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

עבור טור טעון בעומס אקסצנטרי צירית במישור הסימטריה, ניתן לכתוב את הלחצים הרגילים עקב עומס אקסצנטרי כלחצים עקב עומס צנטרי שווה ערך וכיפוף.
בעת תכנון עמודים עם עומסים אקסצנטריים, הלחץ המרבי שיתפתח בטור לא יעלה על הלחץ המרבי המותר. ניתן להסתפק בתנאי זה באמצעות שתי גישות שונות.
שיטת הלחץ המותרת מניחה שהלחץ המותר עבור הטור הטעון באופן אקסצנטרי זהה ללחץ המרבי עבור העמודה הטעונה במרכז. הלחץ המותר עבור העמודה יכול לבוא לידי ביטוי כפונקציה של יחס הדקיקות.
הלחץ המותר להעמסה מרכזית קטן מזה הנובע מרגע הכיפוף. התוצאה היא ששיטת הלחץ המותרת שמרנית מדי. 
מצד שני, שיטת האינטראקציה רואה את הלחץ המותר עקב עומס מרכזי וכיפוף בחשבון.
הוא מספק משוואה ללחץ המרבי תחת עומס מרכזי כאשר אין רגע זוגי. באופן דומה, הוא מגדיר את הלחץ המרבי מכיפוף טהור כאשר אין העמסה.

עיצוב עמודים תחת עומס אקסצנטרי

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 תכנון עמודים כדי לעמוד בעומסים אקסצנטריים הוא היבט קריטי של הנדסת מבנים, מה שמבטיח שמבנים יכולים לתמוך בעומסים מחוץ למרכז ללא תקלה. תהליך תכנון זה חייב לתת את הדעת על הלחצים הנורמליים הנוספים המופעלים על ידי העמסה אקסצנטרית, אשר יכולים להשפיע באופן משמעותי על התפלגות המאמץ של העמוד ועל היציבות הכוללת. עומס אקסצנטרי המופעל על עמוד גורם ללחצים נורמליים שניתן להגדיר כשילוב של מאמצים עקב עומס צנטרי שווה ערך ומאמצי כפיפה נוספים. דבר זה מוביל להתפלגות לא אחידה של מאמץ שיש לנתח בקפידה כדי למנוע כשל מבני. שתי שיטות עיקריות משמשות בתכנון של עמודים בעומסים אקסצנטריים: שיטת המאמץ המותר ושיטת האינטראקציה.
 
 שיטת המאמץ המותר היא גישה פשוטה שבה המאמץ המותר עבור עמוד טעון אקסצנטרי משווה למאמץ המרבי המותר עבור עמוד עם עומס אקסצנטרי. שיטה זו מפשטת את תהליך התכנון על ידי התייחסות למאמץ המותר כפונקציה של יחס התמירות של העמוד, המהווה מדד לנטייתו להתכווץ בעומס. עם זאת, שיטה זו מניחה שהמאמץ המותר להעמסה אקסצנטרית מקיף את המאמצים הנוספים עקב כפיפה, מה שמוביל לעיצובים שמרניים שעלולים לא לנצל את מלוא הפוטנציאל של החומר. השמרנות הטמונה בגישה זו מבטיחה בטיחות אך עלולה לגרום לעמודים גדולים ויקרים מהנדרש.
 
 שיטת האינטראקציה מציעה גישה ניואנסית יותר על ידי התחשבות הן במאמצים המותרים עקב עומס אקסצנטרי והן בלחצים הנובעים ממומנטי הכפיפה. שיטה זו מספקת מסגרת לחישוב המאמץ המקסימלי שהעמוד יכול לעמוד בו ללא מומנט (עומס אקסצנטרי טהור) והמאמץ המרבי עקב כפיפה טהורה (ללא עומס צירי). על ידי התחשבות בתנאים אלה בו זמנית, שיטת האינטראקציה מאפשרת הערכה מדויקת יותר ופחות שמרנית של המאמצים המותרים בעמודים טעונים אקסצנטרית.
 
 בפועל, שיטת האינטראקציה מועדפת לרוב בשל יכולתה לאזן בין בטיחות ליעילות החומר. היא דורשת ניתוח מפורט של התפלגות המאמץ בתוך העמוד, תוך התחשבות בעומסים ציריים ובמומנטים של כפיפה.
 
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עבור טור טעון בעומס אקסצנטרי צירית במישור הסימטריה, ניתן לכתוב את הלחצים הרגילים עקב עומס אקסצנטרי כלחצים עקב ...

Education

JoVE Core

Mechanical Engineering

הנדסת מכונות

Unit 1

יחידה 1

Columns

עמודים

KEY TERMS AND CONCEPTS

מונחים ומושגים מרכזיים

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

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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

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

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Spring-Loaded Column Buckling Analysis

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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

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Eccentric Load Stresses in Structural Columns

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