2A1 Chapter 11 Static and Dynamic Forces

2nd Class Power Engineering

What is the study of forces acting on a body at rest or moving at a uniform velocity called?

Statics

What is the study of forces acting on a moving body that is accelerating or decelerating?

Dynamics

What does a moment of a force measure?

The tendency of a body to rotate about a specific point or axis.

What is the equation for calculating the moment of a force?

M = F × l (where M is the moment, F is the force, and l is the perpendicular distance)

What condition must be met for a body to be in equilibrium?

The algebraic sum of all forces or moments acting on it must be zero.

What is a couple in mechanics?

Two parallel forces that are equal in magnitude, opposite in direction, and separated by a perpendicular distance.

What is the arm of a couple?

The perpendicular distance between the two forces.

How do you establish equilibrium in a system of forces?

Ensure that the sum of vertical forces is zero, the sum of horizontal forces is zero, and the sum of clockwise moments equals the sum of anticlockwise moments.

What is the first moment of area?

It is defined as the area multiplied by the distance from a reference point.

What is the center point of an area or volume where the mass is concentrated?

Centroid

How can the centroid of irregular shapes be found?

By dividing the shape into known areas and calculating the algebraic sum of the moments of its component areas.

What is the relationship between centroid and center of mass for objects with consistent density?

The center of mass is at the same location as the centroid.

What is the significance of the modulus of elasticity in mechanics?

It measures the stiffness of a material and its ability to deform elastically when a force is applied.

What is the ratio between the lateral or perpendicular strain and the axial or longitudinal strain called?

Poisson's ratio

What are shear forces?

Forces that cause parts of a material to slide past each other.

What are bending moments?

Moments that cause bending of beams due to applied loads.

What is the fundamental torsion equation?

It relates torque to the shear stress and polar moment of inertia of a shaft.

What is the relationship between torque and power?

Power is the rate at which work is done, and it can be calculated using torque and angular velocity.

How do you calculate stress in coupling bolts due to torque?

By using the torque value and the dimensions of the bolts to determine the shear stress.

What is the significance of calculating centroids in engineering?

It helps in analyzing the distribution of forces and moments in structures.

What happens to a body in equilibrium if an imbalance in moments occurs?

The body will start to rotate or change its state of motion.

What is the unit of moment in mechanics?

Newton-meters (Nm)

What is the purpose of evaluating moments in a system of forces?

To determine the resultant effect of multiple forces acting on an object.

What is the algebraic sum of forces in a static system?

It must equal zero for the system to be in equilibrium.

What is the effect of applying a couple on an object?

It creates a rotational effect around the midpoint between the forces.

What is the significance of the distance between forces in a couple?

It determines the magnitude of the resultant moment.

What is the role of the first moment of area in finding centroids?

It helps in determining the location of the centroid for irregular shapes.

How is the first moment of area calculated?

Using the equation: moment = area × distance

What is the second moment of area used for?

To determine resistance to bending and torsion in shafts and beams.

What is the load applied slowly and held at a constant magnitude?

Static load

What is the constant load applied over a long period of time?

Sustained load

What is the load applied suddenly in a very short time period?

Impact (shock) load

What is the load that increases and decreases in magnitude over time?

Repeated (cyclic) load

What is the load applied to a small area relative to the total area?

Concentrated load

What is the load spread along a length or area?

Distributed load

What is the force acting through the centroid producing uniform tension or compression?

Axial load

What is the force that is parallel but not in the same plane, causing varying stress?

Shear load

What is the load applying an angular moment or twisting force to a beam or shaft?

Torsional load

What is the force applied perpendicular to the axis of an object?

Bending load

What is the load caused by thermal expansion or contraction due to temperature changes?

Thermal load

What is the load caused by more than one type of load applied to an object?

Combined load

What is the internal resistance resulting from the application of an external load?

Stress

What is the formula for direct stress?

σ = load / area

What are the units of stress?

N/m² or Pascals (Pa).

What happens when the cross-sectional area is not constant?

It can lead to increased local stress or stress concentrations.

What is tension in a material?

When forces are in opposite directions, causing the object to stretch.

What is compression in a material?

When forces are directed towards each other, causing the object to shorten.

How is stress calculated for a circular column with a compressive load?

Stress = P / A, where P is the load and A is the area.

How is the maximum allowable force calculated from direct stress?

P = Direct stress × Area.

What is produced by equal and opposite parallel forces that cause one part of the material to slide over another?

Shear stress

How is shear stress calculated?

Shear stress (τ) = Force / Area under shear.

What stress occurs when stress is applied on one plane of a rivet?

