1. Concepts about the science of "Strength of Materials" tasks, consistency, uniformity, priority, brief history

29. Select allowable stress. Strength reserve factor (stress: allowable, finite; reserve factor, material: plastic, brittle).
Allowable Stress: The allowable stress, also known as the design stress or working stress, is the maximum stress that a material can safely withstand under normal operating conditions. It is determined based on various factors such as the material properties, loading conditions, safety factors, and design codes or standards.
The selection of the allowable stress depends on the type of material being used and the specific application. Different materials have different strength characteristics, such as yield strength, ultimate tensile strength, or allowable stress limits specified by standards. The allowable stress is typically chosen to be a fraction of the material's ultimate strength to provide a safety margin and account for uncertainties in loading, material properties, and other factors.
Strength Reserve Factor: The strength reserve factor, also known as the safety factor or factor of safety, is a measure of the structural safety margin or reliability. It is defined as the ratio of the material's capacity or strength to the applied stress.
In the context of a plastic material, which exhibits ductile behavior, the strength reserve factor is calculated by dividing the material's yield strength (or another appropriate measure of strength) by the applied stress. A higher strength reserve factor indicates a greater safety margin, as it implies that the material's capacity is higher than the applied stress.
On the other hand, for brittle materials that do not exhibit significant plastic deformation before failure, the strength reserve factor is calculated by dividing the material's ultimate strength or fracture strength by the applied stress. In this case, a higher strength reserve factor is desired to ensure a sufficient safety margin against catastrophic failure.


31.
Conditions of strength and uniformity in tension and compression ( maximum stress, permissible, three types of problems: strength check, safe strength, design; deformation, uniformity)
When considering the strength and uniformity of materials under tension and compression, several conditions need to be examined. Let's explore these conditions and the three types of problems associated with them:

1. 
   Maximum Stress: The maximum stress is the highest stress experienced in a material or structure under tension or compression. It is determined by dividing the applied force by the cross-sectional area of the material. In strength analysis, the maximum stress is compared to the material's permissible or allowable stress limit.
   
2. 
   Permissible Stress: Permissible stress refers to the maximum stress that a material can safely withstand under tension or compression. It is determined based on factors such as the material's strength properties, safety factors, and design codes or standards. The permissible stress is typically lower than the material's ultimate strength to provide a safety margin.
   
3. 
   Three Types of Problems:
   

a. Strength Check: The strength check problem involves evaluating whether the maximum stress in the material or structure remains below the permissible stress limit. This check ensures that the material or structure can safely withstand the applied tension or compression forces without failure.
b. Safe Strength Problem: The safe strength problem focuses on ensuring a sufficient safety margin between the applied forces and the material's strength. It involves selecting appropriate safety factors and determining the permissible stress level that provides an acceptable level of safety against failure.
c. Design Problem: The design problem entails selecting suitable dimensions, materials, and configurations to ensure that the material or structure meets the required strength and performance criteria. It involves considering factors such as load capacity, stress distribution, and appropriate safety margins.

4. 
   Deformation: Deformation refers to the change in shape or size of a material or structure under tension or compression. In addition to strength considerations, it is important to assess the deformation characteristics of the material. Excessive deformation can affect the functionality, aesthetics, or structural stability of the system.
   
5. 
   Uniformity: Uniformity refers to the even distribution of stresses and deformations across the material or structure. In tension or compression, uniformity is important to ensure that no localized areas experience significantly higher stresses or deformations than others. Non-uniform stress or deformation distribution can lead to material failure or structural instability.