Name: eccentric load stresses in structural columns
Uploaded: 2024-05-23T13:00:08.000Z
Duration: 1 min 21 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Physics

PHYS.2

PHYS.2.D

design-of-columns-under-an-eccentric-load

Design of Columns under an Eccentric Load

Для колонны, нагруженной эксцентриковой осевой нагрузкой в плоскости симметрии, нормальные напряжения от эксцентрической нагрузки могут быть записаны как напряжения, вызванные эквивалентной центральной нагрузкой и изгибом.
При проектировании колонн с эксцентриковыми нагружениями максимальное напряжение, развиваемое в колонне, не должно превышать максимально допустимого напряжения. Это условие может быть выполнено с помощью двух различных подходов.
Метод допустимого напряжения предполагает, что допустимое напряжение для эксцентрично нагруженной колонны совпадает с максимальным напряжением для колонны с центральной нагрузкой. Допустимое напряжение для колонны может быть выражено как функция коэффициента гибкости.
Допустимое напряжение при центрической нагрузке меньше, чем из-за изгибающего момента. Это приводит к тому, что метод допустимого напряжения является чрезмерно консервативным. 
С другой стороны, метод взаимодействия учитывает допустимые напряжения из-за центрического нагружения и изгиба.
Он предоставляет уравнение для максимального напряжения при центральном нагружении, когда нет парного момента. Точно так же он определяет максимальное напряжение от чистого изгиба при отсутствии нагрузки.

Проектирование колонн под эксцентричной нагрузкой

Проектирование колонн, способных выдерживать эксцентрические нагрузки, является важнейшим аспектом проектирования конструкций, гарантирующим, что конструкции смогут без разрушений выдерживать внецентренную нагрузку. Этот процесс проектирования должен учитывать дополнительные нормальные напряжения, возникающие из-за нецентральной нагрузки, которые могут существенно повлиять на распределение напряжений и общую устойчивость колонны. Эксцентричная нагрузка, приложенная к колонне, вызывает нормальные напряжения, которые можно представить как комбинацию напряжений, вызванных эквивалентной центральной нагрузкой и дополнительными изгибающими напряжениями. Это приводит к неравномерному распределению напряжений, которое необходимо тщательно анализировать, чтобы предотвратить разрушение конструкции. При проектировании колонн под внецентренные нагрузки используются два основных метода: метод допустимых напряжений и метод взаимодействия.

Метод допустимого напряжения представляет собой простой подход, при котором допустимое напряжение для колонны с внецентренной нагрузкой приравнивается к максимальному допустимому напряжению для колонны с центральной нагрузкой. Этот метод упрощает процесс проектирования, рассматривая допустимое напряжение как функцию коэффициента гибкости колонны, который является мерой ее склонности к короблению под нагрузкой. Однако этот метод предполагает, что допустимое напряжение для центральной нагрузки включает в себя дополнительные напряжения из-за изгиба, что приводит к консервативным конструкциям, которые могут не использовать весь потенциал материала. Консерватизм, присущий этому подходу, обеспечивает безопасность, но может привести к созданию более крупных и дорогих колонн, чем необходимо.

Метод взаимодействия предлагает более тонкий подход, учитывающий как допустимые напряжения из-за центральной нагрузки, так и напряжения, возникающие из-за изгибающих моментов. Этот метод обеспечивает основу для расчета максимального напряжения, которое колонна может выдержать без парного момента (чистая центральная нагрузка) и максимального напряжения из-за чистого изгиба (без осевой нагрузки). Благодаря одновременному учету этих условий, метод взаимодействия позволяет более точно и менее консервативно оценить допустимые напряжения в эксцентрично нагруженных колоннах.

На практике метод взаимодействия часто предпочитают из-за его способности сочетать безопасность с эффективностью использования материалов. Он требует детального анализа распределения напряжений внутри колонны с учетом как осевых нагрузок, так и изгибающих моментов.

Для колонны, нагруженной эксцентрической осевой нагрузкой в плоскости симметрии, нормальные напряжения от эксцентрической нагрузки могут быть записаны как напряжения, вызванные ...

Education

JoVE Core

Mechanical Engineering

Машиностроение

Unit 1

Раздел 1

Columns

Столбцы

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

eccentric load stresses in structural columns

Structural columns under eccentric load must be designed for both axial force and bending stress. An eccentric load is an off-center load, and it creates a non-uniform stress pattern across the column. Engineers must analyze this stress distribution carefully to reduce the risk of failure.

