4.17. Simple Tension and compression tests on a brittle material reveal that failureoccurs by fracture at o, = 260 MPa and o,` = 420 MPa, respectively. In an actualapplication, the material is subjected to perpendicular tensile and compressivestresses, oj and o2, respectively, such that o1/02=-1/4. Determine the limiting values ofaccording 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 givenloading 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` = 650MPa) is describe by 0,= 0, oy= -180 MPa, and tgy = 200 MPa. Determine whetherfailure 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 producinga tensile stress of 3o/4. Applying the principal stress theory of failure, determine theshear stress produced by a torque that acts simultaneously on the chalk and theorientation of the fracture surface.4.21. The ultimate strengths in tension and compression of a material are 420 and 900MPa, respectively. If the stress at a point within a member made of this material is200 150150MPa20Determine the factor of safety according to the following theories of failure: (a)maximum principal stress and (b) Coulomb-Mohr.

Answered: Image /qna-images/answer/2710de9c-6918-4e62-a9c9-f21d0b9783ea.jpg

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

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: At a point in an elastic material under strain, there are normal stresses of 60 N/mm2 and 40 N/mm2…

Q: Question- In a two-dimensional stress system, the two principal stresses are 180 N/mm² (tensile) and…

A: given principal stress σ1= 180 N/mm2Let other principal stress=σ2yield stress=240 N/mm2Poisson's…

Q: A solid bar with dimensions Lxwxw is stretched along its length by 8%. During the deformation the…

A: Given Stretch in longitudinal direction 8% Change in volume 0

Q: itude of maximum shear stress in the

A: This question has been taken from Solid mechanics

Q: 3. Given the following stress functions, = 3x² + 3y² − σ₁ = 3y² o₂ = 3x+y-z+ 6x = -Z Tay=z-6xy-² T₁₂…

A: Given data,

Q: At a point on the surface of a machine component the stresses acting on the x face of a stress…

A: step 1-

Q: Can you please answer the following question in the picture and show all of your work in, please.

A: Detailed step by step solution is given below, still if you have any query please feel free to…

Q: At a point in elastic medium normal stresses in two mutually perpendicular directions are 120 MPa,…

A: Normal stresses : = 120 MPa = 40 MPaTangential stress = 30 MPaTo Find :Principal stresses ?

Q: Question A structural element is subjected to a two dimensional stress system, wherein ₁ = 225 N/mm²…

A: Given- Stresses- σ1=225 N/mm2,σ2=compressive,Possion's ratio μ=0.25, It is needed to find the value…

Q: 1. Aluminum-alloy cover sheets are bonded to a plastic core to form the sandwich beam whose cross…

Q: At a point in a machine component that is subjected to plane stress, the normal and shear stresses…

A: Given data: σx=40 MPaσy=-95 MPaτxy=42 MPaE=73 GPav=0.32It is asked to calculate εx, εy, εz, γxy

Q: At a point in a machine component that is subjected to plane stress, the normal and shear stresses…

A: Determine the strain components of machine?

Q: The stresses on two perpendicular planes through a point in a body are 160 MPa and 100 MPa, both…

Q: At a point in a machine component that is subjected to plane stress, the normal and shear stresses…

Q: Q- Principal stress at a point in an elastic material are 1.5 o (tensile), o (tensile) and 0.5o…

A: Given- Principal stress- σ1=+1.5σ σ2=+σ σ3=-0.5σ Elastic limit E=210 MPa, Poisson's ratio- μ=0.3,…

Q: A homogenous isotropic material of size 20 cm x 20 cm x 20 cm is placed inside a rigid box of…

A: Consider the free body diagram;Given;Young modulus, E=Poisson ratio, v=0.3

Q: At a point in a machine component that is subjected to plane stress, the normal and shear stresses…

Q: The stresses on two perpendicular planes through a point in a body are 160 MPa and 100 MPa, both…

Q: At a point in a machine component that is subjected to plane stress, the normal and shear stresses…

Q: In a two dimensional stress system, the two principal stresses are a, of is 240 N/mm² and Poisson's…

Q: In terms of oxx , O yy and the material properties having a plane strain state; write the expression…

Q: Consider a metal single crystal oriented such that the normal to the slip plane and the slip…

A: Note* According to the guidelines given by Bartley since you have asked multiple questions, we will…

Q: 0.2 In a material there is a horizontal tensile stress of 200 MPa, a vertical tensile stress of 50…

Q: On the cross-section of a steel beam under bending, which one of the following statements is…

A: The maximum normal stress always occurs on the planes of zero shearing stress. The maximum and…

Q: (a) the modulus of elasticity. (b) Poisson's ratio. (c) the change in the bar width b.

