. The strength of materials; a text-book for engineers and architects. material glass could be bent cold withoutfracture when placed in a liquid under great hydraulic pres-sure. Marble has been bent without fracture by ProfessorE. D. Adams of McGill University when placed in steel cylin-ders and compressed, and Professor Ira H. Woolson crushed BEHAVIOUR OF MATERIALS UNDER TEST 43 a cylinder of concrete encased in steel into the form shownin Fig. 18, and yet when the encasing cylinder of steel wasremoved the strength of the concrete was found to be notappreciably different from that of concrete
. The strength of materials; a text-book for engineers and architects. material glass could be bent cold withoutfracture when placed in a liquid under great hydraulic pres-sure. Marble has been bent without fracture by ProfessorE. D. Adams of McGill University when placed in steel cylin-ders and compressed, and Professor Ira H. Woolson crushed BEHAVIOUR OF MATERIALS UNDER TEST 43 a cylinder of concrete encased in steel into the form shownin Fig. 18, and yet when the encasing cylinder of steel wasremoved the strength of the concrete was found to be notappreciably different from that of concrete which had notbeen similarly treated. The question therefore resolves itselfwhether tension or shear is the cause of failure, and we havereason to believe that in ductile materials such as mild steelfailure occurs by shear and in brittle materials such ascement or concrete by tension. We will return to this afterconsidering the various theories of failure; there are fourprincipal theories which we will consider. 1. Principal Stress or Rankine Theory.—^According to. Fig. 18. this theory, which was adopted by the great Glasgow professor,Rankine, the failure occurs when the maximum principal stressexceeds a certain value. We have seen (p. 19) that for anormal or direct stress / and shear stress s the principal stressis given by the relation / , 1 , or ?9 = -^ + 2 V/2 + 4^2 (16) and the inclination 0 of this stress to the normal stress and to the shear stress is given by the relation tan 20 = —r. This stress p is the simple normal stress (tension or com-pression) equivalent in effect to the combined normal andshear stresses. 44 THE STRENGTH OF MATERIALS In the limiting case in Avhich the direct stress / is zero weget p = s and tan 2 $ = infinite, i. e. 0 = 45°, i. e. a shearstress is equivalent to a normal stress of the same intensityand is at 45° to it, or the shear and tensile strengths of thematerial should be equal. 2. Principal Strain or St. Venant Theory.—Accordingto
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