Name: equivalent resultant loads on beams
Uploaded: 2023-09-22T11:49:23.000Z
Duration: 1 min 21 s
Channel: JoVE

שקול קרן מחודדת OB קבוע בקצה אחד נתון עומס מבוזר.
קבע את הכוח המתקבל המקביל של העומס המשתנה ואתר את מיקומו על הקורה.
ראשית, חלק את העומס המבוזר לשני אזורים משולשים.
לאחר מכן, גודל העומס המתקבל המקביל של האזור המשולש השמאלי והימני שווה לשטח של כל משולש.
כל עומס שנוצר פועל בצנטרואידים, הממוקמים בשליש מאורך הבסיס מהצד האנכי AD של המשולש.
ניתן לקבוע את העומס המתקבל המקביל על ידי הוספת העומס המתקבל הבודד של כל אזור משולש.
ניתן לקבוע את המומנט על נקודה O על ידי הוספת המומנט הבודד הפועל עקב כל עומס שנוצר.
נזכיר את עקרון המומנט, הקובע כי המומנט של העומס המתקבל המקביל על נקודה O שווה למכפלה של העומס המתקבל השווה והמרחק מנקודה O.
על ידי החלפת הערכים במשוואה, ניתן לקבוע את מיקום העומס המתקבל המקביל.

<ol>
	<li>היבלר, R.C. (2016). מכניקה הנדסית - סטטיקה ודינמיקה. הובוקן, ניו ג'רזי: אולם פירסון פרנטיס, עמ' 194-195</li>
</ol>

עומסים מבוזרים: פתרון בעיות

<div style="direction:rtl">קורות הן אלמנטים מבניים המשמשים בדרך כלל ביישומים הנדסיים הדורשים כושר נשיאת עומס שונה. השלב הראשון בניתוח קורה בעומס מבוזר הוא לפשט את הבעיה על ידי חלוקת העומס לאזורים קטנים יותר, מה שמאפשר לשקול כל אזור בנפרד ולחשב את גודל העומס הנוצר המקביל הפועל על כל חלק של הקורה. ניתן לקבוע את גודל העומס הנוצר השקול עבור כל אזור על ידי חישוב השטח של האזורים המתאימים, המייצג את הכוח המופעל על ידי העומס בכל אזור. לאחר מכן, אתר את המיקום של כל עומס שנוצר על הקורה. ניתן לעשות זאת על ידי מציאת המוקדים של האזורים, שהם הנקודות שבהן מסת האזורים יכולה להיחשב מרוכזת. העומסים הבודדים הנוצרים פועלים במוקדים אלה, מפעילים את כוחם בנקודות ספציפיות לאורך הקורה. ניתן לחשב את העומס הנוצר השקול עבור הקורה כולה עם הגדלים והמיקומים של העומסים הנוצרים הנפרדים שנקבעו. זה כרוך בהוספת העומסים הנוצרים הבודדים של האזורים השונים כדי לקבל את העומס הנוצר המקביל הכולל הפועל על הקורה. השלב הבא הוא לקבוע את המומנט לגבי נקודה מסוימת, בדרך כלל הקצה הקבוע של הקורה. המומנט מודד את ההשפעה הסיבובית של הכוח הפועל על הקורה. ניתן לקבוע את המומנט המתקבל על ידי הוספת המומנטים הבודדים הפועלים עקב כל עומס. המומנט של כל עומס שווה למכפלת הכוח ולמרחק שלו מהנקודה שצוינה. <img alt="Equation 1" src="/files/ftp_upload/14280/14280_PT_Equation_1.svg" style="text-align: center; height: 11px;"> על ידי היזכרות בעקרון המומנט, הרגע של העומס הנוצר השקול סביב הנקודה שצוינה שווה למכפלה של העומס הנוצר השקול והמרחק מאותה נקודה. <img alt="Equation 2" src="/files/ftp_upload/14280/14280_PT_Equation_2.svg" style="text-align: center; height: 13px;"> על ידי ארגון מחדש של המשוואה והחלפת המונחים, ניתן לקבוע את מיקומו של העומס השקול המקביל לאורך הקורה. <img alt="Equation 3" src="/files/ftp_upload/14280/14280_PT_Equation_3.svg" style="text-align: center; height: 35px;"></div>

קורות הן אלמנטים מבניים המשמשים בדרך כלל ביישומים הנדסיים הדורשים יכולות נשיאת מטען שונות. הצעד הראשון בניתוח ...

Education

JoVE Core

Mechanical Engineering

הנדסת מכונות

Unit 1

יחידה 1

Force System Resultants

תוצאות מערכת כוחות

KEY TERMS AND CONCEPTS

מונחים ומושגים מרכזיים

Distributed Loads: Problem Solving

equivalent resultant loads on beams

Equivalent resultant loads on beams can be found by breaking a distributed load into smaller regions. This makes the beam easier to analyze. Each region can then be handled on its own before the results are combined.

The magnitude of the equivalent resultant load for each region comes from the area of that region. In this setting, area represents the force applied by the distributed load over that part of the beam. After finding the force for each region, the position of each resultant load must be located.

The position is found by using the centroid of each region. A centroid is the point where the region’s mass can be treated as concentrated. The individual resultant loads act at these centroids, so each force is placed at a specific point along the beam.

Once the separate forces and locations are known, they are combined to find the equivalent resultant load for the full beam. This is done by adding the individual resultant loads from the different regions. The result gives the overall force acting on the beam.

