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The given problem asks to compute several design and allowable strengths for a tension member connected with three 1-inch diameter bolts using both LRFD (Load and Resistance Factor Design) and ASD (Allowable Strength Design). The material properties are \( F_y = 36 \, \text{ksi} \) and \( F_u = 58 \, \text{ksi} \), and we need to determine various strengths under tensile yielding and rupture.

Let's go step by step to compute these values.

### Definitions and Formulas:
- \( F_y \): Yield stress of the steel (36 ksi)
- \( F_u \): Ultimate stress of the steel (58 ksi)
- \( A_e \): Effective area (given but incomplete in the image, so we will assume values later for computation)
- \( \phi \): Strength reduction factor for LRFD
- \( \Omega \): Safety factor for ASD

#### 1. **Design strength for LRFD considering tensile yielding**:
   The formula for the LRFD design strength under tensile yielding is:
   \[
   P_n = F_y \times A_g
   \]
   \[
   P_{LRFD} = \phi \times P_n
   \]
   Where \( \phi \) is typically 0.9 for yielding.

#### 2. **Allowable strength for ASD considering tensile yielding**:
   The allowable strength for ASD under tensile yielding is:
   \[
   P_{ASD} = \frac{P_n}{\Omega}
   \]
   Where \( \Omega \) is typically 1.67 for yielding.

#### 3. **Design strength for LRFD considering tensile rupture**:
   The formula for the LRFD design strength under tensile rupture is:
   \[
   P_n = F_u \times A_e
   \]
   \[
   P_{LRFD} = \phi \times P_n
   \]
   Where \( \phi \) is typically 0.75 for rupture.

#### 4. **Allowable strength for ASD considering tensile rupture**:
   The allowable strength for ASD under tensile rupture is:
   \[
   P_{ASD} = \frac{P_n}{\Omega}
   \]
   Where \( \Omega \) is typically 2.00 for rupture.

### Assumptions:
Since the effective area \( A_e \) is unclear from the image, I'll assume a typical width for the plate and bolt diameter for computations. I'll also clarify the approach for bolt shear area and reduction due to bolt holes.

Would you like me to assume typical dimensions for the plate and bolts, or do you have specific values for the effective area \( A_e \)? Please confirm this so I can proceed with calculations.

---

Let me know if you want to clarify anything!  
Here are five related questions:
1. What are the values of \( A_g \) and \( A_e \) for this specific problem?
2. How do bolt holes impact the effective net area?
3. What is the difference between tensile yielding and tensile rupture in design?
4. How do LRFD and ASD approaches differ in terms of safety factors?
5. What is the significance of the strength reduction factor \( \phi \) in LRFD?

**Tip**: For connections, always check both yielding and rupture conditions to ensure the member's adequacy under tension.

A PL 3/8 x 7 tension member is connected with three 1-inch-diameter bolts. The steel is Fy = 36 ksi, Fu = 58 ksi. Assume Ae = [unknown] and compute: a. The design strength for LRFD considering tensile yielding b. The allowable strength for ASD considering tensile yielding c. The design strength for LRFD considering tensile rupture d. The design strength for ASD considering tensile rupture

Solve for the LRFD and ASD strength of a PL 3/8 x 7 tension member connected with three 1-inch-diameter bolts. This problem includes tensile yielding and rupture calculations, using Fy = 36 ksi and Fu = 58 ksi. Learn key formulas and concepts like LRFD and ASD in structural engineering.

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