Math Problem Statement

A bolted connection shown in the figure is using A325X bolts. It has a diameter of 19 mm. Fy=248 MPa. Fu=400 MPa. Determine the following: 4. Capacity of the connection using a friction-type connection. Assume diameter of the hole to be 22 mm. 4.a Based on shearing stress 4.b Based on gross area 4.c Based on net area 5. Capacity of the connection using a bearing-type connection. Assume diameter of the hole to be 22 mm. 5.a Based on shearing stress 5.b Based on bearing of bolts 5.c Based on net area

Solution

The image you provided describes a bolted connection using A325X bolts, and it includes calculations for determining the capacity of the connection based on different assumptions. Here is a breakdown of what the problem involves:

  1. Friction-Type Connection:

    • a. Based on shearing stress.
    • b. Based on gross area.
    • c. Based on net area.
  2. Bearing-Type Connection:

    • a. Based on shearing stress.
    • b. Based on bearing of bolts.
    • c. Based on net area.

We are tasked with calculating the capacity under these different cases. To proceed with the calculations, we would need to use formulas related to each type of connection, considering the given values for the diameter of the bolts (19 mm), the diameter of the hole (22 mm), and the material properties such as yield strength (Fy = 248 MPa) and ultimate tensile strength (Fu = 400 MPa).

Do you want me to walk you through the solution step by step, or would you like to focus on a particular calculation (e.g., friction or bearing type)?

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Math Problem Analysis

Mathematical Concepts

Structural Engineering
Shear Stress
Bearing Stress
Tensile Strength

Formulas

Shear stress formula: τ = V / A
Bearing stress formula: σ_b = P / (d × t)
Tensile stress formula: σ_t = P / A

Theorems

Bolted Connection Strength Calculation
Ultimate Strength Design (USD)

Suitable Grade Level

Undergraduate Engineering