Name: impact loading on a fixed rod
Uploaded: 2024-05-23T13:00:12.000Z
Duration: 1 min 19 s
Channel: JoVE

K12 Standards

Arizona Science Standards

High School

Physical Science

HS+Phy.P3

HS+Phy.P3U2.5

Impact Loading

Consider a rod of uniform cross-sectional area fixed at one end. When another moving object hits the free end of the rod, the rod deforms, and stress is developed within it. 
As the rod reaches the maximum stress, it vibrates about the mean position. The stress that has built up disappears as it comes to rest. These events are known as impact loading.
Here, it is assumed that the striking body transfers its entire energy to the rod, meaning no heat dissipation occurs, and the striking body does not bounce off the rod.
So, the strain energy corresponding to the maximum stress equals the kinetic energy of the striking body.
In the elastic regime of the deformation, the strain energy can be rewritten in terms of the maximum stress and the modulus of elasticity.
Rearranging the terms, an expression for the maximum stress in terms of the velocity of the striking body is obtained.
The assumption used here results in a conservative design for the impact loading, as the assumptions are not valid in real systems.

impactbelasting

<div>
 Impactbelasting vindt plaats wanneer een bewegend object in botsing komt met een stilstaande structuur, zoals een staaf met een uniform dwarsdoorsnedeoppervlak dat aan één uiteinde is bevestigd. Onder deze omstandigheden absorbeert de staaf de kinetische energie van het treffende object, wat leidt tot vervorming en daaropvolgende spanningsontwikkeling. Terwijl de staaf terugkeert naar zijn oorspronkelijke positie en maximale spanning bereikt, wordt de geabsorbeerde energie, die zich aanvankelijk manifesteert als kinetische energie, volledig omgezet in spanningsenergie.
 
 In gevallen van elastische vervorming, waarbij het materiaal terugkeert naar zijn oorspronkelijke vorm zonder blijvende schade, is de spanningsenergie die wordt verzameld op het punt van maximale vervorming gelijk aan de kinetische energie van het bewegende object. Deze gelijkwaardigheid gaat ervan uit dat er geen energie verloren gaat door hitte of terugslag, een idealisering die doorgaans niet in praktische omgevingen wordt aangetroffen. Uit deze relatie kan de maximale spanning worden afgeleid die de staaf ondervindt, gebaseerd op de snelheid en massa van het treffende object en de elasticiteitsmodulus van de staaf.
 
 <img alt="Equation 1" src="/files/ftp_upload/15686/15686_Equation_1v2.svg" style="text-align: center; height: 40px;">
 De aannames in deze analyse leiden tot een conservatieve benadering van technisch ontwerp, waardoor constructies onverwachte krachten kunnen weerstaan. Deze aanpak resulteert vaak in over-engineering, waarbij veiligheidsfactoren worden ingebouwd om rekening te houden met energieverliezen en andere dynamieken die niet door het theoretische model worden gedekt.
 
</div>

Consider a rod of uniform cross-sectional area fixed at one end. When another moving object hits the free end of the rod, the rod deforms, and stress is ...

Education

JoVE Core

Mechanical Engineering

Werktuigbouwkunde

Unit 1

Energy Methods

Energiemethoden

KEY TERMS AND CONCEPTS

BELANGRIJKE TERMEN EN CONCEPTEN

impact loading on a fixed rod

Impact loading on a fixed rod happens when a moving object strikes a stationary rod that has a uniform cross-sectional area and is fixed at one end. The impact makes the rod deform and begin to develop stress. This setup shows how a sudden hit can store energy in a structure.

As the rod moves back toward its original shape, the stress rises to a maximum. At that point, the energy from the moving object has changed from kinetic energy into strain energy. Kinetic energy is the energy of motion, and strain energy is the energy stored during elastic deformation.

For elastic deformation, the rod returns to its original shape without permanent damage. In that ideal case, the strain energy at maximum deformation is equal to the kinetic energy of the striking object. This relationship assumes that no energy is lost as heat or through rebound, which is rarely true in real situations.