Q: The state of stress at a point is given by: o= 80 MPa, oy=100 MPa and tauxv =60 MPa. If the yield…

A: State of stresses-σx=80 MPaσy=100 MPaτxy=60 MPayield strength-fy=150 MPa

Q: Q.1 At a point in a material there is a horizontal tensile stress of 150 MPa, a vertical compresaive…

Q: 34A tate of plane stress is shown in figure below: y 105 MPa 7 56 MPa If the minimum principal…

Q: A homogenous isotropic material of size 20 cm x 20 cm x 20 cm is placed inside a rigid box of…

Q: The stresses on two perpendicular planes through a point in a body are 160 MPa and 100 MPa, both…

Q: Sketch the stress-strain curve of the following tension test??? In the tension test of a metal…

A: this test in conducted in uniform tension machine. standardization of this test is follow by…

Q: For the state of plane stress shown, determine (a) the largest value of o, for which the maximum…

Q: If the principal stresses in a plane stre.ss problem, are 0, = 100 MPa, 0z = 40 MPa, the magnitude…

Q: At a point in a strained material, tensile stress of 100 MPa and compressive stress of 60 MPa are…

Q: The state of two dimensional stresses acting on a concrete lamina consists of a direct tensile…

A: Given data- State of 2-D stress given- Direct tensile stress- σx=1.5 N/mm2, Shear stress- τ=1.20…

Q: At a point in a machine component that is subjected to plane stress, the normal and shear stresses…

Concept explainers

Solid Mechanics

Engineering mechanics is a branch of science that deals with forces causing bulk motion in bodies and the effect that these forces cause on the bodies. Engineering mechanics does not deal with the internal changes that occur on account of these external forces. The internal effects in a body or a material under the action of external forces are studied in a new branch of science called solid mechanics, the strength of materials, or the mechanical behavior of engineering materials.

Question

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.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.

Similar questions

Question: Principal stresses at a point are 80 N/mm2 and 40 N/mm² both tensile. The yield stress in simple tension for this material is 200 N/mm2 The values of factors of safety according to maximum principal stress theory and maximum shear stress theory, respectively, are
The polymer bar shown in the figure below has a width of b = 42 mm, a depth of d = 97 mm, and a height of h = 253 mm. At a compressive load of P = 125 kN, the bar height contracts by Ah = -2.40 mm, and the bar depth elongates by Ad = 0.40 mm. At this load, the stress in the polymer bar is less than its proportional limit. Determine: (a) the modulus of elasticity. (b) Poisson's ratio. (c) the change in the bar width b. Rigid plate h Rigid base (a) E = i (b) v = i (c) Ab = i GPa mm b
The stresses on two perpendicular planes through a point in a body are 160 MPa and 100 MPa, both compressive, along with a shear stress of 80 MPa. What is the normal stress on a plane inclined at 30° to the plane of 160 MPa stress? (a) -42.4 MPa (b) -75.7 MPa (c) -59.1 MPa (d) -86.3 MPa
At a point in a machine component that is subjected to plane stress, the normal and shear stresses are σx=σx= 60 MPa, σy=σy= 80 MPa, and τxy=τx⁢y= 42 MPa, acting in the directions shown in the figure. At this point, determine the strain components εxεx, εyεy, εzεz, and γxyγx⁢y. Assume that E = 72 GPa and v = 0.29 for the machine component.
If €, and e y are the maximum and minimum strains, respectively in the neighbourhood of a point in a stressed material, then what is the expression for the maximum principal stress?
A critical point in a part made of a ductile material is subject to the following state of plane stress: 15ksi, 30 ksi, 15 ksi, Ox,min = -35 ksi, Oy,min = 30 ksi, Txy,min = -15 ksi. Ох,max бу,max Тxy,max %3D There are no stress concentrations. The load line is propositional. The material has a yield strength of Sy = 130 ksi, an ultimate strength of Su = 200 ksi, and a fully corrected endurance limit of Sn : 75 ksi. Calculate the: (a) Static factor of safety using the MSSTF, (b) Static factor of safety using the DETF, (c) Fatigue factor of safety using the Soderberg criterion, (d) Fatigue factor of safety using the Goodman criterion, (e) Fatigue factor of safety using the ASME elliptic criterion.
Question- Principal stress at a point in an elastic material are 1.50 (tensile), o (tensile) and 0.50 (compressive). The elastic limit in tension is 210 MPa and poisson's ratio=0.3. Find the value of o at the failure when computed by the maximum principal strain theory.
5. A plane stress state is given by ơ1 =-3 0o, 02 = 2 and 112 = 00 The yield stress for this material is Oy. Assume now that the governing stress o, is increased monotonically. 5.1. At what value of o, will yielding occur according to Tresca's criterion? 5.2. At what value of o, will yielding occur according to Von Mises' criterion? 5.3. Which is the more conservative and by how much (%)?
At a particular point in a structural member a direct tensile stress of 60 N/mm² exists on a plane perpendicular to the longitudinal axis of the member while a direct compressive stress of 40 N/mm? occurs on a plane parallel to this axis; in addition shear and complementary shear stresses of 50 N/mm? act on these planes. If Young's modulus E is 200000 N/mm² and Poisson's ratio v is 0.3 calculate the direct and shear strains on these planes and hence, using a graphical method, determine the principal strains at the point, the maximum shear strain and the angle the plane of maximum principal strain makes with the longitudinal axis of the member. Finally, calculate the principal stresses at the point. Ans. E= 3.6x104, ɛ, = -2.9x104, Yy=6.5x10-4 ɛ1 = 4.95x10, 01 = 80.8 N/mm², o1=-60.8 N/mm. Ɛ11 =-4.25x10 Ymax=9.2x10-, 67.5°
3. The material is subjected to biaxial loading producing uniform normal stress ox and o, as shown. The strains are e, = -0.00065 and e, = -0.00040. Use E = 207 GPa and v = 0.35. Determine the following: (a) oz. Indicate tension or compression. Use 2 decimal places. (b) ơy. Indicate tension or compression. Use 2 decimal places. (c) Change in the thickness of the material. Indicate elongation or contraction. Use 5 decimal places and scientific notation of x 10-3 (Example: . (25 pts) x 10-3) y Oy x. Oy t = 16 mm