Consider the following strain state: [0.0016 [o] = 0.0003 0 0.0003 0.0008 0 0 0 0.0004] a. Determine the strain matrix for this strain state if the axes are rotated 30° counterclockwise around z-axis. b. Plot Mohr's circle for this strain state.

Consider the following strain state: [0.0016 [o] = 0.0003 0 0.0003 0.0008 0 0 0 0.0004] a. Determine the strain matrix for this strain state if the axes are rotated 30° counterclockwise around z-axis. b. Plot Mohr's circle for this strain state.

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 7.6.13P: A solid spherical ball of magnesium alloy (E = 6.5 × l0-6 psi, v = 0.35) is lowered into the ocean...

See similar textbooks

Related questions

Q: Question No #06: Analyze the telescoping link AB at the instant represent and determine its angular…

Q: As shown in figure a mass of 100 kg is held between two springs. The natural frequency of vibration…

Q: draw shear force diagram and moment diagram

A: According to the question a loading beam ACDEB is given We need to find Shear force diagram and…

Q: The least radius of gyration of a ship is 8 m and meta-centric height 70 cm. Calculate the time…

A: Given:Least radius of gyration of ship, k=8 mMeta centric height of the ship, GM=70 cm or 0.7…

Q: In simple harmonic motion, the displacement is maximum when the: O acceleration is zero O kinetic…

A: This question is based on the concept of Simple Harmonic motion.

Q: The pins at C and A are in double shear, and the pin at B is in single shear. All pins have a…

Q: IVOS cooler mixer H2SO4 SEPARATOR cooler 23 condenser STEAM reactor evaporater condenser 19…

A: Given: There are various components shown in the figure above in which all incoming and outgoing…

Q: B Fig. P2.40 Fig. P2.41 E F 12 in. O C 500 mm D 400 mm 2.41 A brass bolt (E, = 15 x 106 psi) of…

Q: A 1D two-node bar element as shown below is considered. The displacement of node 1 is q₁=0.002 mm,…

A: q1 = 0.002 mm qp = 0.013 mm let take, X1 = 10 mm Xp = 15 mm X2 = 35 mm To find out:- Displacement…

Q: The rigid beam is supported by a pin at C and an A-36 steel guy wire AB. Part A If the wire has a…

Q: 1. What is the enthalpy of saturated steam (water) at 20°C and 73°F in both kJ/kg and BTU/lbm?

Q: Determine the shear force V and bending moment M at a cross section located 16 ft from the…

A: Let the vertical reaction at point A be RA . The loaded beam is shown below -

Q: then rounding-off to 5 decimal places yields 1.23457 and that is the value which you need to type in…

A: Given: Horizontal force→P=2600 lb Cross sectional area of the truss→A=2 in2=0.013 ft2 Youngs…

Q: 22: The springs connecting with a rigid weightless bar as hown. The stiffness of beam (Kb) is 5 kN/m…

A: To find: The natural frequency for the system. Given: The stiffness of the beam is kb=5 kN/m. The…

Q: e kinematic viscosity of water is 0.01sto

A: Given:kinematic viscosity of water=0.01 stokesor ϑ=0.01×10-4 m2/sd=200 mm or 0.2 mv=3 m/s L=5…

Q: To maximise power in Pelton turbine, the bucket speed must be (1) equal to the jet speed (2) equal…

A: Given:Pelton wheel impulse turbine,Find,At what condition the power of turbine is maximum?

Q: Two plates are positioned at distance of 1.3 mm from each other. One of the plates is moving at…

Q: 2.3 a. For the spring assemblage shown in Figure P2-3, obtain the global stiffness matrix by direct…

Q: A horseshoe player throw the horseshoe with an initial speed vo = 40 ft/sec. calculate the ranges…

Q: A Carnot refrigerator has working temperatures of -30°C and 35°C. If it operates with Refrigerant…

A: The answer is given below,

Q: The resultant force of the three forces shown in (Figure 1) is FR = {9j} kN.

Q: 2. Heavy fuel oil flows from A to B through a 1000-m steel pipe. The horizontal 150-mm-diameter…

Q: A two-dimensional fluid element rotates like a rigid body. At a point within the element, the…

A: Given:2-D fluid element,Pressure=1 unit,Find,radius of the mohr's circle?