From this energy balance, the maximum stress in the rod can be derived using the mass and velocity of the moving object and the rod’s modulus of elasticity. The result gives engineers a conservative design approach. It can also lead to over-engineering, with safety factors added to account for energy losses and other effects not included in the model.

Impact Loading on a Fixed Rod

strain energy

Load-Deformation and Stored Strain Energy

Strain energy is the energy stored in a material when it deforms under load. It is a key idea in materials science and structural engineering. A loaded rod fixed at one end shows this clearly. When an axial force pulls on the free end, the rod stretches and stress builds inside it. As the axial force increases, the rod elongates more. This creates a direct link between the applied force and the amount of deformation. Engineers can show this relationship with a load-deformation plot. The plot...

strain-energy density

Energy Stored in Loaded Rods

Energy stored in a rod under axial load helps show how a material will respond to stretching and breaking. When the rod elongates, it stores strain energy as potential energy inside the material. Strain energy density is the amount of that energy per unit volume. In the elastic region, stress and strain have a linear relationship that follows Hooke's Law. The strain energy density in this region is found from the area under the stress-strain curve up to the elastic limit. This recoverable...

elastic strain energy for normal stresses

elastic-strain-energy-for-normal-stresses

Strain Energy in Stressed Materials

Strain energy in stressed materials describes the energy stored when a material deforms under load. It is an important idea in materials science and engineering. For axial loading with a uniform stress distribution, the stress is the internal force divided by the cross-sectional area, and the strain follows from the stress through the modulus of elasticity. When the stress is uniform, the strain energy density can be found from the product of stress and strain. That density is then integrated...

elastic strain energy for shearing stresses

elastic-strain-energy-for-shearing-stresses

Shear Energy Stored in Twisted Shafts

Shear energy stored in twisted shafts depends on elastic strain energy in a material. This energy is stored when a solid is deformed within its elastic limit. It comes from internal work done against the cohesive forces inside the material. When a material carries shearing stress, it also develops shearing strain. The strain energy density is the energy stored per unit volume. Within the elastic limit, stress is proportional to strain through the modulus of rigidity, so the strain energy...

impact loading

Impact loading on a fixed rod happens when a moving object strikes a stationary rod that has a uniform cross-sectional area and is fixed at one end. The impact makes the rod deform and begin to develop stress. This setup shows how a sudden hit can store energy in a structure. As the rod moves back toward its original shape, the stress rises to a maximum. At that point, the energy from the moving object has changed from kinetic energy into strain energy. Kinetic energy is the energy of motion,...

impact loading on a cantilever beam

Dropped-Weight Bending of a Cantilever Beam

Dropped-weight bending of a cantilever beam shows how impact loading changes a beam’s shape and stress. The beam has a circular cross-section and is fixed at one end. An object is dropped on the free end from a height h, so its potential energy from gravity becomes kinetic energy at impact. After the object hits the beam, the beam bends and develops a bending moment along its length. The bending is not uniform. The fixed end carries the highest strain energy, which is the energy stored in the...

castigliano&#39;s theorem

Using Strain Energy to Find Deflection

Castigliano's theorem uses strain energy to find deflection and rotation in elastic structures. Strain energy is the work done by external loads during elastic deformation. The theorem links that energy to the movement caused by the load. The key idea is simple. The partial derivative of the total strain energy with respect to a specific force gives the displacement at the point where that force acts. The same method also works for a moment, where the derivative gives the rotation at the point...

castigliano&#39;s theorem: problem solving

Beam Deflection from Central Load

Beam deflection from a central load can be found with Castigliano's theorem. The method applies to a simply supported beam with a point load at the center. It links the deflection at the load point to the strain energy stored in the beam. For this beam, the supports share the load equally. Each support carries half of the force. The bending moment at any point along the beam comes from these reactions and is written using the distance from the nearest support. Castigliano's theorem says the...

key terms and concepts

Learn how a moving object striking a fixed rod creates stress, strain energy, and maximum stress in elastic deformation, with a conservative design model.

