Roark’s formulas

Roark s Formulas for Stress and Strain, 6th edition, McGraw-Hill, 1989. 

Young WC, Budynas RG (2002) Roark s formulas for stress and strain, 7th edn. McGraw-Hill, Boston... 

W.C. Young. Roark s Formulas for Stress and Strain, 6th edition, McGraw-Hill, Inc., New York, 1989, p. 101. 

Notes 1 The results from the EUROCOMP tables are compared to those obtained using ANSYS and the tables in Roark s Formulae for Stress and Strain. 

Roark s Formulas. Bilayered discs are considered in Roark s formulas. When the bilayered disc is subjected to biaxial moment, the stresses at the top and the bottom surfaces of the disc are given by [36]... 

It should be noted that instead of the actual ring-on-ring tests, the following loading configuration is considered in Roark s formulas. The disc is simply supported at its edge i.e., R = a in Fig. 1(b), and is subjected to a uniform annular line loading at r = Z). In this case, the biaxial moment is related to the load, P, by [36]... 

The moment-load relation has different signs between Eqs. (5) and (8) because of different conventions in defining the moment. Roark s formulas have been adopted by the researchers in the dental community to predict stresses for bilayered dental ceramics subjected to ring-on-ring tests. 

However, because the specimen radius is required to be greater than the support ring radius in actual ring-on-ring tests, it is impractical to use the condition of i = a in Roark s formulas, and modification of Roark s formulas is required. This modification has been considered by Hsueh and Thompson [42], such that for R > a in ring-on-ring tests, the moment-load relation in Roark s formulas i.e., Eq. (8), should be replaced by... 

The modified Roark s formulas, which are pertinent to ring-on-ring tests, can be obtained by combining the biaxial stress-biaxial moment and the biaxial moment-load relations i.e., Eqs. (6a), (6b), and (11). 

Equations (21a) and (21b) can be compared with Roark s formulas. However, while Hsueh etal. s formulas give the stress distribution through the disc thickness, Roark s formulas give only stresses on the top and the bottom surfaces of the disc. For the special case of monolayered discs i. e., n = 1, Hsueh et a/. s formulas become identical to ASTM formulas. 

Fig. 2. The biaxial stress through the thickness of a zirconia monolayered disc subjected to ring-on-ring loading of f = 1000 N showing the comparison among ASTM formulas, Roark s formulas, modified Roark s formulas, Hsueh et al. s formulas, and FEA results.

Roark s formulas for torsional stress from a twisting motion can be expressed for beam loading conditions [4], e.g., for a power transmission application. Shear stress developed in a material subjected to a specified torque in a torsion test is estimated by [5]... 

Beams are often subject to different boundary conditions and forces in MEMS design. A comprehensive reference for the bending of beams in different situations is Roark s formulas for stress and strain [4]. We considered a fixed-free cantilever beam that is subjected to a point load at its free end in the spring analysis above. The fixed-free boundary condition means that one end is fixed, so that both its displacement and slope do not change under the applied force. The other end of the beam is free to both move and change its slope in response to a point load F, as shown in Figure 2.7. In that case the deflection of the beam y(j ) as a function of position x is given by... 

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