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Chapter 27

Energy Methods

طاقة الإجهاد
طاقة الإجهاد
Consider a rod fixed at one end and subjected to an axial force at the free end, which induces stress and leads to elongation in the rod.  As the ...
كثافة الإجهاد والطاقة
كثافة الإجهاد والطاقة
An axial load causes a rod to elongate, and store strain energy in it. The strain energy density in the rod is the energy per unit volume. Here, the ratio ...
طاقة إجهاد مرنة للضغوط العادية
طاقة إجهاد مرنة للضغوط العادية
When a material is subjected to an axial loading, it experiences normal stress, leading to strain energy generation. This equation is valid for uniformly ...
طاقة إجهاد مرنة لضغوط القص
طاقة إجهاد مرنة لضغوط القص
When the material is subjected to a shearing stress, the strain energy density can be expressed in integral form as the product of the shearing stress and ...
تأثير التحميل
تأثير التحميل
Consider a rod of uniform cross-sectional area fixed at one end. When another moving object hits the free end of the rod, the rod deforms, and stress is ...
تحميل التأثير على شعاع ناتئ
تحميل التأثير على شعاع ناتئ
Consider a cantilever beam fixed at one end, having a circular cross-section. If an object is dropped on the free end of the cantilever from a height h, ...
نظرية كاستيجليانو
نظرية كاستيجليانو
Castigliano's theorem is useful for determining displacements and rotations in structures undergoing elastic deformations. It states that the partial ...
نظرية كاستيجليانو: حل المشكلات
نظرية كاستيجليانو: حل المشكلات
Consider a simply supported beam PQ of length L, carrying a point load F at the center. What will be the deflection at the center of the beam? Here, the ...
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