Q: In the following application, a temperature switch controls a heating contactor and a flow switch is…

A: Signal devices in the circuit: Cold air. Supply air. Heating contractor. Alarm. On delay…

Q: A steam power plant operates on an ideal reheat Rankine cycle and uses water as the working…

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

Q: The actual sales of car manufacturer in January is 120 units but the car manufacturer underestimated…

A: Given:smoothing constant, α=0.2Find,sales forecast for the month of february?

Q: Determine the magnitudes and components of vectors F1�1 and F2�2 and the angles α� and β�. Make sure…

A: According to the given data F1 and F2 forces are carrying the load(W) We need to find F1 and F2

Q: 1.3. 10. A polytropic process of air from 150 psia, 300°F, and 1 ft occurs to p2= 20 psia in…

A: GivenPolytropic processP1=150 psia=150×144=21600 psfT1=300oF=(300°F − 32) × 5/9 + 273.15 =…

Q: A tank contains 100 gallons of brine. Three gallons of brine, each containing 2 pounds of dissolved…

A: Given flow rate at exit and inlet. Required: Initial concentration.

Q: In a power plant operating with water and steam, the following measurements and observations were…

Q: Determine the force P required to force the 16° wedge under the 99-kg uniform crate which rests…

A: Mass m= 99 Kg Coeff of friction μ = 0.47 Lenght L=1.5 m Height h= 0.7 m θ1 =16° θ2 = 4° To…

Q: 3.49 To loosen a frozen valve, a force F with a magnitude of 70 lb is applied to the handle of the…

Q: a reversible, nonflow, constant volume process decreases the internal energy by 316.5kJ for 2.268…

Q: P10 The velocity field of a flow is described byu=4x,v=5y+2, andw=3t2+3. What is the pathline of a…

Q: A 200-kg dragster (racing car) exerts a constant force of 4000 N during a race. The coefficient of…

A: As per the guidelines we are subjected to solve only three subparts of a question. Please repost the…

Q: A piston cylinder device shown in Figure P2.6 contains 0.1 kg of air initially at a pressure of 4…

Q: # Find the shortest length of duminium tubes 50mm outer diameter x 45 mm inner diameter with minimum…

Q: A vehicle collides with an immoveable concrete embankment. Estimate the number of 'gs' the occupant…

Q: 19 Both portions of the rod ABC are made of an aluminum for which E = 70 GPa. Knowing that the…

Q: Problems 1.85 through 1.92 refer to a linkage that is to act as a crank-rocker mechanism Link…

Q: 7. If 10 kgm/min of air are compressed isothermally from p1 = 96 kPa and V1 = 7.65 m³/min to p2 =…

A: According to the question data m=10kg/min P1=96kPa P2=620kPa V1=7.65m3/min Process 1 to 2 is an…

Q: 4. Three pounds of a perfect gas with R = 38 ft.lby/lb.R and k = 1.667 have 300 Btu of heat added…

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

A: Given: twall=30.48 mmkwall=0.1 W/mKkins=0.01 W/mKTfurnance=T1=650…

Q: rod of length L having uniform cross-sectional area A is subjected to a tensile force P . If the…

A: Given: A rod of length L having uniform cross-sectional area A is subjected to a tensile force P…

Q: 2. Two cables BG and BH are attached to frame ACD as shown. Knowing that the tension in cable BG is…

A: Given tension in cable BG Required: Components of the force exerted by cable BG.

Q: Start from first principle to show that, for perfect gas the velocity of the sound is given by: C=…

Q: A line of slope 4:10 has been scribed on a cold-rolled yellow-brass plate, 6 in. wide and in. thick.…

Q: Draw the shear force diagram and bending moment diagram . A is roller and B is hinge.

