Name: statics problem-solving steps for beams
Uploaded: 2023-09-22T11:49:19.000Z
Duration: 1 min 28 s
Channel: JoVE

K12 Standards

Arizona Science Standards

High School

Physical Science

HS.P3

HS.P3U2.7

Problem Solving in Statics

정역학은 평형 상태에 있는 물체에 대한 연구이며, 정역학에서 문제를 해결하려면 여러 단계가 필요합니다.
첫 번째 단계는 문제를 공식화하는 것입니다. 지지부 중 하나에서 특정 거리에 있는 단순하게 지지된 빔에 작용하는 점 하중의 예를 생각해 보십시오.
여기서 핵심 지점의 반력과 굽힘 모멘트를 추정해야 합니다.
이 문제를 해결하기 위해 몇 가지 가정이 이루어집니다. 빔의 너비와 같은 소량은 길이와 같은 많은 양에 비해 무시됩니다. 물리량의 방향을 나타내기 위해 적절한 부호 규칙이 사용됩니다.
추가 분석을 위해 자유물체 다이어그램이 그려집니다. 그들은 특정 섹션에서 빔에 작용하는 힘을 분석하고 알짜 힘과 굽힘 모멘트에 대한 수학 방정식을 제공하는 데 도움이 됩니다.
굽힘 모멘트 표현식은 모든 힘과 해당 거리를 대체하여 반력을 계산하는 데 사용됩니다.
점 c의 굽힘 모멘트는 R,a, d1의 곱으로 제공됩니다.
결과는 굽힘 및 전단력 다이어그램을 사용하여 보고됩니다.

<ol>
	<li>히벨러, R.C. (2016). Engineering Mechanics \u2012 정역학 및 동역학. 뉴저지 호보켄: 피어슨 프렌티스 홀. 12쪽</li>
	<li>맥주, F.P.; 존스턴, ER; 마주렉, D.F; 크롬웰, PJ 및 셀프, BP (2019). 엔지니어를 위한 벡터 역학 \u2012 Statics and Dynamics. 뉴욕 : McGraw-Hill. 14, 15, 14쪽</li>
	<li>메리암, J.L.; Kraige, L.G. 및 Bolton, J.N. (2020). 엔지니어링 역학 \u2012 정역학. 뉴저지 호보켄: 존 와일리. 14, 15, 17</li>쪽
</ol>

정역학에서의 문제 해결

정역학의 문제 해결은 평형 상태의 물체와 관련된 문제를 해결하는 것과 관련된 공학 및 물리학의 중요한 측면입니다. 대부분의 경우 문제 해결에는 정확한 결과를 얻기 위해 여러 단계가 필요합니다. 이러한 단계는 솔루션이 정확하고 실용적인지 확인하는 데 중요합니다.
물리적 상황과 수학적 모델링을 고려해야 합니다. 그러나 수학적 모델링을 사용하여 모든 물리적 상황을 표현하는 것은 어렵습니다. 근사치와 가정의 도움으로 문제를 공식화할 수 있습니다.
근사를 수행하는 동안 큰 거리에 비해 매우 작은 거리는 무시됩니다. 예를 들어, 직사각형의 너비는 길이보다 몇 자릿수 작은 경우 무시할 수 있습니다. 각도 변위가 다른 치수보다 작은 경우 작은 각도 근사치를 사용할 수 있습니다. 근사치의 한 가지 예는 힘이 신체나 물체 전체에 분산되는 경우입니다. 이는 점하중으로 간주될 수 있습니다. 가정은 순전히 필요한 결과의 정확성에 따라 달라집니다.
정역학 문제 해결의 첫 번째 단계는 문제를 공식화하는 것입니다. 문제를 공식화하려면 물리적 시나리오를 이해하고 그 안에 있는 변수를 결정해야 합니다. 예를 들어, 지지대 중 하나로부터 특정 거리에 있는 단순 지지 보에 작용하는 점하중의 예를 생각해 보십시오. 이 시나리오에서는 주요 지점의 반력과 굽힘 모멘트를 추정해야 합니다.
문제를 공식화한 후 문제를 해결하기 위해 몇 가지 가정을 합니다. 보의 길이에 비해 보의 폭을 무시하는 것처럼 큰 것에 비해 작은 양을 무시하는 등의 가정이 이루어집니다. 보의 지지된 양 끝단의 굽힘 모멘트는 0으로 가정됩니다. 또 다른 가정은 하중으로 인해 보가 변형되지 않는다는 것입니다. 또한 물리량의 방향을 나타내는 적절한 부호 규칙이 사용됩니다. 이러한 가정은 문제를 단순화하고 보다 간단한 솔루션을 만드는 데 도움이 됩니다.
정역학 문제 해결의 다음 단계는 자유물체 다이어그램을 준비하는 것입니다. 자유물체 도표는 특정 단면에서 보에 작용하는 힘을 분석하고 순 힘과 굽힘 모멘트에 대한 수학 방정식을 결정하는 데 사용됩니다. 이 자유물체 도표는 물체에 작용하는 힘의 합을 식별하고 굽힘 모멘트의 방향과 방정식을 배치하는 데 도움이 됩니다. 이는 고려 중인 상황에 대한 명확한 그림을 제공하고 취해야 할 다음 단계를 결정하는 데 도움이 됩니다.
자유물체 도표가 작성되면 계산을 수행하여 반력을 결정할 수 있습니다. 굽힘 모멘트 계산을 통해 굽힘 모멘트를 결정하고 반력을 계산하는 데 사용할 수 있습니다. 이 계산은 시나리오와 관련된 반력을 정확하게 추정합니다.
굽힘력 및 자유물체 도표는 보 길이에 따른 굽힘력 및 전단력의 변화를 보여줍니다. 이러한 자유물체 도표는 엔지니어가 고려 중인 신체 상태를 더 잘 이해하고 잠재적인 관심 영역을 식별하는 데 도움이 됩니다.
결과를 표현하기 위해 대수 기호를 사용할 수 있습니다. 수치 계산을 수행하는 동안 방정식 전체에서 일관된 단위를 사용해야 합니다. 또 다른 중요한 단계는 답변을 확인하는 것입니다. 계산 단계의 오류는 답을 대수 방정식에 대입하여 다시 확인할 수 있습니다.

