Roark's formulas for stress and strain

[...]... Plane Stress and the corresponding stress element, viewed three-dimensionally and down the z axis, is shown in Fig 2.5 2.2 Strain and the Stress Strain Relations As with stresses, two types of strains exist: normal and shear strains, which are denoted by e and g, respectively Normal strain is the rate of change of the length of the stressed element in a particular direction 14 Formulas for Stress and Strain. .. from the tangential forces DFxy and DFxz as well, and since these forces are tangential, the stresses are shear stresses Similar to Eq (2.1-1), txy ¼ dFxy dAx ð2:1-2Þ txz ¼ dFxz dAx ð2:1-3Þ y Standard engineering practice is to use the Greek symbols s and t for normal (tensile or compressive) and shear stresses, respectively 12 Formulas for Stress and Strain Figure 2.3 [CHAP 2 Stress components Since,... nx 0 ¼ 0 ny 0 ¼ 0 nz 0 ¼ 1 The last rows and columns of the stress matrices are zero so the stress matrices can be written as  ½sŠxy ¼ Figure 2.11 Plane stress transformations sx txy txy sy  ð2:3-13Þ 24 Formulas for Stress and Strain [CHAP 2 and  ½sŠx0 y0 sx 0 ¼ tx0 y0 tx0 y0 sy0  ð2:3-14Þ Since the plane stress matrices are 2  2, the transformation matrix and its transpose are written as  cos... mz0 ¼ cos yz0 y ; nz0 ¼ cos yz0 z ð2:3-5Þ 18 Formulas for Stress and Strain Figure 2.8 [CHAP 2 The stress at a point using different coordinate systems It can be shown that the transformation matrix 2 lx0 ½TŠ ¼ 4 ly0 lz0 mx0 my0 mz0 3 nx 0 ny 0 5 nz0 ð2:3-6Þ SEC 2.3] Figure 2.9 Stress and Strain: Important Relationships 19 Coordinate transformation transforms a vector given in xyz coordinates, fVgxyz... Methods Chapter 2 Stress and Strain: Important Relationships Understanding the physical properties of stress and strain is a prerequisite to utilizing the many methods and results of structural analysis in design This chapter provides the definitions and important relationships of stress and strain 2.1 Stress Stress is simply a distributed force on an external or internal surface of a body To obtain a physical... useful general principles are stated; analytical and experimental methods of stress analysis are briefly described, and information concerning the behavior of material under stress is given In Part 3 the behavior of structural elements under various conditions of loading is discussed, and extensive tables of formulas for the calculation of stress, strain, and strength are given Because they are not believed... the end of this chapter gives transformation matrices for this 20 Formulas for Stress and Strain [CHAP 2 EXAMPLE The state of stress at a point relative to an xyz coordinate system is given by the stress matrix 2 ½sŠxyz À8 ¼4 6 À2 3 6 À2 4 25 2 À5 MPa Determine the state of stress on an element that is oriented by first rotating the xyz axes 45 about the z axis, and then rotating the resulting axes... 2.4 Stress and Strain: Important Relationships 13 Stresses on three orthogonal surfaces as earlier defined This state of stress can be written in matrix form, where the stress matrix ½sŠ is given by 2 3 sx txy txz ½sŠ ¼ 4 tyx sy tyz 5 ð2:1-5Þ tzx tzy sz Except for extremely rare cases, it can be shown that adjacent shear stresses are equal That is, tyx ¼ txy , tzy ¼ tyz , and txz ¼ tzx , and the stress. .. Fahrenheit,  F In stress analysis, the unit of length used most often is the inch ties associated with loading, including energy, work, and power; and stress analysis properties such as deformation, strain, and stress Two basic systems of units are employed in the field of stress analysis: SI units and USCU units.y SI units are mass-based units using the kilogram (kg), meter (m), second (s), and Kelvin (K)... bending of straight and curved beams; torsion; bending of flat plates; columns and other compression members; shells of revolution, pressure vessels, and pipes; direct bearing and shear stress; elastic stability; stress concentrations; and dynamic and temperature stresses Each chapter contains many tables associated with most conditions of geometry, loading, and boundary conditions for a given element . Formulas for Torsional Deformation and Stress 401 10.2 Formulas for Torsional Properties and Stresses in Thin-Walled Open Cross-Sections 413 10.3 Formulas for the Elastic Deformations of Uniform. 608 13.4 Formulas for Discontinuity Stresses and Deformations at the Junctions of Shells and Plates 638 13.5 Formulas for Thick-Walled Vessels Under Internal and External Loading 683 14.1 Formulas for. Shear, Moment, Slope, and Deflection Formulas for Long and Short Thin-Walled Cylindrical Shells under Axisymmetric Loading 601 13.3 Formulas for Bending and Membrane Stresses and Deformations in Thin-