Answered: For the three stress states given, find…

For the three stress states given, find all principal normal stresses using the eigenvalue method. σxx = 25 MPa, σyy = -50 MPa, ?xy = 25 MPa (clockwise)

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter7: Analysis Of Stress And Strain

Section: Chapter Questions

Problem 7.3.2P: Repeat the preceding problem using sx= 5.5 MPa. ??y= 4 MPa. and txy= 3.2 MPa.

See similar textbooks

Related questions

Q: tress-strain diagram for a steel alloy having an original diameter of 0.80 in. and a ength of 2 in.…

Q: A gate having the shape shown in Figure 1.11 is located in the vertical side of an open tank…

Q: determine forces in cable AB, AC,AD

A: Given F= 450 lb Required: forces in cable AB, AC,AD

Q: A Based on observations, the speed of a jogger can be approximated by the relation v = 6.4 (1 −…

A: Given data: v = 6.4×(1-0.03x)0.4 (note: the given data format is corrected accordingly) x = 0 when…

Q: Determine the resultant force of the blood on the artery bifurcation shown. Take d₁ = 8 mm, d₂ = 7…

A: Given data: d1 = 8mm, d2 = 7mm, d3 = 5mm, Q1 = 14mL/s. Q2 = 9 mL/s, p1 = 110 mmHg, p2 = 80 mmHg, and…

Q: 4. Determine the range of P for which the system of two blocks will be in equilibrium. Friction is…

Q: A rear-wheel-drive 3150-lb drag race car has a 230-inch wheelbase and a center of gravity 32 inches…

A: Weight transfer: The transfer of weight from one end of a vehicle to the other when it undergoes…

Q: Calculate the work associated with a system when its volume is compressed from 81.6 L to 30.9 L…

A: According to the given data V1=81.6 L V2=30.9L P=1.23bar We need to find Work done

Q: Hello i dont undertsnad the steps, where do they get the 0.13333 from?? and the 0.7?? can you…

A: According to the question We need to explain steps which does not explain properly.

Q: 5. An electric motor draws a current of 10 A with a voltage of 110 V. The output shaft develops a…

Q: Consider the force shown in (Figure 1). gure F = (-6i+4j+8k) kN Determine the x, y, z, components…

Q: 2-41. Determine the magnitude of the resultant force and its direction, measured counterclockwise…

Q: A, B, and D are rectangular ducts as shown. Pipe-C is a round pipe. (a) (b) Pipe-A Pipe-B Pipe-C…

Q: CAREFUL WITH UNITS !! a) Find the magnitude F and point of application y R of the water force on the…

A: Given: The gate dimensions and gate depth. Required: Force F and its point of application.

Q: Forging procedures may be classified in part by how much room there is for movement in the die.…

A: To explain: The primary classes of forging procedure. Concept used: Forging procedure: Forging is a…

Q: 3. A light rod AB of length 600 mm has a fixed hinge at A and a mass of 5 kg concentrated at B. A…

A: The given information in the problem is shown in the following attached image:

Q: 10. The state of an ideal gas is changed in a closed path 1-2-3-4-1. Which of the following is true…

A: To find: The work done on the gas. PV diagram: The PV diagram is shown below.

Q: Convert a -7 kPa (negative 7 kiloPascal) pressure to an absolute pressure in kPa. (Note: the…

Q: 4. Saturated liquid at 300°C the internal energy (u) is A. 2563.6 kJ/kg *************** B. 2345.4…

A: Givensaturated liquid at 300oC

Q: A crack has been discovered along the edge of a reinforcing rib in titanium housing. The rib is 0.5…

A: Given: The rib thickness, t = 0.5 in The rib width, b = 4 in The crack length, a = 1.2 in The…

Q: Calculate for the Carnot heat engine efficiency producing 12 hp of work by transferring energy…

A: Given:Work produced by the Carnot heat engine, W=12 hpTemperature of the source, TH=250oFTemperature…

Q: Write the vector loop equations and indicate the fixed constants, variables, and constraint…

A: The vector loop equations, and indicate the fixed constants, variable and constraint equation.…

Q: 2. Determine the resultant moment of the four forces acting on the rod shown about point O.