The stress in an eccentrically loaded column can be treated as the sum of two parts. One part comes from an equivalent centric load, which is a load applied through the center of the column. The other part comes from bending stresses caused by the load being off-center.

Two common design approaches are used for these columns. The allowable stress method sets the allowable stress for an eccentrically loaded column equal to the maximum stress allowed for a centrally loaded column. This method uses the column slenderness ratio, which describes how likely a column is to buckle.

The allowable stress method is simple, but it is also conservative. It assumes the centric-load allowable stress already covers the extra bending stress from eccentric loading. As a result, the column may be larger and more expensive than needed, even though the design is safe.

The interaction method gives a more detailed design check. It considers both the allowable stress from centric loading and the stress from bending moment at the same time. It compares the case of pure centric loading, with no couple moment, and the case of pure bending, with no axial load.

Because it includes both effects, the interaction method can estimate allowable stress more accurately. It is often preferred when engineers want a better balance between safety and material use. The method requires careful stress analysis of the column under both axial load and bending moment.

Eccentric Load Stresses in Structural Columns

eccentric-load-stresses-in-structural-columns

stability of structures

Critical Load and Structure Stability

Structural stability is an important idea in mechanical engineering. It helps engineers design buildings, vehicles, and machines that stay safe and efficient under load. A simple model for studying this behavior uses two rods joined at a pivot point O with a torsional spring, which is a spring that resists twisting, at the pivot. The setup is similar to a scissor jack used to lift a car. In the example, the linkage arms are vertical, which matches the case where the vehicle has been raised as...

euler&#39;s formula for pin-ended columns

Critical Buckling Load in Pin-Ended Columns

Critical buckling load in pin-ended columns is a key idea in structural engineering. It explains when a column under compressive axial load becomes unstable and starts to buckle. A pin-connected column with a centric load F at one end has a reaction force of F' = -F at the other end. When the applied load rises above the critical load, buckling begins. To find the critical load, the column PQ can be treated like a vertical beam. Point O is chosen on the elastic curve of the beam at a distance...

euler&#39;s formula to columns with other end conditions

euler-s-formula-to-columns-with-other-end-conditions

Euler Buckling for Different Column Supports

Euler buckling explains how a column can fail when it is compressed. In structural engineering, it helps predict the critical load, which is the load level where a column is likely to buckle. The formula uses the modulus of elasticity, the moment of inertia of the cross-section, and the column length. The same idea also helps describe critical stress. Critical stress is found by dividing the critical load from Euler's formula by the cross-sectional area of the column. This leads to the...

euler&#39;s formula to columns: problem solving

euler-s-formula-to-columns-problem-solving

Spring-Loaded Column Buckling Analysis

Spring-loaded column buckling analysis uses static equilibrium to find the critical load in a rigid bar system. The setup has two equal-length rigid bars, AB and BC, joined at pivot point B. A tension spring with constant k is attached to B and pulls horizontally. A vertical load F is applied at point A, and the bars rotate around the pivot like a knee joint. As point B moves, the spring stretches by an amount X. The spring then pushes back against the sideways motion of B. To study the...

eccentric loading

Column Bending Under Off-Center Load

Eccentric loading shows how a column bends when a force is applied off-center. In structural engineering, this matters because the load no longer acts along the centroidal axis, so the column sees both direct compression and bending stress. The off-center force can be treated as two parts. One part is a centric load F that acts along the column’s axis. The other part is a couple moment created by the eccentricity, or distance, between the load and the centroidal axis. To study the column...

design of columns under a centric load

Column Buckling and Load Design Basics

Column design under a centric load is a key part of structural engineering. It helps engineers keep buildings and other structures stable and safe. The main tools used here are Euler’s formula and Secant’s formula. Euler’s formula is used when a column is assumed to be perfect, straight, and uniform. It also applies when the material stays within its elastic limit. The critical load from Euler’s formula depends on the material’s modulus of elasticity and the column’s shape. This formula works...

design of columns under an eccentric load

Structural columns under eccentric load must be designed for both axial force and bending stress. An eccentric load is an off-center load, and it creates a non-uniform stress pattern across the column. Engineers must analyze this stress distribution carefully to reduce the risk of failure. The stress in an eccentrically loaded column can be treated as the sum of two parts. One part comes from an equivalent centric load, which is a load applied through the center of the column. The other part...

key terms and concepts

Learn how eccentric loads create combined axial and bending stresses in columns, and compare the allowable stress and interaction methods used in design.

