Name: sizing beams for safe bending loads
Uploaded: 2024-05-23T12:59:46.000Z
Duration: 1 min 23 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Physics

PHYS.2

PHYS.2.D

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 generally obtained from a table of material properties or design specifications. Alternatively, it can be computed by dividing the material&#39;s ultimate strength by a suitable safety factor.
Then, the shear force and the bending moment diagrams corresponding to the specified loading conditions are drawn.
Next, the maximum absolute value of the bending moment is calculated using the shear force diagram.
The minimum allowable section modulus is then calculated using the beam&#39;s absolute bending moment value and allowable stress.
When a timber beam is designed, the ratio characterizing the shape of its cross-section is usually specified. The unknown dimensions are identified using the relationship between the dimensions of the beam and the section modulus.
While designing a rolled-steel beam, a table containing properties of the rolled-steel beam is referred to, and only those beam sections with a section modulus greater than or equal to the minimum required section modulus are considered.

design of prismatic beams for bending

The design of prismatic beams, structural elements with a uniform cross-section, focuses on ensuring safety and structural integrity under load. The design process begins by determining the allowable stress, either from material properties tables, or by dividing the material&#39;s ultimate strength by a safety factor. This safety factor is essential for accommodating uncertainties, and varies depending on the material&#8212;timber, steel, or concrete&#8212;with each having unique strength and stress characteristics. Its value will depend on the selected material and the structure&#39;s intended use.
Next, plot shear force and bending moment diagrams to visualize load distribution and identify maximum bending stress points. This visualization is key to optimizing beam dimensions to maximize safety and efficiency of the beam.
Finally, calculate the minimum section modulus that will allow the beam to resist bending stress. Higher moduli indicate a greater resistance. For timber beams, the designer specifies a&#160;&#160; cross-section shape ratio that will produce the desired modulus. For steel beams, the designerselects from pre-existing sections, ensuring the beam&#39;s modulus exceeds the calculated minimum. This selection guarantees that the beam can withstand bending forces, maintaining structural safety and stability.
This systematic approach combines safety considerations with material and load analysis, ensuring the chosen beam upholds the structure&#39;s integrity and reliability under anticipated loads, ultimately securing long-term structural performance.

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

Education

JoVE Core

Mechanical Engineering

Unit 1

Analysis and Design of Beams for Bending

KEY TERMS AND CONCEPTS

sizing beams for safe bending loads

Prismatic beams have a uniform cross-section, and their design focuses on safe bending under load. The goal is to keep stress within a level the material can handle while the structure stays strong and stable.

The first step is to find the allowable stress for the chosen material. Designers can use values from material property tables, or they can divide the material's ultimate strength by a safety factor. This safety factor helps account for uncertainty, and its value depends on the material and the intended use of the structure.

Timber, steel, and concrete each have different strength and stress behavior, so the design method depends on the material. After selecting the material, the designer plots shear force and bending moment diagrams. These diagrams show how the load is distributed and help locate the points where bending stress is highest.

The final step is to calculate the minimum section modulus needed to resist bending stress. A higher section modulus means greater resistance to bending. For timber beams, the designer chooses a cross-section shape ratio that gives the needed modulus. For steel beams, the designer selects a standard section whose modulus is at least as large as the calculated minimum. This process helps the beam carry bending forces safely and maintain structural integrity over time.

Sizing Beams for Safe Bending Loads

Prismatic beams have a uniform cross-section, and their design focuses on safe bending under load. The goal is to keep stress within a level the material can handle while the structure stays strong and stable. The first step is to find the allowable stress for the chosen material. Designers can use values from material property tables, or they can divide the material's ultimate strength by a safety factor. This safety factor helps account for uncertainty, and its value depends on the material...

prismatic beams: problem solving

Timber Beam Design Under Distributed Load

Timber beam design under a distributed load uses the beam’s size and the wood’s properties to keep the structure safe. The beam’s length and width are known at the start. The timber’s grade and species also matter because they affect the allowable stress, which is the highest stress the material can safely handle. The first step is to treat the beam as a free body. A free-body diagram shows the forces and moments acting on the beam. From this, the support reactions can be found by balancing...

singularity functions for shear

Beam Shear Diagrams with Macaulay Brackets

Beam shear diagrams can be written with singularity functions when the load changes suddenly along the beam. In structural analysis, these functions help show discontinuous shear force with one mathematical expression, even when the loading is complex. They make it easier to describe how shear changes from one point to the next. The method starts with a free-body diagram of the beam. Then the beam is cut at specific points to check the shear force in each section. For a beam with width W and...

singularity functions for bending moment

Beam Load Modeling with Singularity Functions

Singularity functions help model beam loads and bending moments when the loading changes along the beam. They make it possible to write the bending moment with one mathematical expression instead of separate equations for each section. In this method, Macaulay’s brackets are often used to show where a load starts or stops. For a simply supported beam AB, the load is uniform from the midpoint M to the right support B. To find the bending moment, the beam is cut at different points. A cut...

key terms and concepts

Learn how prismatic beams are sized for bending by finding allowable stress, using shear and moment diagrams, and choosing the right section modulus.

Sizing Beams for Safe Bending Loads | 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 ...

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 ...

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

Design of Columns under an Eccentric Load

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:

Sizing Beams for Safe Bending Loads

Description

Transcript

Tags

More videos by Standards