정역학의 문제 해결은 평형 상태의 물체와 관련된 문제를 해결하는 것과 관련된 공학 및 물리학의 중요한 측면입니다. ...

Education

교육

JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

An Introduction to Statics

정역학 입문

KEY TERMS AND CONCEPTS

주요 용어 및 개념

statics problem-solving steps for beams

Statics problem-solving uses a step-by-step method to analyze bodies in equilibrium, especially beams. It is an important part of physics and engineering because the goal is to find practical and accurate answers for real situations. The process usually starts with a physical situation and then turns it into a mathematical model.

That model often needs approximations and assumptions. Very small distances can be ignored when they are much smaller than the main dimensions, such as beam width compared with beam length. Small angle approximations can also be used when the angular displacement is smaller than the other dimensions. A distributed force may be treated as a point load. The exact assumptions depend on how accurate the final result needs to be.

The first major step is to formulate the problem. This means understanding the situation and identifying the variables involved. For example, a point load can act on a simply supported beam at a certain distance from one support, and the reaction forces and bending moments at key points must be estimated.

After the problem is set up, more assumptions are made to simplify the analysis. The width of the beam may be neglected compared with its length. The bending moments at both supported ends are assumed to be zero, and the beam is assumed not to deform under the loading. Sign conventions are also used so the directions of physical quantities stay consistent.

Free-body diagrams come next. A free-body diagram shows the forces acting on a beam or on a chosen section of it. These diagrams help form equations for net force and bending moment, and they give a clear picture of the situation being studied.

Once the free-body diagrams are ready, calculations can be carried out to find the reaction forces. Bending moment calculations support this step and help determine the forces at the supports. The results can then be shown with bending force diagrams and shear force diagrams, which display how bending and shear change along the beam. Algebraic symbols are used to represent the results, and consistent units must be used in every numerical calculation. The final step is to verify the answer by substituting the solution back into the algebraic equations and checking for errors.

Statics Problem-Solving Steps for Beams

an introduction to mechanics

Mechanics in Physics and Engineering

Mechanics is a key branch of physics that explains how objects stay at rest or move when forces act on them. It also has major uses in engineering and science. The topic helps students understand everyday motion, machine behavior, and the way many systems work. The recorded history of mechanics begins with Aristotle, who lived from 384 to 322 BC. He linked mechanics with physical theory and looked for a broad universal explanation. Later, Newton defined mechanics as the study of objects at...

basic concept

Fundamental Quantities in Engineering Mechanics

Engineering mechanics begins with four basic quantities: length, time, mass, and force. These ideas help describe how objects move and how they respond to loads. They also support many other engineering fields. Length measures the distance traveled by an object. Engineers describe this distance with coordinates relative to a reference point. Length is also useful for showing the geometry of physical systems. Time measures the succession of an event. A bus traveling from city X to city Y is a...