Impact Loading on a Fixed Rod | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Newton's Law of Gravitation

Our everyday observation tells us that all objects close to the Earth naturally tend to fall to the ground. Early philosophers assumed that this downward ...

Newton's Law of Universal Gravitation

Source: Ketron Mitchell-Wynne, PhD,&#160;Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of ...

Gravity between Spherical Bodies

Newton&#39;s law of gravitation describes the gravitational force between any two point masses. However, for extended spherical objects like the Earth, ...

gravitation-between-spherically-symmetric-masses

Gravitation Between Spherically Symmetric Masses

The gravitational potential energy between two spherically symmetric bodies can be calculated from the masses and the distance between the bodies, ...

/files/media/science-education/science-education-thumbs/14717.jpg

Potential Energy due to Gravitation

Since gravitational force is a conservative force, the amount of work done to move an object between two points in the gravitational field in which it ...

Electric Charges

From lightning during thunderstorms to electronic devices, the phenomenon of electromagnetism is all around us. The electromagnetic force is one of the ...

sources-and-properties-of-electric-charge

Sources and Properties of Electric Charge

All objects we see around us consist of atoms, which combine to form molecules. The lightest element in the universe is hydrogen, and a hydrogen atom ...

Coulomb's Law

Experiments with electric charges have shown that if two objects each have an electric charge, they exert an electric force on each other. The magnitude ...

coulomb-s-law-and-the-principle-of-superposition

Coulomb's Law and The Principle of Superposition

Coulomb&#39;s Law describes the force experienced by two point charges under each other&#39;s presence. But what if there are more than two charges? For ...

comparison-between-electrical-and-gravitational-forces

Comparison Between Electrical And Gravitational Forces

There are four fundamental forces in nature: the gravitational force, the electromagnetic force, the strong nuclear force, and the weak nuclear force. To ...

Develop and use mathematical models of Newton’s law of gravitation and Coulomb’s law to describe and predict the gravitational and electrostatic forces between objects.

HS+Phy.P3U1.2

Introduction to Vectors

To define some physical quantities, there is a need to specify both magnitude as well as direction. For example, when the U.S. Coast Guard dispatches a ...

vector-components-in-the-cartesian-coordinate-system

Vector Components in the Cartesian Coordinate System

Vectors are usually described in terms of their components in a coordinate system. Even in everyday life, we naturally invoke the concept of orthogonal ...

Vectors in Multiple Directions

Source: Nicholas Timmons, Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of California, Irvine, CA

...

Position and Displacement Vectors

To describe the motion of an object, one should first be able to describe its position (where it is at any particular time). More precisely, the position ...

average-and-instantaneous-velocity-vectors

Average and Instantaneous Velocity Vectors

To calculate other physical quantities in kinematics, the time variable must be introduced. The time variable not only allows us to state where an object ...

Acceleration Vectors

In everyday conversation, accelerating means speeding up. Acceleration is a vector in the same direction as the change in velocity, &#916;v, therefore the ...

Direction of Acceleration Vectors

Acceleration occurs when velocity changes in magnitude (an increase or decrease in speed), direction, or both. Although acceleration is in the direction ...

Projectile Motion

An object thrown in the air follows a parabolic path under the influence of Earth&#39;s gravitational force. The motion of such an object is called ...

/files/media/science-education/science-education-thumbs/12634.jpg

Projectile Motion: Equations

Projectile motion is commonly observed in our day-to-day life. For example, a basketball thrown by a player, an arrow shot from a bow, and kids jumping ...

Projectile Motion: Example

The theory of projectile motion is very useful for players of several sports to improve their performance. For example, a javelin thrower needs to throw ...