Single shear stress

What stress occurs when a bolt experiences shear force in two locations, reducing the stress by half?

Double shear stress

What occurs only in torsion or angular stress?

Pure shear stress

What is linear or direct strain?

It is the change in length relative to the original length.

What is the formula for calculating direct strain?

Direct strain (ε) = extension / original length

What are the units of strain?

It has no units of measure.

What does Hooke's Law state?

Strain is directly proportional to stress within the elastic region.

What is the strain that occurs while an external force produces stress, and the material returns to its original shape once the force is removed?

Elastic strain

What is the maximum elastic strain a material can handle before permanent deformation occurs?

Elastic limit (yield strength)

What is the strain that occurs when the material is deformed beyond its elastic limit and does not return to its original shape?

Plastic strain

What is the ratio of the elastic limit and the maximum expected working stress?

Factor of safety

What is the ratio of direct stress to direct strain, indicating material stiffness?

Modulus of Elasticity (Young’s Modulus)

What are typical units for Modulus of Elasticity?

Pascals (Pa) or gigapascals (GPa).

What is the ratio of shear stress to shear strain?

Modulus of Rigidity (G)

What is the deformation of a body due to shear stress, which is measured in terms of the angle through which the deformation occurs?

Shear strain

What happens to a material when it exceeds its ultimate stress limit?

The material is considered to have completely failed.

What is the relationship between stress and strain as stress increases?

As stress increases, strain also increases until the material fails.

What is the significance of the stress vs. strain curve?

The curve illustrates the relationship between stress and strain, showing elastic and plastic regions.

What is the increase in length formula for a material under tensile load?

Increase in length = Direct strain × Original length.

What is the typical value range for Poisson's ratio in materials?

Typically ranges from 0 to 0.5.

What is the effect of tensile stress on lateral dimensions of a bar?

Tensile stress increases axial length and decreases lateral width.

What is the relationship between tensile and compressive strain?

A tensile stress produces tensile strain in the direction of the stress and compressive strain in perpendicular directions.

How is shear stress related to the area under shear?

Shear stress is inversely proportional to the area under shear; larger areas result in lower shear stress.

What is the significance of the elastic region in material testing?

The elastic region is where materials deform elastically and return to their original shape after stress is removed.

What is the typical range of Poisson's ratio for most metals?

Between 0.25 and 0.35.

What is the effect of compressive stress on a material?

It causes compressive strain in its own direction and tensile strain in every lateral direction.

How is direct stress calculated?

Direct stress = P/A, where P is the load and A is the area.

What is the formula for calculating strain?

Direct strain (ε) = ΔL / L

What is the coefficient of linear expansion?

It is the longitudinal expansion per unit length for each degree of temperature increase, measured in strain per °C.

What is the thermal strain formula?

Thermal strain (ε) is calculated as α × (T2 - T1), where α is the coefficient of linear expansion and T1 and T2 are the initial and final temperatures.

What happens when a material is fixed and subjected to temperature changes?

Thermal stresses develop due to restricted expansion or contraction.

What is the change in length formula for thermal expansion?

Change in length (ΔL) = L × α × (T2 - T1), where L is the original length.

How do composite bars behave under thermal expansion?

Different materials in composite bars expand at different rates, leading to internal stresses.

What is the relationship between stress and strain in materials?

Stress (σ) is equal to the modulus of elasticity (E) multiplied by strain (ε).

What is the significance of the coefficient of thermal expansion?

It determines how much a material will expand or contract with temperature changes.

What is the effect of fixed ends on thermal expansion?

It causes internal stresses due to the inability of the material to expand freely.

What is the impact of temperature on the modulus of elasticity?

The modulus of elasticity can vary with temperature, affecting stress-strain relationships.

What are the two types of loads evaluated for beams?

Concentrated loads and uniformly distributed loads.

What is a simply supported beam?

A beam with a single support at each end.

What is a cantilever beam?

A beam fixed firmly at one end only.

What is a uniformly distributed load?

A load spread uniformly across a section of the beam or its entire length.

What do shear forces cause in a beam?

They tend to cause the beam to shear in a vertical direction.

What is positive shear?

Shear that moves in a clockwise direction relative to the applied forces.

What is negative shear?

Shear that moves in an anticlockwise direction relative to the applied forces.

How is the bending moment defined?

It is caused by moments created on the beam by applied forces.

What happens to the top surface of a beam under bending?

It experiences compression.

What happens to the bottom surface of a beam under bending?

It experiences tension.

When is a bending moment considered positive?

When it moves in a counter-clockwise direction.

When is a bending moment considered negative?

When it moves in a clockwise direction.