Name: finding resultant loads on a beam
Uploaded: 2023-09-22T11:49:22.000Z
Duration: 1 min 29 s
Channel: JoVE

شعاع بطول L يتعرض لحمل متغير ، وهو مزيج من توزيع الحمل المكافئ وشبه المنحرف على طول المحور السيني.
في الحمل المكافئ ، ضع في اعتبارك عنصرا تفاضليا للقوة dR على الطول dx. يتم الحصول على الحمل الناتج عن طريق دمج العنصر التفاضلي على طول التحميل. يقع في النقطة الوسطى للمنطقة المكافئة ، ويتم تحديد الإحداثيات x للنقطة الوسطى باستخدام مبدأ اللحظة.
يمكن تقسيم المنطقة شبه المنحرفة إلى مناطق مستطيلة ومثلثة ، حيث يعمل الحمل الناتج على المراكز الوسطى. يتم وضع هذه النقاط الوسطى بنصف طول المستطيل وثلث طول القاعدة من الجانب الرأسي للمثلث.
يتم الحصول على الحمل الناتج للمنطقة شبه المنحرفة عن طريق إضافة الأحمال الناتجة الفردية ويمر عبر النقطة الوسطى للمنطقة ، التي يحددها مبدأ اللحظة.
الحمل الكلي الموزع هو مجموع الأحمال الناتجة للمناطق شبه المنحرفة والقطع المكافئ ، التي تمر عبر النقطة الوسطى للمنطقة المدمجة ، والتي يحددها مبدأ اللحظة.

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	<li>بير ، إف بي ؛ جونستون ، إي آر ؛ مازوريك ، د. إف. كرومويل ، بي جيه وسيلف ، ب. (2019). ميكانيكا المتجهات للمهندسين - الإحصاء والديناميكيات. نيويورك: ماكجرو هيل. ص 264</li>
	<li>مريم ، جي إل. كريج ، إل جي وبولتون ، ج. (2020). الميكانيكا الهندسية - الإحصاء. هوبوكين ، نيو جيرسي: جون وايلي. ص 273</li>
	<li>هيبلر ، آر سي (2016). الميكانيكا الهندسية - الإحصاء والديناميكيات. هوبوكين ، نيو جيرسي: قاعة بيرسون برنتيس. ص EM-2</li>
</ol>

التحميل على محور واحد

<div style="direction:rtl">في الهندسة الإنشائية، يُعد تحليل الكمرات المعرضة لأحمال متغيرة جانبًا أساسيًا لفهم سلوك وأداء هذه العناصر الإنشائية. ومن السيناريوهات الشائعة أن تتعرض الكمرة لمزيج من توزيعات الأحمال المختلفة. تخيل كمرة بطول L تخضع لحمل متغير، وهو مزيج من توزيع الحمل على شكل قطع مكافئ وحمل شبه منحرف على طول المحور x. في هذه الحالة، من الضروري تحديد القوى المحصلة، ومواقعها، ومركز الكتلة للمساحة المشتركة للتنبؤ برد فعل الكمرة تحت هذه الظروف التحميلية. أولاً، قم بفحص توزيع الحمل على شكل قطع مكافئ. ضع في الاعتبار عنصرًا تفاضليًا للقوة dR يؤثر على طول صغير dx. لتحديد الحمل المحصل لمنطقة القطع المكافئ، يتم تكامل العنصر التفاضلي dR على طول منطقة التحميل بالكامل. يقع موقع هذا الحمل المحصل عند مركز الكتلة لمنطقة القطع المكافئ. يتم تطبيق مبدأ العزوم لإيجاد الإحداثي x لمركز الكتلة، والذي ينص على أن العزم الأولي للمساحة حول محور ما يساوي حاصل ضرب المساحة والمسافة بين مركز كتلتها والمحور. بعد ذلك، يتم تحليل توزيع الحمل شبه المنحرف عن طريق تقسيمه إلى منطقتين: مستطيلة ومثلثية. تؤثر الأحمال المحصلة لكل من هاتين المنطقتين عند مراكز كتلها الخاصة. بالنسبة للمنطقة المستطيلة، يقع مركز الكتلة في منتصف طول المستطيل. أما بالنسبة للمنطقة المثلثية، فيقع مركز الكتلة على بعد ثلث طول القاعدة من الجانب العمودي للمثلث. من خلال جمع الأحمال المحصلة لكل من المنطقتين المستطيلة والمثلثية، يمكن تحديد الحمل المحصل للمنطقة شبه المنحرفة بالكامل. يمر موقع الحمل المحصل عبر مركز الكتلة للمنطقة شبه المنحرفة، والذي يمكن تحديده أيضًا باستخدام مبدأ العزوم. وبالمثل، يمكن تحديد الحمل المحصل الكلي المؤثر على الكمرة من خلال جمع الأحمال المحصلة لكل من منطقتي القطع المكافئ وشبه المنحرفة،. يمر موقع هذا الحمل المحصل الكلي عبر مركز الكتلة للمساحة الكلية المشتركة، والذي يمكن تحديده بشكل إضافي باستخدام مبدأ العزوم.</div>

في الهندسة الإنشائية ، يعد تحليل الحزم المعرضة لأحمال متفاوتة جانبا مهما لفهم سلوك وأداء هذه ...

Education

JoVE Core

Mechanical Engineering

الهندسة الميكانيكية

Unit 1

الوحدة الأولى

Force System Resultants

محصلات نظام القوى

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

Load along a Single Axis

finding resultant loads on a beam

Structural engineering often requires finding the resultant load on a beam with changing force patterns. Here, a beam of length L carries a varying load made from parabolic and trapezoidal load distributions along the x-axis. The goal is to find the total load, where it acts, and the centroid of the combined area so the beam’s response can be predicted.

The parabolic load is handled first. A small force element, dR, acts over a short distance, dx, and these elements are integrated across the full length of the load. The resultant load for the parabolic area acts at the centroid of that area. The x-coordinate of the centroid is found with the moment principle, which says the first moment of an area about an axis equals the area times the distance to its centroid.

The trapezoidal load is then split into two simpler shapes. One part is rectangular, and the other is triangular. Their resultant loads act at their own centroids. For the rectangle, the centroid lies halfway along its length. For the triangle, the centroid is one-third of the base length from the vertical side.

After those parts are found, their loads are added to get the resultant load of the full trapezoidal area. That load passes through the centroid of the trapezoid, which can also be found with the moment principle. Finally, the resultant loads from the parabolic and trapezoidal areas are combined. Their sum gives the total load on the beam, and its location passes through the centroid of the combined area.

Finding Resultant Loads on a Beam

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Structural engineering often requires finding the resultant load on a beam with changing force patterns. Here, a beam of length L carries a varying load made from parabolic and trapezoidal load distributions along the x-axis. The goal is to find the total load, where it acts, and the centroid of the combined area so the beam’s response can be predicted. The parabolic load is handled first. A small force element, dR, acts over a short distance, dx, and these elements are integrated across the...

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key terms and concepts

Learn how parabolic and trapezoidal loads on a beam are broken into simpler areas, then combined to find the resultant force and centroid.

Finding Resultant Loads on a Beam | 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

Finding Resultant Loads on a Beam

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