newton's law of motion

Newton's Laws and Everyday Motion

Newton's laws explain everyday motion and the forces that change it. These three laws describe why objects move, stay still, or speed up. They also show how force and mass affect motion. Newton's first law is the law of inertia. It says an object at rest stays at rest, and an object in motion keeps moving at a constant speed and direction unless an external force acts on it. A sliding box that slows down on its own is a good example. In that case, friction is the net external force that works...

newton's law of gravitational attraction

Gravity Between Masses and Distance

Newton’s law of gravitational attraction describes how gravity acts between two objects. Sir Isaac Newton built this law from empirical evidence and inductive reasoning. He published it in Philosophiae Naturalis Principia Mathematica, or the Principia, on July 5, 1687. The law says that the gravitational force between any two objects depends on their masses and their distance apart. The force is proportional to mass and inversely proportional to the square of the distance between the objects.

units of measurement

SI and Customary Measurement Systems

Mechanical engineering depends on units of measurement for precise and accurate calculations. These units give engineers a standard way to express and compare physical quantities. They are essential when designing and analyzing machines and mechanical systems. Many historical measurement systems have been used over time. Examples include the Babylonian system, the Roman system, the Egyptian system, the Olympian system, the British system, and the Indus Valley system. Today, the International...

international system of units

SI Units and Metric Prefixes

SI units and metric prefixes provide a standard way to measure size, mass, and time. The International System of Units, or SI system, is used worldwide because it gives scientists a common language for measurement. Its values do not change with location, which helps keep results consistent. The SI system is built on three base units: meter, kilogram, and second. These are the core units for length, mass, and time. The kilogram is the only base unit that already includes a prefix. Prefixes...

numerical calculations

Engineering Notation and Significant Figures

Numerical calculations in engineering depend on clear values, correct units, and careful rounding. Presenting the answer is an important part of engineering practice, so numerically accurate results are preferred. Handheld calculators and computers are often used because they help produce accurate answers. Problems can be solved in several ways. Solving algebraic symbols by hand is common, and the graphical method is often preferred in some cases. Computers are especially useful when many...

accuracy, limits, and approximation

Accuracy and Approximation in Calculations

Accuracy and approximation are important in calculations, especially in engineering. Accuracy means how close a measured value is to the true or actual value. Repeated measurements are often used in engineering mechanics to help make results more precise and accurate. The accuracy of a solution depends on empirical data and the results from different calculations or measurements. A cylindrical container filled with liquid is a simple example. Its volume can be found from the measured...

dimensional analysis

Using Dimensions to Check Physics Equations

Dimensional analysis is a useful way to check physics and engineering equations. It works by writing physical quantities in terms of basic dimensions such as mass, length, and time. Quantities like velocity, acceleration, and force are derived from these basic dimensions. This method helps compare measurements even when the units are different. It also checks whether an equation is dimensionally homogeneous. That means the powers of the fundamental dimensions must match on both sides of the...

problem solving in statics

Statics problem-solving uses a step-by-step method to analyze bodies in equilibrium, especially beams. It is an important part of physics and engineering because the goal is to find practical and accurate answers for real situations. The process usually starts with a physical situation and then turns it into a mathematical model. That model often needs approximations and assumptions. Very small distances can be ignored when they are much smaller than the main dimensions, such as beam width...

key terms and concepts

Learn the step-by-step statics method for beams, including assumptions, free-body diagrams, reaction forces, bending moments, shear diagrams, and answer checks.

Statics Problem-Solving Steps for Beams | 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

Texas Essential Knowledge and Skills

Physics

PHYS.1

IPC.1.G

Chemistry and Physics

IPC.1

new-york-state-science-learning-standards

New York State Science Learning Standards

engineering-technology-and-applications-of-science

Engineering, Technology, and Applications of Science

Engineering Design

HS-ETS1-2.

Position and Displacement

The position of an object defines its location relative to a convenient frame of reference at any particular time. A frame of reference is an arbitrary ...

Average Velocity

To calculate the other physical quantities in kinematics, we must introduce the time variable. The time variable allows us not only to state the position ...

Average Acceleration

The importance of understanding acceleration spans our day-to-day experiences, as well as the vast reaches of outer space and the tiny world of subatomic ...

Instantaneous Acceleration

Acceleration is in the direction of the change in velocity, but it is not always in the direction of motion. When an object slows down, its acceleration ...

velocity-and-position-by-graphical-method

Velocity and Position by Graphical Method

Velocity and position can be calculated from the known function of acceleration as a function of time. The total area under the acceleration-time graph ...

Kinematic Equations - I

When an object moves with constant acceleration, the velocity of the object changes at a constant rate throughout the motion. The kinematic equations of ...

