The state of stress at a point in a structural member is given by 6x = Ax² + By², dy = Cy² + Dz², 6₂ = Ez² +Fx² Txy = Gy + Hz, Txz = Iz+Jx, Tyz = Kx + Ly where A, B,..., L are constants. Find expressions of the body forces to ensure the equi- librium. Units of the stresses are MPa.

The state of stress at a point in a structural member is given by 6x = Ax² + By², dy = Cy² + Dz², 6₂ = Ez² +Fx² Txy = Gy + Hz, Txz = Iz+Jx, Tyz = Kx + Ly where A, B,..., L are constants. Find expressions of the body forces to ensure the equi- librium. Units of the stresses are MPa.

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 7.3.24P: The stresses acting on a stress element on the arm of a power excavator (see figure) are ax= 52 MPa...

See similar textbooks

Related questions

Q: An inverted U-tube manometer containing oil (SG = 0.80) is located between 2 tanks as shown. The…

A: Given:To find:Determine the water height.

Q: Consider the truss shown in (Eigure 1). Figure 1.5 m 2 m- 3 kN D B -2 m Y Part A Identify the…

A: This question is based on the concept of Truss and identifying zero force members.

Q: Problem 3 ( Learning Outcome #13 Steady liquid jet with area A hits a stationary block and splits…

Q: For the bracket shown with the forces P= 650 N and Q = 0 N and distances a = 2.9 m and b= 1.5 m…

A: Write the given data.

Q: load is applied to a beam as shown. Determine the equivalent force and location of the distributed…

Q: -What power output in kW is required to propel a 100kg vehicle up a 30 degree slope at a constant…

Q: Relative Motion Analysis using Rotating Axes, use the formulas attached to find the solution to the…

A: Dear Students

Q: 6.2kg/s of propanol is cooled with water in a shell and tube heat exchanger. The exchanger has one…

Q: ! Required information A uniform steel rod of cross-sectional area A is attached to rigid supports…

Q: Calculate the grain size number of this micrograph using the six red lines already included on the…

Q: A certain Batch manufacturing plant requires one operator to tend to 2 semiautomatic machines used…

A: to determine:the hourly cost of the systemGiven:the operator is paid per hour.machine 1machine…

Q: A steady-flow Carnot cycle uses water as the working fluid. Water changes from saturated liquid to…

A: Carnot cycle: The Carnot cycle is an ideal thermodynamic cycle proposed by French scientist Nicolas…

Q: PART A: Using the data above, if the Dry and Wet Bulb Temperatures are close to each other, what…

A: Given:TrialOutside conditionsWet Bulb TemperatureDry Bulb Temperature1Mostly Sunny14 C20 C2Partly…

Q: 3. A uniform, 200-kg plate is kept in static equilibrium by two hinges, A and B, and a single cable,…

A: The mass of plate is DCE is a single cable.

Q: A gas refrigeration system utilizing air as the working fluid possesses a pressure ratio of 3. The…

A: Pressure ratio, PR = 3Inlet temperature to the compressor, T1 = 5°C = 278KOutlet temperature from…

Q: Calculate the reaction at the supports for the beams shown below A -3 m- 10 KN 10 kN/m -3 m- B

A: Calculate the reaction at the supports for the beams shown below,

Q: 3. A uniform, 200-kg plate is kept in static equilibrium by two hinges, A and B, and a single cable,…

A: The mass of plate is DCE is a single cable.

Q: The principal stresses at a point P in a solid are 70 MPa, -70 MPa and 0. The yield stress of the…

A: In solid mechanics, when a material is subjected to external forces, it experiences internal…

Q: Question: A 2-station flow system operates with m = 1 each. Jobs arrive every 5 minutes on average…

A: To determine:(a) the wait average time for the second station.(b) throughput and cycle…

Q: 2- A 15 m long, 75 mm diameter riser tube receives saturated water at 160 bar and at a velocity of…

Q: Technician A says that coolant hoses should be squeezed to check for hardening or softening.…

A: Solidly squeeze both the upper radiator and radiator hoses. They ought to feel firm, solid, and…

Q: Problem 1 1: Learning Outcome #2 A uniform body A having a width b into the paper is in static…

Q: 3. The pendulum, which consists of the 4-ft light rigid bar and the 14-lb cylinder A, is released…

Q: Calculate μ, Cv, K, and Pr for oxygen at 100, 300, and 1000 K, and 1 atm. Compare your calculated…

Q: Face Plate Items 2 and 5 are to be prepared as subassemblies. If item 2 is placed horizontally on…

A: To establish and maintain a dimension from the bottom surface of item 5 to the lower end of item 2,…

Q: What is the recommended feed for the turning operation above?

