Name: beam deflection from loads and supports
Uploaded: 2024-05-23T13:00:01.000Z
Duration: 1 min 15 s
Channel: JoVE

عنصر حاسم في تصميم الحزم هو تحديد وقياس الانحراف. من الضروري الفهم الشامل للانحرافات عند التعامل مع الحزم غير المحددة.
ضع في اعتبارك شعاعا متدلي يحمل حمولتين مركزتين. يتم حساب التفاعلات عند الدعامات من خلال تحليل مخطط الجسم الحر للحزمة.
باستخدام مخطط الجسم الحر ودعامات رد الفعل ، يتم إنشاء مخطط لحظة الانحناء ، والذي يصور كيفية ثني الحزمة.
يوضح مخطط لحظة الانحناء أن الحزمة تنحني لأعلى بين البداية ونقطة معينة بسبب لحظة الانحناء الموجبة ، وتنحني لأسفل من تلك النقطة إلى نهاية الحزمة بسبب لحظة الانحناء السلبية.
تحدث أكبر قيمة للمنحنى أو أصغر نصف قطر للانحناء عند الدعم حيث تكون لحظة الانحناء في أعلى مستوياتها.
لإجراء تحليل مفصل وتصميم للحزمة ، من الأهمية بمكان الحصول على بيانات دقيقة عن انحراف الحزمة وانحدارها في نقاط مختلفة ، مع التركيز بشكل خاص على فهم الحد الأقصى للانحراف.

تشوه عارضة تحت التحميل العرضي

<div style="direction: rtl;">
 يعد فهم انحراف العارضة، خاصة بالنسبة للعوارض غير المحددة ذات الأجزاء المتدلية والأحمال المركزة المتعددة، أمرًا بالغ الأهمية لضمان السلامة الهيكلية والأداء الوظيفي. تبدأ العملية ببناء مخطط دقيق للجسم الحر، مما يساعد على تحديد القوى والعزوم المؤثرة على العارضة. يعد هذا المخطط أمرًا حيويًا لتصور كيفية اختلاف عزوم الانحناء على طول طول العارضة، مما يؤثر على انحناءها.
 
 تمتد الأفكار المستقاة من مخطط عزم الانحناء إلى تحليل انحناء العارضة. يرتبط انحناء العارضة بعزوم الانحناء على طول العارضة ويرتبط عكسيًا بصلابة العارضة ومقطعها العرضي. تؤدي عزوم الانحناء الأعلى إلى انحناء أكبر، وهو أمر ضروري لفهم ملف انحراف العارضة.
 
 على وجه الخصوص، يتم التركيز على الحد الأقصى للانحراف، حيث أن الانحراف المفرط يمكن أن يؤدي إلى مشاكل هيكلية أو حتى الفشل. يحدث هذا الانحراف الأقصى عادة عندما يكون الانحناء أكبر، وغالبًا ما يكون بالقرب من الدعامات أو مباشرة تحت النقاط التي يتم تطبيق الأحمال عليها. يعد تحديد هذا الانحراف الأقصى أمرًا بالغ الأهمية لضمان توافق تصميمات العوارض مع معايير السلامة وتلبية المتطلبات الوظيفية. من خلال إجراء تحليلات شاملة باستخدام مخططات الجسم الحر وعزم الانحناء، يمكن للمرء تصميم هياكل آمنة ومناسبة لظروف التحميل المحددة والمتطلبات المعمارية بشكل فعال.
 
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عنصر حاسم في تصميم الحزم هو تحديد وقياس الانحراف. من الضروري الفهم الشامل للانحرافات ...

deformation-of-a-beam-under-transverse-loading

Education

JoVE Core

Mechanical Engineering

الهندسة الميكانيكية

Unit 1

الوحدة الأولى

Deflection of Beams

انحراف الكمرات

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

Deformation of a Beam under Transverse Loading

beam deflection from loads and supports

Beam deflection depends on the loads on a beam and the support conditions at its ends. For indeterminate beams, especially those with overhanging parts and multiple concentrated loads, careful analysis is needed to predict how the beam will bend.

The first step is to draw an accurate free-body diagram. A free-body diagram shows the forces and moments acting on the beam. It helps reveal how the bending moment changes along the beam length.

The bending moment diagram also shows how the beam will curve. Beam curvature is related to the bending moment and is affected by the beam’s stiffness and cross-section. When the bending moment is higher, the curvature is greater, so the deflection profile becomes easier to evaluate.

