2A1 Chapter 11 Static and Dynamic Forces

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 is thermal expansion in the context of bars?

It refers to the increase in length of bars due to temperature changes, including reactions under restricted expansion.

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 formula for calculating the moment of total area about ML?

Moment = (area1 × distance1) + (area2 × distance2) + (area3 × distance3) × ycm

What is the second moment of area used for?

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

What is a static load?

A load applied slowly and held at a constant magnitude.

What is a sustained load?

A constant load applied over a long period of time.

What is an impact (shock) load?

A load applied suddenly in a very short time period.

What is a repeated (cyclic) load?

A load that increases and decreases in magnitude over time.

What is a concentrated load?

A load applied to a small area relative to the total area.

What is a distributed load?

A load spread along a length or area.

What is axial load?

A force acting through the centroid producing uniform tension or compression.

What is shear load?

Forces that are parallel but not in the same plane, causing varying stress.

What is torsional load?

A load applying an angular moment or twisting force to a beam or shaft.

What is bending load?

A force applied perpendicular to the axis of an object.

What is thermal load?

A load caused by thermal expansion or contraction due to temperature changes.

What is combined load?

A load caused by more than one type of load applied to an object.

What is stress?

The internal resistance resulting from the application of an external load.

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.

What is the formula for calculating the area of a tie?

A = πr², where r is the radius.

How is the maximum allowable force calculated from direct stress?

P = Direct stress × Area.

What is shear stress?

Shear stress is produced by equal and opposite parallel forces that cause one part of the material to slide over another.

How is shear stress calculated?

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

What is single shear stress?

Single shear stress occurs when stress is applied on one plane of a rivet.

What is double shear stress?

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

What is pure shear stress?

Pure shear stress occurs only in torsion or angular stress.

What is linear or direct strain?

Linear strain 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?

Strain has no units of measure.

What does Hooke's Law state?

Hooke's Law states that strain is directly proportional to stress within the elastic region.

What is elastic strain?

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

What is the elastic limit?

The maximum elastic strain a material can handle before permanent deformation occurs.

What is plastic strain?

Plastic strain occurs when the material is deformed beyond its elastic limit and does not return to its original shape.

What is the factor of safety in engineering design?

The factor of safety is the ratio of the elastic limit to the maximum expected working stress.

What is the Modulus of Elasticity?

The Modulus of Elasticity (E) is the ratio of direct stress to direct strain, indicating material stiffness.

What are typical units for Modulus of Elasticity?

Modulus of Elasticity is commonly measured in Pascals (Pa) or gigapascals (GPa).

What is the Modulus of Rigidity?

The Modulus of Rigidity (G) is the ratio of shear stress to shear strain.

How is shear strain measured?

Shear strain is measured in terms of the angle through which deformation occurs.

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?

Poisson's ratio 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 Poisson's ratio?

The ratio between the lateral strain and the axial strain in a material.

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

Between 0.25 and 0.35.

What happens to a material under tensile stress?

It produces tensile strain in the direction of the stress and compressive strain in every direction perpendicular to it.

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 is calculated using the formula P/A, where P is the load and A is the area.

What is the formula for calculating strain?

Strain (ε) is calculated as the change in length (ΔL) divided by the original length (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) is calculated as α × L × (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 formula for calculating stress in a composite bar?

The stress in each part of the composite bar is related by the equation σs/σb = As/Ab, where A is the cross-sectional area.

What is the increase in stress when a bar is fixed at both ends during temperature increase?

The increase in stress can be calculated using the modulus of elasticity and the thermal strain.

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 formula for calculating the change in length of a brass bar in a composite assembly?

Change in length is calculated as α × (T2 - T1) × L, where α is the coefficient of thermal expansion.

What happens to the brass in a composite bar when heated?

It expands less than it would if heated alone due to being constrained by the steel.

What is the relationship between strains in brass and steel in a composite bar?

The strains can be expressed in terms of stress and the modulus of elasticity.

What is the effect of fixed ends on thermal expansion?

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

How do you calculate the increase in length of a steel bar due to thermal expansion?

Using the formula ΔL = α × L × (T2 - T1).

What is the significance of understanding thermal expansion in engineering?

It is crucial for ensuring structural integrity and performance of materials under temperature variations.