Q: A gas mixture consists of 1 kg of N2 and 1.5kg of He. Determine: Mass fractions (m) of: 1. N2: 2.…

A: Given Mass of N2= 1kgMass of He= 1.5 kg

Q: QUESTION 1 Consider Figures 1 and 2 to answer the following questions. Q(in) T Wnet(out) Work Figure…

A: To determine:Explain if the situations in figure 1 and figure 2 are possible according to second…

Q: y y=mx y=kx² h x

Q: A winch, located at M, pulls a box up an incline with a cable. The distance from the box to the…

A: Given:To find:Speed of the box when it reaches the winch M.

Q: Pressurized eyes Our eyes need a certain amount of internal pressure in order to work properly, with…

A: density of mercury = 13545.848 kg/m3stagnation pressure head = 10.25 mm of Hg

Q: Consider a 210-MW steam power plant that operates on a simple ideal Rankine cycle. Steam enters the…

A: Given:To find:The mass flow rate of the steam.

Q: Link BD consists of a single bar 1 in. wide and 12 in. thick. Knowing that each pin has a 38-in.…

A: The provided system is shown below.To determine:

Q: d b

A: To find the deflection at point B by Castigliano's theoremthe length a = 20 in the length b = 7…

Q: A large room contains moist air at 35 deg C, 104 kPa. The partial pressure of water vapor is 1.8…

A: Given:Find:The relative humidity, Humidity ratio, The dew point temperature, The mass of dry air in…

Q: 4-29. Determine the coordinate direction angles a, ß, y of F, which is applied to the end A of the…

A: GIVENdetermine-coordinate direction angle alpha, beta, gamma

Q: 4. Use the method of joints to determine the forces in members AD, AB, AC, BC, and CD of the simple…

A: Following truss system is given. We need to determine the forces in the member using the method of…

Q: Calculate the total vapor pressure above a solution containing 3 mol of X and 4 mol of Y. (For X, P°…

Q: Suppose you have conducted 25 measurements of a random variable (Temperature) and obtained the…

A: Sample Mean Temperature:The sample mean temperature is the average of all the temperature…

Q: Determine the components of all the forces on member ABCD when 0-90 degrees. Is member DE in tension…

A: Write the given data.

Q: A thin copper rod, 6 m in length, is heated at its midpoint and the ends are held at a constant…

Q: velocity with which the golf ball leaves th second

A: To determine the velocitywhere, mass of the golf club , mass of the ball, striking force time…

Q: What is the length and wall thickness of the vertical bear

A: For figure 2, drawing and the type of symbols present

Q: A fluid flows between two parallel plates held at temperature zero. At the inlet, fluid temperature…

A: Given:To find:Solve the eigenvalue problem.

Q: Select the correct Shear and Bending Moment Diagrams for the loading and supports shown. Note:…

Q: Cable BA is attached to rod BC. Find the tension and shear in the rod that are caused by the cable.…

A: Given:To find:(a) Tension in the rod.(b) Shear in the rod.

Q: R4-5. Replace the force and couple system by an P. equivalent force and couple moment at point

A: Given:To find:Couple moment at P.

Q: Steam at 1.4 MPa and 300°C enters the shell side of a shell and tube heat exchanger. It leaves as…

Q: 1- A boiler plant comprises a boiler, superheater, economizer and air preheater. The feedwater…

Q: Link 2 is isolated from a kinematic diagram and shown in figure P6.13, angles γ = 50°and β= 60°. The…

A: Given data:VA = - 40 ft/s (since rotating clockwise)rOA = 8 in = 8/12 = 0.6667 ftAngular velocity of…

Question

The state of stress at a point in a structural member is given by
=
0x = Ax² + By², ay = Cy² + Dz², oz Ez² + Fx²
Txy = Gy + Hz, Txz = Iz + Jx, Tyz = Kx + Ly
where A, B,..., L are constants. Find expressions of the body forces to ensure the equi-
librium. Units of the stresses are MPa.

