in.= χ^{‾} (in equation for U)

**Note:** T-beam was created in Femap (built-in section) with moment of interiaIyy = 15.3 in^4 (fillets of rolled section weren’t taken into account), but in SDC Verifier moment of inertia was changed to Iyy = 14.4 in^4 according to the input data of the example.

### FEM Loads and Constraints

#### 1..Dead load 40 kips

Definition Title | Load Type | Applied on | Value(s) |
---|---|---|---|

1..Force on Node | Force | Node: 11 | (40000;0;0) |

#### 2..Live load 120 kips

Definition Title | Load Type | Applied on | Value(s) |
---|---|---|---|

1..Force on Node | Force | Node: 11 | (120000;0;0) |

#### 1.Constraint

Definition | Count | Type (DOF) |
---|---|---|

1..Fixed | 1 node(s) | Tx Ty Tz Rx Ry Rz |

2..TY;TZ;RX;RY;RZ | 1 node(s) | Ty Tz Rx Ry Rz |

### Check 1..ANSI / AISC LRFD 360-10

#### Slenderness check

**All (LS1, 18 PropertyShape(s))**

*Check Recommended Slenderness Limit*

#### Axial Check

**All (LS1, 17 Property Shape(s))**

From Chapter 2 of ASCE/SEI 7, the required tensile strength is:

*Tensile Yielding*

Check tensile yielding limit state using AISC Manual Table 5-3.

Comparing results of calculation in SDC Verifier and in Example D.3 we can see that values completely match. Tensile yielding stress is 263 kips > required tensile stress is 240 kips. Slenderness ratio Z is 229 < maximum slenderness limit for members in tension is 300 (AISC 360-10 chapter D.1).

Download SDC Verifier project file, >model and report of Example D.3

Full list of AISC 360-10 Examples