专业英语 第三单元 Reading material 3 Theoties of strength专业英语 第三单元 Reading material 3 Theoties of strength.doc
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专业英语 第三单元 Reading material 3 Theoties of strength专业英语 第三单元 Reading material 3 Theoties of strength
1 Principal Stresses
The state of stress at a point in a structural member under a complex system of loading is described by the magnitude and direction of the principal stresses. The principal stresses are the maximum values of the normal stresses at the point, which act on planes on which the shear stress is zero. In a two-dimensional stress system, Fig.1.11, the principal stresses at any point are related to the normal stresses in the x and y direction, and , and the shear stress at the point by following equation:
Principal stresses,
The maximum shear stress at the point is equal to half the algebraic difference between the principal stresses:
Maximum shear stress,
Compressive stresses are conventionally taken as negative; tensile as positive.
2. Classification of pressure vessels
For the purpose of design and analysis, pressure vessels are sub-divided into two classes depending on the ratio of the wall thickness to vessel diameter; thin walled vessels, with a thickness ratio of less than 1/10, and thick-walled above this ratio.
The principal stresses acting at a point in the wall of a vessel, due to a pressure load, are shown in Fig.1.12. If the wall is thin, the radial stress will be small and can be neglected in comparison with the other stresses, and the longitudinal and circumferential stress and can be taken as constant over the wall thickness. In a thick wall, the magnitude of the radial stress will be significant, and the circumferential stress will vary across the wall. The majority of the vessels used in the chemical and allied industries are classified as the thin-walled vessels. Thick-walled vessels are used for high pressures.
Fig 1.11 and Fig. 1.12
3. Allowable stress
In the first two sections of this unit equations were developed for finding the normal stress and average shear stress in a structural member. These equations can also be used to select the size of a member if the member’s strength is known. The strength of a material can be de
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