Eccentric Load Stresses in Structural Columns | 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

Chemistry and Physics

IPC.2

IPC.2.D

Models, Theories, and Laws

Scientists frequently use models to help them comprehend a specific collection of phenomena. In physics, a model is a condensed version of a physical ...

/files/media/science-education/science-education-thumbs/14686.jpg

Brick Sizes

The dimensions of a brick are determined by three measurements: its width, height, and length.
Typically, bricks are sized to build walls in modules of 4 ...

structural-properties-and-dimensions-of-lumber

Structural Properties and Dimensions of Lumber

Wood fibers align along the tree&#39;s length, giving it up to twenty times higher tensile strength along the fibers than across them. Wood is also ...

Accuracy, limits, and approximation

Accuracy, limits, and approximations are common in many fields, especially in engineering calculations. These concepts are imperative for ensuring that a ...

Design Consideration

While designing a structure, the considerations start with the ultimate strength of a material, which is determined through tests, measuring changes under ...

Dynamics of Structures

Source:&#160;Roberto Leon, Department of Civil and Environmental Engineering, Virginia Tech, Blacksburg, VA
It is rare nowadays that a whole year goes by ...

Material Constants

Source:&#160;Roberto Leon, Department of Civil and Environmental Engineering, Virginia Tech, Blacksburg, VA
In contrast to the production of cars or ...

Estimation of the Physical Quantities

On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as ...

/files/media/science-education/science-education-thumbs/14734.jpg

Identify advantages and limitations of models such as their size, scale, properties, and materials

PHYS.2.A

Introduction to Statistics

The science of statistics involves collecting, analyzing, interpreting, and presenting data. The method of collecting, organizing, and summarizing data is ...

How Data are Classified: Categorical Data

A variable, usually notated by capital letters such as X and Y, is a characteristic or measurement that can be determined for each member of a population. ...

How Data are Classified: Numerical Data

Data that are countable or measurable in specific units are called numerical or quantitative data. Quantitative data are always numbers. Quantitative data ...

Review and Preview

Data are individual items of information obtained from a population or sample. Data may be classified as qualitative (categorical), quantitative ...

What is a Frequency Distribution

A frequency is the number of times a value of the data occurs. The sum of all the frequency values represents the total number of students included in the ...

What is Central Tendency?

Descriptive statistics describe or summarize relevant characteristics of a sample and aid in the analysis of data of interest. When analyzing large ...

Arithmetic Mean

The arithmetic mean is the most commonly used measure of the central tendency of a data set. It is defined as the sum of all the elements constituting the ...

What is a Mode?

The mode is one of the commonly used measures of a central tendency. It is defined as the most frequent value in a data set.
There can be more than one ...

Median

Besides mean, the median is a widely used measure of central tendency. Typically, median is defined as the central or middle value of a data set, measured ...

What is Variation?

Apart from the measures of central tendency, distribution, outliers, and the changing characteristics of data with time, an important characteristic of ...

Standard Deviation

The most commonly used measure of variation is the standard deviation. It is a numerical value measuring how far data values are from their mean. The ...

Standard Error of the Mean

The sampling variability of a statistic is defined as how much the statistic varies from one sample to another. The sampling variability of a statistic is ...

Calculating Standard Deviation

The standard deviation is the most common measure of variation. It is a value that tells us how far a data value is from the mean value in a dataset. ...

Variance

&#160;The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative ...

Coefficient of Variation

The coefficient of variation measures the dispersion of the data points or distribution around the mean. Using the coefficient of variation, we can ...

Probability in Statistics

Probability is the likelihood of an event occurring. The term event is defined as a collection of results of a procedure. An event is a simple event when ...

Random Variables

A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability ...

What is a Hypothesis?

A hypothesis can be a simple sentence or statement about a property or any phenomenon observed or predicted for a population. It is usually a claim about ...

Null and Alternative Hypotheses

The actual hypothesis testing begins by considering two hypotheses. They are termed&#160; the null hypothesis and the alternative hypothesis. These ...

Types of Hypothesis Testing

There are three types of hypothesis tests: right-tailed, left-tailed, and two-tailed.
When the null and alternative hypotheses are stated, it is observed ...

