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

بالنسبة للعمود المحمل بحمل محوري غريب الأطوار في مستوى التماثل ، يمكن كتابة الضغوط العادية الناتجة عن الحمل غريب الأطوار كضغوط بسبب الحمل المركزي المكافئ والانحناء.
أثناء تصميم الأعمدة ذات الأحمال اللامركزية ، يجب ألا يتجاوز الحد الأقصى للضغط المتراكم في العمود الحد الأقصى المسموح به من الإجهاد. يمكن استيفاء هذا الشرط باستخدام طريقتين متميزتين.
تفترض طريقة الإجهاد المسموح به أن الضغط المسموح به للعمود المحمل بشكل غريب الأطوار هو نفس الحد الأقصى للضغط للعمود المحمل مركزيا. يمكن التعبير عن الضغط المسموح به للعمود كدالة لنسبة النحافة.
الضغط المسموح به للتحميل المركزي أصغر من الضغط بسبب لحظة الانحناء. ينتج عن هذا أن تكون طريقة الإجهاد المسموح بها متحفظة بشكل مفرط. 
من ناحية أخرى ، تأخذ طريقة التفاعل في الاعتبار الإجهاد المسموح به بسبب التحميل المركزي والانحناء.
يوفر معادلة للضغط الأقصى تحت التحميل المركزي عندما لا تكون هناك لحظات. وبالمثل ، فإنه يحدد الحد الأقصى للضغط من الانحناء النقي عندما لا يكون هناك تحميل.

تصميم الأعمدة تحت حمل لامركزي

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 يعد تصميم الأعمدة لتحمل الأحمال اللامركزية جانبًا مهمًا في الهندسة الإنشائية، مما يضمن قدرة الهياكل على دعم الأحمال خارج المركز دون فشل. يجب أن تأخذ عملية التصميم هذه في الاعتبار الضغوط العادية الإضافية الناتجة عن التحميل اللامركزي، والتي يمكن أن تؤثر بشكل كبير على توزيع إجهاد العمود والاستقرار العام. يؤدي الحمل اللامركزي المطبق على عمود إلى إحداث ضغوط عادية يمكن تصورها على أنها مزيج من الضغوط بسبب الحمل المركزي المكافئ وضغوط الانحناء الإضافية. وهذا يؤدي إلى توزيع غير منتظم للضغوط التي يجب تحليلها بعناية لمنع الفشل الهيكلي. يتم استخدام طريقتين أساسيتين في تصميم الأعمدة تحت الأحمال اللامركزية: طريقة الإجهاد المسموح به وطريقة التفاعل.
 
 تعد طريقة الضغط المسموح بها طريقة مباشرة حيث يتم مساواة الضغط المسموح به لعمود محمّل بشكل غريب الأطوار مع الحد الأقصى للضغط المسموح به لعمود محمّل مركزيًا. تعمل هذه الطريقة على تبسيط عملية التصميم من خلال التعامل مع الضغط المسموح به كدالة لنسبة رقة العمود، وهو مقياس لميله إلى الالتواء تحت الحمل. ومع ذلك، تفترض هذه الطريقة أن الإجهاد المسموح به للتحميل المركزي يشمل الضغوط الإضافية الناتجة عن الانحناء، مما يؤدي إلى تصميمات محافظة قد لا تستخدم الإمكانات الكاملة للمادة. إن النزعة المحافظة المتأصلة في هذا النهج تضمن السلامة ولكنها قد تؤدي إلى أعمدة أكبر وأكثر تكلفة من اللازم.
 
 تقدم طريقة التفاعل نهجا أكثر دقة من خلال النظر في كل من الضغوط المسموح بها بسبب التحميل المركزي والضغوط الناشئة عن عزوم الانحناء. توفر هذه الطريقة إطارًا لحساب الحد الأقصى للإجهاد الذي يمكن أن يتحمله العمود بدون عزمين (التحميل المركزي النقي) والحد الأقصى للضغط الناتج عن الانحناء النقي (بدون حمل محوري). من خلال حساب هذه الشروط في وقت واحد، تسمح طريقة التفاعل بتقدير أكثر دقة وأقل تحفظًا للضغوط المسموح بها في الأعمدة المحملة بشكل غريب الأطوار.
 
 ومن الناحية العملية، غالبًا ما يتم تفضيل طريقة التفاعل لقدرتها على تحقيق التوازن بين السلامة وكفاءة المواد. ويتطلب تحليلا مفصلا لتوزيع الإجهاد داخل العمود، مع الأخذ في الاعتبار كل من الأحمال المحورية وعزوم الانحناء.
 
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بالنسبة للعمود المحمل بحمل محوري غريب الأطوار في مستوى التماثل ، يمكن كتابة الضغوط العادية بسبب الحمل غريب الأطوار كضغوط بسبب ...

Education

JoVE Core

Mechanical Engineering

الهندسة الميكانيكية

Unit 1

الوحدة الأولى

Columns

أعمدة

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

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

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

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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