The next step is to determine the moment about a chosen point, usually the fixed end of the beam. A moment is the turning effect of a force. The total moment comes from adding the moments created by each load, and each moment equals force times distance from the chosen point.

By using the moment principle, the moment of the equivalent resultant load about that point must equal the force multiplied by its distance from the point. Rearranging that relationship makes it possible to find where the single equivalent load acts along the beam. This gives both the size and location of the load that replaces the distributed loading.

Equivalent Resultant Loads on Beams

moment of a force: scalar formulation

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Net Moment Sign Convention in 2D Forces

Net moment in two-dimensional force systems shows how multiple forces can cause rotation about a fixed point. The scalar formulation helps analyze equilibrium in structures that are acted on by several forces. It focuses on the x-y plane and uses a simple sign rule to describe the direction of rotation. To find the resultant moment, the moments from all forces in the system are considered about a chosen point A. Each moment is assigned a sign based on its sense of rotation. Positive moments...

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Moment of Force and Direction Rules

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cartesian form for vector formulation

Calculating Moment with Cartesian Vectors

Calculating moment with Cartesian vectors shows how position and force vectors work together. The moment of force is the cross product of these vectors, so it is a vector quantity. In Cartesian form, unit vectors help write the vectors in component form. The cross product can be arranged in determinant form. That determinant is then expanded to find the Cartesian vector form of the moment of force. This method gives a clear way to work through the calculation step by step. A revolving door...

resultant moment: vector formulation

Calculating Torque from Multiple Forces

Resultant moment describes the total turning effect of multiple forces acting on an object. It shows how several forces can combine to make a body rotate about a point. In physics, moment is the tendency of a force to cause rotation. The resultant moment of a force system is a vector quantity. That means it can be added and subtracted like other vectors. For a system with two forces, F1 and F2, acting on a pole at points A and B, the resultant moment is written as MR = (rA x F1) + (rB x F2).

principle of moments

Resolving Forces in Moment Calculations

The principle of moments, also called Varignon's theorem, explains how a force creates rotation about a point. It is a key idea in physics and engineering. It also helps describe when a rigid body stays in equilibrium under external forces. The moment of a force is found by multiplying the force by the perpendicular distance from the point of application to the point being studied. A larger force or a larger distance gives a larger moment. This makes the idea useful for checking how strongly a...

principle of moments: problem solving

Torque About an Axis in 3D Systems

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Bicycle Torque and Moment About an Axis

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Torque on a Bicycle Wheel: Vector Method

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Couple Moment in Force Systems

A couple is a pair of parallel forces that are equal in magnitude and opposite in direction. The two forces are separated by a perpendicular distance called the couple arm. Together, they create a turning effect on a body instead of a net push. This turning effect is called the couple moment. It rotates the body about an axis that is perpendicular to the plane of the forces. The SI unit for a couple moment is the Newton-meter (N-m). A common example is tightening a bolt with a lug wrench. In...

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Couple Moments and the Right-Hand Rule

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Equivalent Couples in Mechanical Systems

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Torque from a Couple: Solving Forces

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system of forces and couples

Equivalent Force and Moment Systems

Structural systems often experience several forces and couple moments at the same time. Engineers simplify these loading cases by replacing them with an equivalent force and moment system at a chosen point O. This makes the analysis easier while keeping the same external effects on the member. A key idea in this process is the principle of transmissibility. A force is a sliding vector, which means it can be moved anywhere along its line of action without changing how the body behaves...

simplification of a force and couple system i

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Resultant Forces in Force and Couple Systems

Force and couple systems can be reduced to a simpler equivalent system. This makes rigid body analysis easier because the external effect of the forces is captured with fewer elements. When the resultant force and resultant couple moment have perpendicular lines of action, the system may be reduced further to a single resultant force along a new line of action. Three common force systems can be simplified this way: concurrent, coplanar, and parallel. A concurrent force system has lines of...

simplification of a force and couple system: ii

simplification-of-a-force-and-couple-system-ii

Resultant Force and Wrench Motion

Resultant force and resultant couple moment describe how several forces and moments act together on a rigid body in three dimensions. When many forces act on an object, they can be replaced by one equivalent force. The moments from those forces can also be combined into one equivalent couple moment. In some cases, the resultant force and the resultant couple moment are not mutually perpendicular. That means the angle between them is not 90 degrees. To study this situation, the couple moment is...

distributed loads

Load Distribution on Shelves and Dams

Load distribution helps engineers describe how force spreads across a surface or structure. A distributed load is a continuous force per unit area, rather than a single point force. It is a common idea in many practical situations. A bookshelf full of stacked books is one simple example. The weight of the books is spread along the shelf, so the pressure changes across the surface. This pressure is measured in Newtons per square meter, or Pascals. A hydroelectric dam gives another clear...

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Finding Resultant Loads on a Beam

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distributed loads: problem solving

Equivalent resultant loads on beams can be found by breaking a distributed load into smaller regions. This makes the beam easier to analyze. Each region can then be handled on its own before the results are combined. The magnitude of the equivalent resultant load for each region comes from the area of that region. In this setting, area represents the force applied by the distributed load over that part of the beam. After finding the force for each region, the position of each resultant load...

key terms and concepts

Learn how to replace a distributed load with one equivalent resultant force on a beam by using areas, centroids, and moments to find its location.

Equivalent Resultant Loads on 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

Equivalent Resultant Loads on Beams

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