Kinematics and Projectile Motion

principle-linear-impulse-momentum-for-single-particle-problem

Principle of Linear Impulse and Momentum for a Single Particle: Problem Solving

Consider a massless pulley system consisting of a wooden box and a cylinder of known masses. Determine the speed of the attached objects at a specific ...

Non-uniform Circular Motion

In&#160;uniform circular motion, the particle executing circular motion has a constant speed, and the circle is at a fixed radius. However, not all ...

first-law-particles-in-two-dimensional-equilibrium

First Law: Particles in Two-dimensional Equilibrium

Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic ...

Dynamics of Circular Motion

An object undergoing circular motion, like a race car, is accelerating because it is changing the direction of its velocity. This centrally directed ...

Dynamics Of Circular Motion: Applications

Suppose a car moves on flat ground and turns to the left. The centripetal force causing the car to turn in a circular path is due to friction between the ...

Centrifugal Force

Pseudo forces, or fictitious forces, appear to act on an object in motion in a rotating frame of reference with respect to an inertial reference frame. ...

/files/media/science-education/science-education-thumbs/14696.jpg

Develop a mathematical model, using Newton’s laws, to predict the motion of an object or system in two dimensions (projectile and circular motion).

HS+Phy.P3U1.3

Linear Momentum

The term momentum is used in various ways in everyday language, most of which are consistent with the precise scientific definition. Generally, momentum ...

Force and Momentum

Force and momentum are intimately related. Force acting over time can change momentum, and Newton&#39;s second law of motion can be stated in its most ...

Newton's Third Law: Introduction

Whenever one body exerts a force on a second body, the first body experiences a force equal in magnitude and opposite in direction, to the force that it ...

Impulse

According to Newton&#8217;s second law of motion, the rate of change of the momentum of an object is the net external force acting on it. The total change ...

Impulse-Momentum Theorem

The total change in the motion of an object is proportional to the total force vector acting on it and the time over which it acts. This product is called ...

Conservation of Momentum: Introduction

The total momentum of a system consisting of N interacting objects is constant in time or is conserved. A system must meet two requirements for its ...

Conservation of Momentum

Source: Nicholas Timmons,&#160;Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of California, Irvine, ...

Conservation of Momentum: Problem Solving

Solving problems using the conservation of momentum requires four basic steps:

	Identify a closed system, where the total mass is constant, and no net ...

Types Of Collisions - I

When two objects come in direct contact with each other, it is called a collision. During a collision, two or more objects exert forces on each other in a ...

Types of Collisions - II

When two or more objects collide with each other, they can stick together to form one single composite object (after collision). The total mass of the ...

Elastic Collisions: Introduction

An elastic collision is one that conserves both internal kinetic energy and momentum. Internal kinetic energy is the sum of the kinetic energies of the ...

collisions-in-multiple-dimensions-introduction

Collisions in Multiple Dimensions: Introduction

It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each ...

Center of Mass: Introduction

Any object that obeys Newton&#39;s second law of motion is made up of a large number of infinitesimally small particles. Objects in motion can be as ...

Engage in argument from evidence regarding the claim that the total momentum of a system is conserved when there is no net force on the system.

HS+Phy.P3U1.4

Impact

Impact occurs when two bodies collide, resulting in impulsive forces being exerted between them.
To analyze impact mechanics, consider two colliding ...

Impact: Problem Solving

In an experiment during a Mars mission, a rover fires a projectile with an initial velocity that rebounds after impacting the Martian surface.
With a ...

charpy-impact-test-cold-formed-hot-rolled-steels-under-diverse

Charpy Impact Test of Cold Formed and Hot Rolled Steels Under Diverse Temperature Conditions

Source:&#160;Roberto Leon, Department of Civil and Environmental Engineering, Virginia Tech, Blacksburg, VA
One of the more insidious types of failures ...

Design, evaluate, and refine a device that minimizes or maximizes the force on a macroscopic object during a collision.

Impact Loading on a Fixed Rod

Description

Transcript

Tags

More videos by Standards