Study Design in Statistics

A study design is a set of techniques that allow a researcher to collect and analyze data from different variables defined for a specific research ...

types-of-errors-detection-and-minimization

Types of Errors: Detection and Minimization

Error is the deflection of an obtained result from the expected or true results of an experiment. This happens due to the uncertainty associated with the ...

systematic-error-methodological-and-sampling-errors

Systematic Error: Methodological and Sampling Errors

Systematic errors, depending on their source, are of four types &#8211; sampling, instrumental, method, and personal errors.
Sampling errors occur due to ...

Random Error

Indeterminate or random errors arise from several uncontrollable variables in successive measurements.
Since these errors can neither be predicted nor ...

Analyze data by identifying significant statistical features, patterns, sources of error, and limitations

PHYS.2.B

Numerical Calculations

In engineering applications, the representation of the numerical value is critical. Presenting or reporting the answer is one of the essential parts of ...

Quantitative Analysis

Quantitative analysis is a technique for measuring the amount of specific constituents in a sample. When the sample&#39;s composition is unknown, ...

Statistical Analysis: Overview

An analysis is usually conducted by replicated sampling or repeated measurements on the same sample. This leads to scattered results rather than a single ...

Dimensional Analysis

Dimensional analysis, also known as the factor label method, is a versatile approach for mathematical operations. The main principle behind this approach ...

calculating-and-interpreting-the-linear-correlation-coefficient

Calculating and Interpreting the Linear Correlation Coefficient

The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear ...

variation-normal-distribution-range-and-standard-deviation

Variation: Normal Distribution, Range, and Standard Deviation

In the field of psychology, there are&nbsp;several ways to organize measurements of a trait, feature, or characteristic (i.e., variables). Qualitative ...

Regression Analysis

Regression analysis is a statistical tool that describes a mathematical relationship between a dependent variable and one or more independent variables.
...

Microsoft Excel: Regression Analysis

Regression analysis is critical in statistics. Consider the data as shown here in the Microsoft Excel worksheet. The scatter plot of variables has a ...

5-Number Summary

In a dataset, the 5-number summary includes the minimum data value, the data value of the first quartile, the median data value or data value of the ...

The Small x Assumption

If a reaction has a small equilibrium constant, the equilibrium position favors the reactants. In such reactions, a negligible change in concentration may ...

Use mathematical calculations to assess quantitative relationships in data

PHYS.2.C

Experimental Designs

An experimental design is a systematic process that allows researchers to evaluate the relationship between dependent and independent variables. There are ...

from-theory-to-design-the-role-of-creativity-in-designing-experiments

From Theory to Design: The Role of Creativity in Designing Experiments

Source: Laboratories of Gary Lewandowski, Dave Strohmetz, and Natalie Ciarocco&#8212;Monmouth University

Research studies come into being when a ...

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 ...

Design of Prismatic Beams for Bending

The design process for prismatic beams subjected to bending begins by determining the allowable stress for the chosen material.
The allowable stress is ...

Fatigue of Metals

Source: Roberto Leon, Department of Civil and Environmental Engineering, Virginia Tech, Blacksburg, VA
The importance of studying metal fatigue in civil ...

Stress-Strain Characteristics of Steels

Source:&#160;Roberto Leon, Department of Civil and Environmental Engineering, Virginia Tech, Blacksburg, VA
The importance of materials to human ...

Heat Exchanger Analysis

Source: Alexander S Rattner and Christopher J Greer; Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, ...

electrical-safety-precautions-and-basic-equipment

Electrical Safety Precautions and Basic Equipment

Source: Ali Bazzi, Department of Electrical Engineering, University of Connecticut, Storrs, CT.
Electric machines and power electronics experiments ...

For a column loaded with an eccentric axial load in the plane of symmetry, the normal stresses due to eccentric load can be written as stresses due to an ...

design-example-strain-gauge-bridge-or-wheatstone-bridge

Design Example: Strain Gauge Bridge or Wheatstone Bridge

A strain gauge, a transducer that converts mechanical strain into electrical signals, is often used to measure force.
The engineer&#39;s role involves ...

Evaluate experimental and engineering designs

Scientific and engineering practices. The student analyzes and interprets data to derive meaning, identify features and patterns, and discover relationships or correlations to develop evidence-based arguments or evaluate designs. The student is expected to:

Eccentric Load Stresses in Structural Columns

Description

Transcript

More videos by Standards