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4.17. Simple Tension and compression tests on a brittle material reveal that failure occurs by fracture at o, = 260 MPa and o, = 420 MPa, respectively. In an actual application, the material is subjected to perpendicular tensile and compressive stresses, ơj and 02, respectively, such that o1/02=-1/4. Determine the limiting values of according to (a) the Mohr theory for an ultimate stress in torsion of tu = 175 MPa and (b) the Coulomb-Mohr theory. Hint: For case (a), the circle representing the given loading is drawn by a trail-and-error procedure. %3D

4.17. Simple Tension and compression tests on a brittle material reveal that failure occurs by fracture at o, = 260 MPa and o, = 420 MPa, respectively. In an actual application, the material is subjected to perpendicular tensile and compressive stresses, ơj and 02, respectively, such that o1/02=-1/4. Determine the limiting values of according to (a) the Mohr theory for an ultimate stress in torsion of tu = 175 MPa and (b) the Coulomb-Mohr theory. Hint: For case (a), the circle representing the given loading is drawn by a trail-and-error procedure. %3D

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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4.17. Simple Tension and compression tests on a brittle material reveal that failure occurs by fracture at o, = 260 MPa and o,` = 420 MPa, respectively. In an actual application, the material is subjected to perpendicular tensile and compressive stresses, oj and o2, respectively, such that o1/02=-1/4. Determine the limiting values of according to (a) the Mohr theory for an ultimate stress in torsion of tu = 175 MPa and (b) the Coulomb-Mohr theory. Hint: For case (a), the circle representing the given loading is drawn by a trail-and-error procedure. 4.18. The state of stress at a point in a cast-iron structure (ơu = 290 MPa, ou` = 650 MPa) is describe by 0,= 0, oy= -180 MPa, and tgy = 200 MPa. Determine whether failure occurs at the point according to (a) the maximum principal stress criterion and (b) the Coulomb-Mohr criterion. 4.20. A piece of chalk of ultimate strength o, is subjected to an axial force producing a tensile stress of 3o/4. Applying the principal stress theory of failure, determine the shear stress produced by a torque that acts simultaneously on the chalk and the orientation of the fracture surface. 4.21. The ultimate strengths in tension and compression of a material are 420 and 900 MPa, respectively. If the stress at a point within a member made of this material is 200 150 150 MPa 20 Determine the factor of safety according to the following theories of failure: (a) maximum principal stress and (b) Coulomb-Mohr.
Transcribed Image Text:4.17. Simple Tension and compression tests on a brittle material reveal that failure occurs by fracture at o, = 260 MPa and o,` = 420 MPa, respectively. In an actual application, the material is subjected to perpendicular tensile and compressive stresses, oj and o2, respectively, such that o1/02=-1/4. Determine the limiting values of according to (a) the Mohr theory for an ultimate stress in torsion of tu = 175 MPa and (b) the Coulomb-Mohr theory. Hint: For case (a), the circle representing the given loading is drawn by a trail-and-error procedure. 4.18. The state of stress at a point in a cast-iron structure (ơu = 290 MPa, ou` = 650 MPa) is describe by 0,= 0, oy= -180 MPa, and tgy = 200 MPa. Determine whether failure occurs at the point according to (a) the maximum principal stress criterion and (b) the Coulomb-Mohr criterion. 4.20. A piece of chalk of ultimate strength o, is subjected to an axial force producing a tensile stress of 3o/4. Applying the principal stress theory of failure, determine the shear stress produced by a torque that acts simultaneously on the chalk and the orientation of the fracture surface. 4.21. The ultimate strengths in tension and compression of a material are 420 and 900 MPa, respectively. If the stress at a point within a member made of this material is 200 150 150 MPa 20 Determine the factor of safety according to the following theories of failure: (a) maximum principal stress and (b) Coulomb-Mohr.
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