A differential element on the bracket is subjected to plane strain that has the following components: ₂ = 160(106), y = 190(106), Yzy = -700(10-6). Use the strain-transformation equations and determine the equivalent in plane strains on an element oriented at an angle of = 60° counterclockwise from the original position. (Figure 1) gure K 1 of 1 Determine the normal strain E Express your answer using three significant figures. ▼ € = Submit ▼ Part B Ey! = IVE ΑΣΦΑ Submit Part C Request Answer Determine the normal strain Express your answer using three significant figures. vec V—| ΑΣΦ ↓↑ vec Request Answer a ? ?

A differential element on the bracket is subjected to plane strain that has the following components: ₂ = 160(106), y = 190(106), Yzy = -700(10-6). Use the strain-transformation equations and determine the equivalent in plane strains on an element oriented at an angle of = 60° counterclockwise from the original position. (Figure 1) gure K 1 of 1 Determine the normal strain E Express your answer using three significant figures. ▼ € = Submit ▼ Part B Ey! = IVE ΑΣΦΑ Submit Part C Request Answer Determine the normal strain Express your answer using three significant figures. vec V—| ΑΣΦ ↓↑ vec Request Answer a ? ?

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 7.7.25P: On the surface of a structural component in a space vehicle, the strains arc monitored by means of...

See similar textbooks

Similar questions

On the surface of a structural component in a space vehicle, the strains arc monitored by means of three strain gages arranged as shown in the figure. During a certain maneuver, the following strains were recorded: e, = 1100 X l0_6, 6h = 200 X lO_6, and e = 200 X 10-6. Determine the principal strains and principal stresses in the material. which is a magnesium alloy for which E = 6000 ksi and v = 0.35. Show the princ ipal strains and principal stresses 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.
The state of strain in a plane element is Ex = -300 x 10-6 , Ey= 450 x 10-6, and Yxy = 275 x 10-6. (a) Use the strain transformation equations to determine the equivalent strain components on an element oriented at an angle of 0 = 30° counterclockwise from the original position. (b) Sketch the deformed element due to these strains within the x-y plane.
Figure Q2 (b) shows a strain rosette that is attached on the surface of a production equipment.The strain readings are εa = -200(10-6), εb = -65(10-6) and εc = 130(10-6).i) Determine the in-plane principal strains and sketch the strain element.ii) Determine the maximum in-plane shear strain and sketch the strain element.iii) What is the angle of orientation (with respect to x-axis) that leads to εx’ = 0?
A set of strain rosette with three strain gauges at 120° apart is attached onto a steelstructure surface, point P for strain measurement. The state of stress at point P is thendetermined from the acquired strain measurement. The orientation of strain rosette isshown in Figure Q2. When the structure is being loaded the readings of the gaugesare 200μ, -100μ and -200μ at the directions of a, b and c respectively. a) Find the strains values in the x-y directions and draw the strain elementdiagram of that direction.b) Find the principal strain values and draw the strain element diagram of thatdirection.c) Find the maximum shear strain value and draw the strain element diagram ofthat direction.d) If the properties of the structure has E = 208 GPa and ν = 0.28, find themagnitude of the Principal Stresses and draw its stress element diagram.e) Give your comment without calculation on what happen to maximumprincipal strain of the steel (E = 208 GPa) is changed to titanium (E = 110GPa)?
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.
The Poisson ratio formula for an auxetic structure given in the figure is given as follows: H = 8 cm L = 4 cm α = 50 ° t = 5 mm The strain value of the structure in the same direction as a result of the pull applied in the X axis from the bottom was measured as 0.26 mm / mm. Under the same loading condition: a) Calculate the strain on the Z axis of the structure. b) In this case, what is the strain type of the structure in the Z axis?
The Poisson ratio formula for an auxetic structure given in the figure is given as follows:H = 8 cm L = 4 cm α = 50 ° t = 5 mmThe strain value of the structure in the same direction as a result of the pull applied in the X axis from the bottom was measured as 0.26 mm / mm. Under the same loading condition:a) Calculate the strain on the Z axis of the structure.b) In this case, what is the strain type of the structure in the Z axis?
A material is subjected to the following strain system,ex=200x10-6, ey=-56x10-6,yxy=230x10-6. Using graphical method, determine A. The principal strains B. The directions of principal strain axes C. The linear strain on an axis inclined at 50o counter clockwise to the direction of ex Given that young's modulus for the material is 207GN/m2 and the poisson's ratio is 0.27, determine the principal stresses
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)?
If the displacements applied to a 3D isotropic material element is defined as functions of (x,y,z), Determine the following: 1- Stress at point (2,3,4). Assume E = 12.08 MPa and v = 0.25 2- Strain at point (1,2,2) 3- If you consider a plane stress condition for the above problems show how will the 2D assumption change the stress at the same point
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.