A: Given

Q: The wall of the furnace is 30.48 mm thick and is insulated from outside. Thermal conductivity of the…

A: In this problem, we will calculate the overall heat transfer by the conduction per unit area and the…

Q: The cart impacts the safety barrier with speed vo = 3.75 m/s and is brought to a stop by the nest of…

Q: 3.59 The triangular plate ABC is supported by ball-and-socket joints at B and D and is held in the…

Q: The bar shown has a rectangular cross section. For a given load P, determine (1) the force…

Q: cing r pendu ith th

A: DISCLAIMER FOR MULTIPLE Since you have asked multiple questions, we will solve the first question…

Q: If the water mass flow rate is doubled, (i) What is the minimum horizontal force required to hold…

A: Introduction In this problem, we will calculate the inlet and outlet velocities of the nozzle, the…

Q: . Determine the principal stresses at point A on the cross section of the wrench at section a-a.…

A: The value of force is P=70 lb

Q: 1. A group of curious 9B students are listening to sound generated by standing waves in a tube of…

A: Given: The initial distance between node and antinode =0.6 m The final distance between node and…

Q: 8 kN/m 18.38 j 10 i 18.38 j -15.38 i-5 j 0i-15.38 j Correct Submit Previous Answers Part B 1.5 m-…

Q: A heat pump based on the vapor-compression refrigeration cycle uses R-134a as the working fluid. The…

A: Given that, working fluid of the heat pump cycle is R134a. Condenser pressure is 1.2 MPa and…

Q: Which of these propositions are right (multiple answers) a. A heat pump and a chiller works…

A: Disclaimer: “Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: 2m A 2 KN B F C E 4 kN 3 kN D

Q: What are key things for forced-air method of food commodities?

A: Forced air method for food commodities is used for food preservation for long term.

Q: A machine of mass 203.5 kg is mounted on four parallel springs each of stiffness 1.6 x 105 N/m. When…

Q: Part B Determine the magnitude of the resultant moment of these forces about the blader Express your…

A: According to the given data A force system is given with F1=14N F2=30N we need to find Resulting…

Q: A deep geothermal system delivers 50000 [MWh] heat at 60 [oC] yearly. The average heating demand of…

A: Introduction Geothermal energy is heat energy that originates from the ground (heat). Geothermal…

Q: Question A 1.2 m x 1.2 m square gate located in the vertical side of an open tank is pivoted about…

A: “Since you have posted multiple questions with multiple sub-parts, we will provide the solution only…

Q: 4. Determine the magnitude of the moment of the force F = {50i-20j - 80k} N about the a) base line…

A: Given that: The force is: F→ = 50i^ - 20j^ - 80k^ N It is required to determine the magnitude of the…

Q: A power plant using a CCGT cycle with .4 electrical efficiency 0.6 and with 8 % non-usable heat and…

A: The usable heat delivered by a Combined Cycle Gas Turbine (CCGT) plant can be calculated using the…

Q: 8. Total annual primary energy You want a new gas boiler for your house. The annual space heating…

A: To find: The primary energy consumption. Given: The annual space heating demand is 8000 kWh. The…

Q: 4. A circuit contains a 20-92 resistor and an inductor with an inductance of 0.093 H. If the circuit…

A: Given: Resistance and inductance Required: Total impedance.

Q: 4/67 Determine the forces in members AD and DG. J d P F G L d d E D L d d B A 0.8 d L

A: Given: The forces at point G ,D and A are L in downward direction. And the distances of point G , D…

Q: A block of mass m₁ = 3.50 kg on a frictionless plane inclined at angle 0 = 26.8° is connected by a…

A: According to the given data

Q: What are the roles of heat, pressure, and moisture in the process used to make corrugated…

A: Heat, pressure, and moisture play important roles in the process of making corrugated fiberboard.…

Q: P23-1. Member ABCE is supported by three separate cables, DB, DC, and EF. The load at G has a weight…

A: To Find : The reaction at the ball and socket joint A and the tension in each of the wire. Free Body…

Q: vapor-compression A water cooler based on the refrigeration cycle uses refrigerant R- 134a as the…

Q: Q.2) The system is held in static equilibrium in the position shown when an 18 lb lamp is supported…

Question

For the three stress states given, find all principal normal stresses using the eigenvalue method.

