The railcar docklight is supported by the (1)/(8) -in.-diameter pin at A. If the lamp weighs 4 l

step 1 So here in this question firstly the shear stress in the pin is given by tau is equals to m by a

The railcar docklight is supported by the (1)/(8)...

The railcar docklight is supported by the $\frac{1}{8}$ -in.-diameter pin at $A$. If the lamp weighs 4 lb, and the extension arm $A B$ has a weight of $0.5 \mathrm{lb} / \mathrm{ft}$, determine the average shear stress in the pin needed to support the lamp. Hint: The shear force in the pin is caused by the couple moment required for equilibrium at $A$

Key Concepts

Pins in Load-Bearing Structures

Pins are often used as pivot points or connectors in load-bearing structures and are typically subjected to shear forces due to applied moments. Their design must ensure that the material and geometry, such as diameter, are sufficient to resist these forces without yielding.

Equilibrium Conditions

Equilibrium conditions require that the sum of forces and the sum of moments acting on a system are zero. Maintaining equilibrium ensures that the structure or component remains stationary under loading, a fundamental principle in statics.

Cross-Sectional Area of Circular Members

The cross-sectional area of a circular member is calculated from its diameter using the formula A = ?d²/4. This area is critical for computing stresses, such as shear stress, because it directly influences the distribution of applied forces.

Shear Stress

Shear stress is the stress that occurs when forces are applied parallel or tangential to a material's cross-sectional area. It quantifies the internal resistance of a material to deformation under shear loads and is typically calculated by dividing the applied force by the area over which it acts.

Couple Moment

A couple moment is produced by two equal and opposite forces acting at a distance from each other, creating a rotational effect without a net force. It is a key concept in static equilibrium, as the moment must be balanced to prevent rotation of the component.

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