Q: Three forces act on the gusset plate as shown in (Figure 1). Figure F₁ = 650 N 0- 100- 00 45° F₂750…

Q: a) Find the indices for the directions indicated by the two vectors in the shown sketch below 0.5 mm…

A: Hi! Thank you for the question, As per the Honor code, we are allowed to answer one question in case…

Question

Consider the following strain state:
[0.0016 0.0003
[0] = 0.0003 0.0008
0
0
0
0
0.0004]
a. Determine the strain matrix for this strain state if the axes are rotated 30°
counterclockwise around z-axis.
b. Plot Mohr's circle for this strain state.

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step by step

Solved in 5 steps with 2 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, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

A solid spherical ball of magnesium alloy (E = 6.5 × l0-6 psi, v = 0.35) is lowered into the ocean to a depth of 8000 ft. The diameter of the ball is 9.0 in. (a) Determine the decrease ?d in diameter, the decrease, ?V in volume, and the strain energy U of the ball. (b) At what depth will the volume change be equal to 0.0324% of the original volume?
Using the equations of strain in isotropic elasticity, find the stress tensor that cause the following strain state determined from an experiment (material has Young’s modulus of 190 GPa): ?? = 0.001 0.001 0 0.001 −0.002 0.0005 0 0.0005 0shear moduli is 70GPa.
For the given plane strain state, use Mohr's circle to determine the strain state associated with the x' and y' axes rotated to θ indicated in the table: \epsilon_x \epsilon_y \gamma_{xy} θ -500\mu 250\mu 120\mu -15°
A 60º strain rosette, or delta rosette, is composed of three electrical resistance strain gauges arranged as shown in figure 5. Strain gauge A measures the normal strain εa in the x-axis direction. Strain gauges B and C measure the strains εb and εc in the indicated inclined directions. Using Mohr's Circle, obtain the equations for the strains εxx, εyy and γxy associated with the x and y axes.
PROPAGATION OF ERRORS Determine the range of values to which the strain will be calculated.F = 150000 +/- 150 lbfSide length = 1.2 +/- 0.025 inModulus of Elasticity = 25000 +/- 11.5 ksiDetermine the relative error. Is it above or below the accepted 5% relative error?
For some element, the displacement is obtained as u = [1 + 3x +4y +5xy]x10^(-3) mm. The normal strain along x-axis at point (1.2, 0.8) m located inside the element is
A differential element on the bracket is subjected to plane strain that has the following components: , Ex = 300 x 10-6, Ey = 200 x 10-6, Exy = -500 x 10-6. Use the strain-transformation equations and determine the normal strain Ex' in the x' direction on an element oriented at an angle of 60°. Note, a positive angle is counter clockwise.
For a linear elastic isotropic material, prove that a state of plane stress result in a strain field description that satisfies the strain compatibility equations.
Three (3) strain gauges are fixed on the surface of point A of a structure to analyse strainconditions at point A on a structure, in the respective directions as shown in Figure Q2. When the structure is being loaded the readings of the gauges are 200µ, 350µ and -100µ and the directions of x, a and b respectively. a) Find the strains values in the x-y directions and draw the strain element diagram of thatdirections.b) Find the principal strain values and draw the strain element diagram of that directions.c) Find the maximum shear strain value and draw the strain element diagram of thatdirections.d) If the properties of the structure has E = 208 GPa and n = 0.28, find the magnitude of the Principal Stresses and draw its stress element diagram.e) Give your comment without calculation on what happen to maximum principal strain ofthe steel (E = 208 GPa) is changed to copper (E = 110 GPa)?
QB3 TWO DIMENTIONAL STRAINThree strain gauges were arranged in the form of a rectangular rosette and positioned on atest surface. The measured strains were as follows: 1 = 200x 10-6 2 = 100 x 10-6 3 = 50 x 10-6Determinea) the principal strains and the principle stressesb) the direction of the greater principal strain relative to gauge 1 and sketch the Mohrstrain circle. Take the Young Modulus of Elasticity value to be E = 200 GN/m2 andPoisson’s ratio  = 0.28.
A loading causes the wires to elongate into the dashed shape. Explain how to determine the normal strain PAB in wire AB. The displacement Δ and the distances between all lettered points are known.
What strain will be produced by a stress of 80 x 106 N/m2, for a given modulus of elasticity 200GPa. a. 0.0008 b. 0.0004 c. 0.004 d. 0.002