σ_xx = 25 MPa, σ_yy = -50 MPa, ?_xy = 25 MPa (clockwise)

Expert Solution

Step 1

In eigenvalue approach, the eigenvalue represents the principal normal stresses and eigenvectors (unit normal vector) represents the direction of principal stresses.

According to eigenvector approach, we have following relations

$σ_{i j} n_{j} = λ n_{j}$

where,

$σ_{i j} = s y m m e t r i c s e c o n d o r d e r s t r e s s t e n s o r λ = e i g e n v a l u e o f t e n s o r k n o w n a s p r i n c i p a l s t r e s s v a l u e n = u n i t n o r m a l v e c t o r k n o w n a s e i g e n v e c t o r o r p r i n c i p a l d i r e c t i o n$

Thus,

$(σ_{i j} - λ I) n_{j} = 0$

where, I = unit matrix

To determine the eigenvalue, we need to determine the determinant of above equation. i.e.

$|σ_{i j} - λ I| = 0$

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

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, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

.4 The stresses on an clement arc known to be sx= 120 MPa, sy= 100 MPa, and txy= 75 MPa. Find the stresses on an inclined section through the element at an angle ? = 45°.
Solve the preceding problem if the cross- sectional dimensions are b = 1.5 in. and h = 5.0 in., the gage angle is ß = 750, the measured strains are = 209 × 10-6 and B = -110 × 10, and the material is a magnesium alloy with modulus E = 6.0 X 106 psi and Poisson’s ratio v = 0.35.
Repeat the preceding problem using sx= 5.5 MPa. ??y= 4 MPa. and txy= 3.2 MPa.
The stresses on an element are sx= 1000 Psi. sy= 500 psi, and txy= 350 psi. Find the stresses acting on an element oriented at an angle 0 = 250. Show these stresses on the rotated element.
The state of stress on an element of material is shown in the figure. Calculate the unit volume change of the element if the stresses x and y. are -20 ksi and 10 ksi, respectively. Assume E = 10,600 ksi and v = 0.33.
A strain rosette (see figure) mounted on the surface of an automobile frame gives the following readings: gage A,310 × 10-6:gage B,180 × l0-6; and gage C. -160 × 10-6. Determine the principal strains and maximum shear strains, and show them on sketches of properly oriented elements.
An clement of material in plane strain (see figure) is subjected to strains ex= 480 × 10-6, Ey= 70 × l0-6, and yxy= 420 × l0-6. Determine the following quantities: (a) the strains for an element oriented at an angle 0 = 75°, (b) the principal strains, and (c) the maximum shear strains. Show the results on sketches of properly oriented elements.
Solve the preceding problem using the fol low-data: W 8 × 21 section, L = 84 in., P = 4.5 kips, a = 22.5°.
A circular aluminum tube subjected to pure torsion by torques T(sec figure) has an outer radius r2equal to 1.5 times the inner radius r1. (a) If the maximum shear strain in the tube is measured as 400 × 10-6 rad, what is the shear strain y1at the inner surface? (b) If the maximum a1lo-abk rate of twist is 0.125 °/m and the maximum shear strain is to be kept at 400 × 10-6 rad by adjusting the torque T, that is the minimum required outer radius ( r2)Min?
An element in pure shear is subjected to stresses ??xy= 3750 psi, as shown in the figure. Using Mohr’s circle, determine the following: (a) The stresses acting on an clement oriented at a slope of 3 on 4 (sec figure). (b) The principal stresses. Show all results on sketches of properly oriented elements.
The strains for an element of material in plane strain (see figure) are as follows: x = 480 ×10-6. y = 140 × l0-6, and xy = —350 x 10”. Determine the principals strains and maximum shear strains, and show these strains on sketches of properly oriented elements.
Solve Problem 7.7-12 by using Mohr’s circle for plane strain.