Question: A cylindrical rock sample with a diameter of 54 mm in the uniaxial compressive strength...

Question: A cylindrical rock sample with a diameter of 54 mm in the uniaxial compressive strength test

It was broken by applying a force of 160.2 kN. Since the angle between the applied load direction and the breaking surface is 30 °, the stresses acting on the breaking surface;

(a) Solve using the Mohr diagram (graphic method).

(b) Solve by analytical method.

Expert Solution

I have derived formulae for calculating the stresses on an inclined plane as shown below,

A)

Apply these formulae and calculate the stresses

b)

Plot the mohr's circle for given loading system and find the stress at inclined to 60 degrees from the x-axis

Hope this helps,

Please feel free to comment for further any queries,

all the best :)

Ally Wells answered 10 months ago

(a) Schematically explain how size of a rock sample affects the strength of the rock in...

(a) Schematically explain how size of a rock sample affects the strength of the rock in a triaxial experiment. (4.0 mark) (b) Using a schematic graph explain how different loading rates affect the elastic properties and strength of the rock. (4.0 mark)

A civil engineer is analyzing the compressive strength of concrete. Compressive strength is approximately Normally distributed...

A civil engineer is analyzing the compressive strength of concrete. Compressive strength is approximately Normally distributed with variance ? 2 = 1000 psi2 . A random sample of ? = 12 specimens has a mean compressive strength of ?̅= 3179.5 psi. Let ? be the true mean compressive strength of all specimens from this type of concrete. (a) Test ?0: ? = 3200 against ??: ? < 3200 at ? = 0.05. Give the rejection region. (b) If the true...

Estimate the axial infinite fatigue strength (10⁶) and 10³ fatigue strength for a 25 mm diameter...

Estimate the axial infinite fatigue strength (10⁶) and 10³ fatigue strength for a 25 mm diameter reversed axially loaded steel bar having Su =950 Mpa, Sy = 600 Mpa and is made from a “cold drawn” steel. Assume: T< 840º F, 99 % Reliability, CG = .8

A cylindrical specimen of some metal alloy 8.6 mm in diameter is stressed in tension. A...

A cylindrical specimen of some metal alloy 8.6 mm in diameter is stressed in tension. A force of 9070 N produces an elastic reduction in specimen diameter of 0.0048 mm. Calculate the elastic modulus (in GPa) of this material if its Poisson's ratio is 0.33.

A cylindrical bucket sitting on the edge of a table has a 2.95 mm diameter hole...

A cylindrical bucket sitting on the edge of a table has a 2.95 mm diameter hole near the bottom. Water squirts out the hole as shown in the figure below. If the height of the table is H = 2.00 m, determine the height h of the water level in the bucket. The answer is not 15.23 cm

A laser emits a cylindrical beam of light 4.0 mm in diameter. The average power of...

A laser emits a cylindrical beam of light 4.0 mm in diameter. The average power of the laser is 2.8 mW . The laser shines its light on a perfectly absorbing surface. How much energy does the surface receive in 14 s ? What is the radiation pressure exerted by the beam?

Diameter (mm) E. coli R/S Diameter (mm) S. aureus R/S Activity Range Oregano 27 54 Thyme...

Diameter (mm) E. coli R/S Diameter (mm) S. aureus R/S Activity Range Oregano 27 54 Thyme 26 54 Clove 14 18 Lavender 10 14 Sage 11 14 Chloramphenicol 14 27 Use the table to answer the following 6 questions about essential oils. Do essential oils appear to have the possibility of having some practical antibacterial use? Explain your reasoning. What could be some of the impracticalities and/or problems of using essential oils as an antibacterial agent given the information presented?...

A sample of concrete which is a cylinder 150 mm in diameter and 300 mm in...

A sample of concrete which is a cylinder 150 mm in diameter and 300 mm in length is placed in a test fixture. A load of 12,000 N is applied to the concrete specimen along the cylindrical axis and the length is observed to change 1 mm. Calculate Young's modulus in GPa.? Please reply as soon as possible

To what temperature (in °C) must a cylindrical rod of one metal 10.045 mm in diameter...

To what temperature (in °C) must a cylindrical rod of one metal 10.045 mm in diameter and a plate of second metal having a circular hole 9.990 mm in diameter have to be heated for the rod to just fit into the hole? Assume that the initial temperature is 25°C and that the linear expansion coefficient values for metals one and two are 4.9 x 10-6 (°C)-1 and 17 x 10-6 (°C)-1, respectively.

As part of a heat treatment process, cylindrical, 304 stainless steel rods of 100-mm diameter are...

As part of a heat treatment process, cylindrical, 304 stainless steel rods of 100-mm diameter are cooled from an initial temperature of 500ºC by suspending them in an oil bath at 25ºC. If a convection coefficient of 500 W/m2·K is maintained by circulation of the oil, how long does it take for the centerline of a rod to reach a temperature of 52ºC, at which point it is withdrawn from the bath? If 9 rods of length 1 m are...

Question