2-9 Bearing and Shear

Overview of Chapter One Concepts

Stress Types

• Normal Stress:

  • Results when loads are applied perpendicular to the material surface.
  • If there is breaking, it is often under normal stress conditions.

• Shear Stress:

  • Results when loads are applied parallel to the material surface.
  • Understanding shear stress is crucial when discussing structural integrity.

  Types of Shear Stress

  • Single Shear:
  • A condition where the shear force is applied at one section of the material.
  • Double Shear:
  • A condition where the shear force is divided among two sections of the material.

Example Problems

• Example 1 (Chapter 1.4): Determining Minimum Acceptable Diameter for a Pin

  • Setup: Two chain members are connected by a shackle and a pin.
  • Given:
  • Axial force in the chain, $F = 28 ext{ kN}$.
  • Allowable shear stress in the pin, $au_{ ext{max}} = 90 ext{ MPa}$.
  • Objective: Determine the minimum effective diameter for the pin.
  • Calculation Steps:
  1. Identify shear forces acting on the pin:
     • Apply load ($P = 28 ext{ kN}$) enters the shear area.
  2. Each shear carries half the applied load in double shear:
     • $\frac{P}{2} = 14 ext{ kN}$ for each shear surface.
  3. Calculate shear area required:
     • V = rac{P}{A}
       ightarrow A = rac{P}{ au_{ ext{max}}}.
  4. Use the cross-sectional area equation for circular sections:
     • $A = \frac{ ext{Diameter}^2 imes ext{π}}{4}$ to back-calculate the diameter.
  • Important Note: Ensure any assumptions made, such as defining the mode of loading (single vs double shear).

• Free Body Diagram:

  • Useful for visualizing the forces acting on the pin and determining reaction forces.

Addressing Forces in Example

• For evaluating reaction forces along points, necessary to account for various forces affected by the system.
• Define unknowns and relationships between them using equilibrium equations:
  • Equilibrium in X direction:
  • $C<em>x + F</em>{ab} = 0$ (sum of horizontal forces)
  • Equilibrium in Y direction:
  • $C_y - T - 15 = 0$ (sum of vertical forces)
  • Moment about point C:
  • Calculate clockwise moments for determining forces applied.
• After identifying forces, use derived equations to solve for unknowns systematically.

Punching Example

• Punching Setup:
  • Downward punching force required to remove material from a steel plate.
  • Given data:
  • Punching force: $32 ext{ tons}$.
  • Punch diameter: $0.75 ext{ in}$.
  • Thickness of plate: $0.25 ext{ in}$.
  • Acknowledge the relationship between force applied, area of the punch, and the resultant shear stresses:
  • $ext{Shear Stress} = \frac{F}{A}$,
  • with area denoted as $A = \frac{ ext{Punch Diameter}^2 imes ext{π}}{4}$.

Transition to Bearing Stress

• Concept of Bearing Stress:
  • Similar to normal stress but focuses on the area of contact between two materials under normal load.
  • Defined as:
  • $ext{Bearing Stress} = \frac{F}{A_{ ext{contact}}}$.
• Characteristics of Bearing Stress:
  • Contact area must be correctly identified to ensure accurate calculations.
  • Different types of materials may yield different resistance to bearing stress.

Future Topics

• Next discussion will focus on:
  • Inclined Stress: How it relates to shear and normal stress under load conditions.
  • Revisit concepts of bearing stress, illuminating its applications in different contexts.

Important Reminders

• Final Exam Date: May 13, from 8 AM to 10 AM in the classroom.
• Always refer to specific equations for calculations and reinforce with practical examples.
• Maintain accuracy in hand calculations and application of theoretical frameworks to practical situations.