The main goal is to find the maximum deflection. Too much deflection can cause structural problems or even failure. This largest deflection often appears where curvature is greatest, such as near supports or directly under applied loads. Using free-body and bending moment diagrams helps engineers design beams that stay safe and meet functional requirements under specific loading conditions.

Beam Deflection from Loads and Supports

deformation of a beam under transverse loading

Beam deflection depends on the loads on a beam and the support conditions at its ends. For indeterminate beams, especially those with overhanging parts and multiple concentrated loads, careful analysis is needed to predict how the beam will bend. The first step is to draw an accurate free-body diagram. A free-body diagram shows the forces and moments acting on the beam. It helps reveal how the bending moment changes along the beam length. The bending moment diagram also shows how the beam...

equation of the elastic curve

Beam Deflection and Boundary Conditions

Beam deflection and boundary conditions help describe how a beam bends under load. In structural engineering, the curvature of a plane curve shows how sharply the beam bends. That curvature is found from the curve’s first and second derivatives. A cantilever beam with a point load at its free end is a common example. A diving board works like this type of beam. When slopes are small, the beam’s elastic curve becomes the main shape used in the analysis. The governing equation connects bending...

elastic curve from the load distribution

Beam Deflection Under Distributed Load

Beam deflection under distributed load is a key part of beam analysis in engineering. It helps predict how a beam bends and reacts when a load is spread along its length. Engineers use this relationship to judge whether a structure will stay safe and functional. The analysis starts with the link between load, shear force, and bending moment. These quantities can be written in differential form. When beam flexibility is treated as constant, further differentiation leads to a higher-order...

deflection of a beam

Beam Slope and Deflection by Singularity

Beam slope and deflection can be found with singularity functions when beam loading is hard to write as one simple equation. This method is useful in structural engineering because it helps describe beams under several loads without breaking the problem into many separate cases. Singularity functions are mathematical tools for showing discontinuities in a load, shear force, or bending moment equation. They are especially helpful when a load acts at a single point or over a set interval. In the...

method of superposition

Beam Deflection Under Combined Loads

Beam deflection under combined loads can be found with the method of superposition. This structural engineering method is used to analyze how multiple loads affect a beam. It works by finding the slope and deflection from each load separately, then adding those results together. The method applies only when the beam stays within its elastic limit. In that range, the material deforms in a linearly elastic way. That makes it valid to combine the effects of separate loads without changing the...

moment-area theorems

Beam Deflection Using Moment-Area Rules

The moment-area theorems help describe beam bending in structural engineering. They are often used for building floor supports and other beams under load. The theorems use the elastic curve, which is the shape a beam takes as it deforms. The first theorem links slope change to area on an M/EI diagram. Here, M is the bending moment, E is the modulus of elasticity, and I is the moment of inertia. When M/EI is plotted along the beam length, the area under the curve gives the total rotation...

beams with symmetric loadings

Moment-Area Method for Cantilever Deflection

The moment-area method is used in structural engineering to find the slope and deflection of a beam under load. It is especially useful for a cantilever beam with a concentrated load and a moment at the free end. The analysis begins with a free-body diagram. This diagram helps calculate the reactions at the fixed end. After that, the bending moment diagram is drawn to show how the bending moment changes along the beam. Points where the bending moment is zero are important in this step. Next,...

beams with unsymmetric loadings

Beam Deflection and Level Points

Beam deflection and level points can be found for a supported beam under unsymmetrical loadings using moment-area theorems. This type of analysis helps show how a beam bends when forces are spread unevenly along it. It is an important part of structural engineering because it links load patterns to beam response. The first moment-area theorem is used to find the slope at any point on the beam. It states that the change in slope between two points equals the area under the moment diagram over...

maximum deflection

Locating the Beam’s Highest Deflection

Maximum deflection in a supported beam depends on where the load is placed. With an unsymmetrical load, such as a train moving across a bridge, the beam may bend most at a point that is not the midpoint. Finding that point is important for judging stress and deflection in the structure. The point of maximum deflection is called point O. At point O, the tangent to the deflection curve is horizontal. That means the slope is zero there. To locate point O, the slope at any point X along the beam...

key terms and concepts

Learn how free-body diagrams and bending moment diagrams help predict beam deflection, identify maximum deflection, and check structural safety under load.

Beam Deflection from Loads and Supports | 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

Beam Deflection from Loads and Supports

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