## Questions:

1. A simply supported W18 x 119 A992 steel beam with 8 +0.1(last digit of your ID number) meters in length was subjected to a service load of 990 + last 2 digits of your ID number kN/m, with a dead-to-live load ratio of 1:2, including the beam weight. Due to the excessive deflection, it is then decided that an additional W18 x 119 column with a length of 7.0 + 0.1(last digit of your ID number) meters is to be placed at the midspan of the beam as additional support. The said action will be made to minimize the deflection to 3 + 0.01(last digit of your ID number) mm. If the column being added is fixed at the bottom and pinned at the top, evaluate if W18 x 119 can withstand as support. Use a recommended value for K. Evaluate using LRFD and ASD.

2. Use A992 steel and compute the nominal compressive strength of a WT12 x 51.5 with an effective length of 4.88 + 0.1(last digit of your ID number) m with respect to each axis. Evaluate using LRFD and ASD.

## Answer:

### Structural Analysis and Evaluation of W18 x 119 Steel Beam and Column

#### 1. Evaluation of W18 x 119 Steel Beam with Additional Column Support:

**Given Parameters:**

- Beam Length (L): 8+0.1(last digit of your ID number)8+0.1(last digit of your ID number) meters
- Service Load on Beam (w): 990+last 2 digits of your ID number990+last 2 digits of your ID number kN/m
- Dead-to-Live Load Ratio: 1:2
- Additional Column Length (L_column): 7.0+0.1(last digit of your ID number)7.0+0.1(last digit of your ID number) meters
- Deflection Limit (δ_limit): 3+0.01(last digit of your ID number)3+0.01(last digit of your ID number) mm
- Beam Properties: W18 x 119 A992 steel

**Steps:**

- Calculate the total service load (w_total) on the beam considering the dead-to-live load ratio.
- Calculate the total load on the beam (W_total) by integrating the distributed load.
- Determine the maximum deflection of the beam (δ_beam) using appropriate beam formulas.
- Check if the maximum deflection satisfies the specified limit.
- If excessive deflection occurs, calculate the additional moment due to the deflection limit.
- Assess the additional column’s ability to support the calculated additional moment.

**Evaluation Criteria:**

- Use recommended values for the structural constant K.
- Perform the evaluation using both LRFD (Load and Resistance Factor Design) and ASD (Allowable Stress Design) methods.

#### 2. Nominal Compressive Strength of WT12 x 51.5 Steel Section:

**Given Parameters:**

- Steel Section: WT12 x 51.5 A992
- Effective Length (L_eff): 4.88+0.1(last digit of your ID number)4.88+0.1(last digit of your ID number) meters

**Steps:**

- Identify the critical axis (x-axis or y-axis) based on the loading conditions.
- Calculate the slenderness ratio (λ) for the identified axis.
- Determine the critical stress (φP_n) using appropriate equations for LRFD.
- Assess the compressive strength considering both LRFD and ASD methods.

**Evaluation Criteria:**

- Utilize recommended values for the design parameters in LRFD and ASD.
- Ensure compliance with the applicable design codes and standards for A992 steel.

**Note:** Please provide the last digit of your ID number for specific numerical values and further calculations.