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: Determine the given data

VIEW

Step 2: Derive the expression

VIEW

Solution

VIEW

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

Similar questions

Two sections of steel drill pipe, joined by bolted flange plates at Ä are being tested to assess the adequacy of both the pipes. In the test, the pipe structure is fixed at A, a concentrated torque of 500 kN - m is applied at x = 0.5 m, and uniformly distributed torque intensity t1= 250 kN m/m is applied on pipe BC. Both pipes have the same inner diameter = 200 mm. Pipe AB has thickness tAB=15 mm, while pipe BC has thickness TBC= 12 mm. Find the maximum shear stress and maximum twist of the pipe and their locations along the pipe. Assume G = 75 GPa.
Solve the preceding problem if F =90 mm, F = 42 kN, and t = 40°MPa
The stresses acting on a stress element on the arm of a power excavator (see figure) are ax= 52 MPa and txy= 33 MPa (sec figure). What is the allowable range of values for the stress if the maximum shear stress is limited to = 37 MPa?
The strength-to-weight ratio of a structural material is defined as its load-carrying capacity divided by its weight. For materials in tension, use a characteristic tensile stress obtained from a stress-strain curve as a measure of strength. For instance, either the yield stress or the ultimate stress could be used, depending upon the particular application. Thus, the strength-to-weight ratio RS/Wfor a material in tension is defined as Rs/w= in which a is the characteristic stress and 7 is the weight density. Note that the ratio has units of length. Using the ultimate stress Uas the strength parameter, calculate the strength-to-weight ratio (in units of meters) for each of the following materials: aluminum alloy 606I-T6, Douglas fir (in bending}, nylon. structural steel ASTM-A57.2, and a titanium alloy. Obtain the material properties from Tables [-1 and 1-3 of Appendix I. When a range of values is given in a table, use the average value.
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.
A wine of length L = 4 ft and diameter d = 0.125 in. is stretched by tensile forces P = 600 lb. The wire is made of a copper alloy having a stress-strain relationship that may be described mathematically by =18,0001+30000.03(=ksi) in which is nondimensional and has units of kips per square inch (ksi). (a) Construct a stress-strain diagram for the material. (bj Determine the elongation, of the wire due to the Forces P. (c) IF the forces are removed, what is the permanent set of the bar? (d) If the forces are applied again, what is the proportional limit?
-26 A rectangular plate of dimensions 125 mm × 75 mm is subjected to tensile stress sy= 67 kPa and compressive stress a. If it is known that the normal stress along the diagonal t—t is ??t= -6.57 kPa, find stress ??y on element A. a
A specimen used in a coupon test is shown in the figure. The stresses on element A are known to be sy= -1500 psi. Use Mohr’s circle to: (a) Find the stresses acting on the element oriented at an angle ?? = -35°. (b) Find maximum normal and shear stresses and show them on sketches of properly oriented elements.
In a volume element with dimensions dx, dy, dz the negatíve y-face has a 2 MPa stress in the positivex-direction, a 3 MPa stress in the negative z-direction, and a 4 MPa stress in the negatíve y-direction. Which of the following describes the stresses per elasticity convention? Oyy = 4 MPa Oyr = -2 MPa 3 MPa A MPa
At point O of a part subjected to plane stress made of steel material (E = 210 GPa and %3D ww v= 0.3) The tensile components are given below. 240 %3D - 30 MPa *yz yz a) The principal stress components (01, 02 and o3) and their angles with respect to the x-y-z axes of the planes where they are formed calculate b) Calculate the maximum shear stress (tmax) and the angles of the plane in which it is formed with respect to the x-y-z axes. c) Drawthe 2-D and 3-D Mohr circles for the stress components. d) At point O in a section plane passing through point O and having an angle of 30° counterclockwise with the +x-axis Calculate the resulting stress components. e) Calculate the strain components (Exx, EW, Ezz, YXV, YXz and Yyz) and draw the 2-D and 3-D Mohr circles for the strain components.
F2 Q1) Axial displacement of point C in the system shown on the left is 0.01 cm. Find the maximum elongation of the bar and the maximum normal stress. A F1 A. GIVEN: F2 = 100 kN, (1 = 240 cm, €2= 160 cm, bi = 5 cm, bz=10 cm, h=5 cm, E=2.107 N/em², a=20 cm Note: neglect stress concentration. h bị b2 A-A section
A planar stress element has the stress state: 0₂ = 16 MPa, 0 = 44 MPa and ty = 39 MPa. Through what angle would you rotate the element to find the orientation that has zero shear stress? Units for your solution will be degrees. Ţ: Txy Tor 6 + 8