Kinematic Equations: Problem Solving

When analyzing one-dimensional motion with constant acceleration, the problem-solving strategy involves identifying the known quantities and choosing the ...

Force

Forces affect every moment of our life. Our bodies are held to the Earth by force, and they are held together by the forces of charged particles. When we ...

Mass and Weight

Mass and weight are often used interchangeably in everyday conversation. For example,&#160; medical records often show our weight in kilograms, but never ...

Newton's Laws of Motion

Source: Andrew Duffy, PhD, Department of Physics, Boston University, Boston, MA
This experiment examines at various situations involving two interacting ...

Newton's First Law: Introduction

Motion draws our attention. Motion itself can be beautiful, causing us to marvel at the forces needed to create spectacular sights, such as that of a ...

first-law-particles-in-one-dimensional-equilibrium

First Law: Particles in One-dimensional Equilibrium

Newton&#39;s first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a ...

Newton's Second Law

Newton&#39;s second law is closely related to his first law of motion. It mathematically gives the cause-and-effect relationship between force and changes ...

Force and Acceleration

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

Second Law: Motion under Same Force

Newton&#39;s laws can be applied to bodies at rest and bodies in motion. Newton&#39;s first law is applied to bodies in equilibrium, whereas the second ...

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 ...

Drawing Free-body Diagrams: Rules

The first step in describing and analyzing most phenomena in physics involves the careful drawing of a free-body diagram. Free-body diagrams are useful in ...

Free Body Diagrams: Examples

Solving problems that involve forces is easy using free-body diagrams. A free-body diagram is a sketch showing all the external forces that are acting on ...

Equilibrium and Free-body Diagrams

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

Collect, analyze and interpret data regarding the change in motion of an object or system in one dimension, to construct an explanation using Newton’s Laws.

HS.P3U1.6

Solving Problems in Physics

Problem-solving is the ability to apply general physical principles to specific situations, usually expressed by equations. It is an essential skill in ...

Problem-solving in statics is a crucial aspect of engineering and physics that involves resolving issues associated with bodies in a state of equilibrium. ...

An Introduction to Mechanics

Humans have been making ships, shelters, pyramids, weapons, agricultural equipment, and many more items without recording the process or theory behind ...

Introduction to Structures

A structure is defined as a system of interconnected members designed to support or transfer forces and successfully withstand the loads acting on them. ...

Simple Trusses

A truss is a structural framework consisting of slender members connected at joints, designed to support external loads while minimizing material usage ...

Method of Joints

The method of joints is a commonly used technique to analyze the forces in structural trusses. The method is based on the principle of equilibrium, which ...

Rigid Body Equilibrium Problems - I

A rigid body is said to be in static equilibrium when the net force and the net torque acting on the system is equal to zero. To solve for rigid body ...

Stability of structures

Consider two rods connected at point O by a pin and a torsional spring of constant k. The ends of both the rods are pin-connected.
If both the rods are ...

Buckling of Steel Columns

Source:&#160;Roberto Leon, Department of Civil and Environmental Engineering, Virginia Tech, Blacksburg, VA
In the design of civil works, it is important ...

Machines

Machines are complex structures consisting of movable, pin-connected multi-force members that work together to transmit forces. One example of a machine ...

DC Motors

Source: Ali Bazzi, Department of Electrical Engineering, University of Connecticut, Storrs, CT. 
The DC machine operates with DC currents and voltages as ...

Rolling Resistance

When a solid cylinder rolls steadily on a rigid surface, the normal force applied by the surface on the cylinder is perpendicular to the tangent at the ...

Propulsion and Thrust

Source: Alexander S Rattner; Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA
Aircraft, rockets, ...

Rocket Propulsion in Empty Space - I

The driving force for the motion of any vehicle is friction, but in the case of rocket propulsion in space, the friction force is not present. The motion ...

aerodynamic-performance-of-a-model-aircraft-the-dc-6b

Aerodynamic Performance of a Model Aircraft: The DC-6B

Source: Jose Roberto Moreto and Xiaofeng Liu, Department of Aerospace Engineering, San Diego State University, San Diego, CA
The low-speed wind tunnel is ...

airfoil-behavior-pressure-distribution-over-a-clark-y-14-wing

Airfoil Behavior: Pressure Distribution over a Clark Y-14 Wing

Source: David Guo, College of Engineering, Technology, and Aeronautics (CETA), Southern New Hampshire University (SNHU), Manchester, New Hampshire
An ...

Use mathematics and computational thinking to explain how Newton’s laws are used in engineering and technologies to create products to serve human ends.

Statics Problem-Solving Steps for Beams

Description

Transcript

Tags

More videos by Standards