Relative to the x-, y-, and z-axes, the state of stress at a point in a component is found to be proportional to the matrix 40-3 05 -3 2-3 2 MPa Determine the normal, shear, and resultant stresses that act on a plane whose normal is inclined at 45° to the z-axis and the projection of the normal on the xy- plane makes 50° with the yz-plane (Figure P2.7). Find also the direction of the resultant stress.

Relative to the x-, y-, and z-axes, the state of stress at a point in a component is found to be proportional to the matrix 40-3 05 -3 2-3 2 MPa Determine the normal, shear, and resultant stresses that act on a plane whose normal is inclined at 45° to the z-axis and the projection of the normal on the xy- plane makes 50° with the yz-plane (Figure P2.7). Find also the direction of the resultant stress.

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 7.7.7P: A thin square plate in biaxial stress is subjected to stresses ?? and ??., as shown in part a of the...

See similar textbooks

Related questions

Q: 4 The state of stress on an element at a point is described by the Figure shown. Stress magnitudes:…

A: The objective of the question.(a) Neatly sketch the Mohr's Circle, identifying the locations of the…

Q: A point on a thin plate is subjected to the two stress components as shown in Figure 7. Determine…

A: For the first element on the left, the sign convention is:

Q: The state of stress in a body is uniform and is given by: 0xx = 3MPa ; Txy = 2 MPa; Txz = 4MPa Tyy =…

A: Given state of stress in the matrix formgiven stress Tensor for the above matrix the eigen values…

Q: 3-20* A plate undergoing plane strain is deformed into the dashed shape shown in Fig. P3-20.…

Q: 1. A circular shaft with a keyway can be approximated by the section shown in Fig. r=b r 0 r =…

A: To Find : The value of constant K. Given : The prandtl stress function form is ψ=Kb2-r21-2acosθr The…

Q: A thin plate of uniform thickness is subject to pressure as shown in the figure below O Ľ Under the…

A: Plane stress is defined as the in a single plane , all stress is applied in .two-dimensional state…

Q: A very thick structure is subjected to certain traction boundary conditions on its surface. The…

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

Q: A sheet of material is subjected to a two-dimensional stress system in the x-y plane. At a given…

Q: Q2 a) Define the term of the neutral axis. b) The steel rod having a diameter of 20 mm is subjected…

A: Given data Diameter of shaft d= 20mm Internal moment M = 450N-m To determine a) Stresses created…

Q: Determine the maximum shear stress acting at section a-a of the cantilevered structure, as shown in…

Q: Calcuate Shear and Bending From Point A to Point B and Point A to Point C. Draw a FBD from point A…

A: For the solution refer below images.Find F.B.D. and shear and bending diagram for portion AB and…

Q: Prob. 2.4-5. A tension specimen (diameter = do = 13 mm, gage length = Lo = 50 mm) was used to obtain…

Q: A body is subjected to multiple applied loads. The resultant stress at point location (0, 1, 4)…

Q: Determine the equivalent state of stress if an element is oriented 20° clockwise from the element…

Q: For each of the plane stress states listed below, draw a Mohr's circle diagram properly labeled,…

A: Given Data:a.) sigma,x = - 12 kpsi, sigma,y = 22 kpsi, txy = 12 kpsi cwb.) sigma,x = 30 kpsi,…

Q: P= 2 MPa K= 3 MPa B ñ = РА K P (MPa) 2 + k =i+ √6 √6 √6 C a-)Find the principal normal stresses and…

A: The value of P is 2 MPa. The value of K is 3 MPa. The unit normal vector of the ABC plane is…

Q: A 10 cm diameter solid aluminum post is subjected to a horizontal force of V= 7.1 kN and a…

A: Diameter of the aluminium post (D) = 10 cm = 0.1 mHorizontal force (V) = 7.1 kN = 7100 NConcentrated…

Q: Given the quadragonal element for plane stress. (5,4) (1,3) (0,1) 2 (6,0) (a) Introduce a "parent…

Q: the f Oy =4 MPa %3D Oyr = -2 MPa Oyz = 3 MPa Oyy = -4 MPa Oye = 2 MPa Oyz = -3 MPa

A: Given

Q: A state of plane stress is illustrated in the stress element in Figure 3. (a) (b) 30 MPa Figure 3.…

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

Q: 1) For the state of stress shown in figure, use the Mohr's circle method to determine (a) The…

Q: 3. An axial pull of 35000 N is acting on a bar consisting of three lengths as shown below. If the…

Question

Relative to the x-, y-, and z-axes, the state of stress at a point in a component is found to
be proportional to the matrix
FIGURE P2.7
40-3
05
-3 2-3)
Determine the normal, shear, and resultant stresses that act on a plane whose
normal is inclined at 45° to the z-axis and the projection of the normal on the xy-
plane makes 50° with the yz-plane (Figure P2.7). Find also the direction of the
resultant stress.
40°
45
2 MPa
50⁰

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Given data

VIEW

Step 2: Resultant stress

VIEW

Step 3: Direction of resultant stress

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 12 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

An clement m plane stress from the frame of a racing car is oriented at a known angle 8 (sec figure). On this inclined clement, the normal and shear stresses have the magnitudes and directions shown in the figure. Determine the normal and shear stresses acting on an clement whose sides are parallel to the \y axes, that is, determine crv, tr(_, and t, Show the results on a sketch of an clement oriented at B .
An clement m plane stress from the frame of a racing car is oriented at a known angle 8 (sec figure). On this inclined clement, the normal and shear stresses have the magnitudes and directions shown in the figure. Determine the normal and shear stresses acting on an clement whose sides are parallel to the xy axes, that is, determine crv, tr(_, and t. Show the results on a sketch of an clement oriented at B = 10
-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
-27 A square plate with side dimension of 2 in. is subjected to compressive stress a and tensile stress The stresses on element A oriented at angle ?? x1=45° aresy1= 75 psi. tx1y1= 275 psi. . Find the state of stress on the element lilt is rotated clockwise to align the x3 axis with the horizontal x axis.
An element in plane stress on the fuselage of an airplane (figure part a) is subjected to compressive stresses with a magnitude of 42 MPa in the horizontal direction and tensile stresses with a magnitude of 9.5 MPa in the vertical direction (sec figure part b). Also, shear stresses with a magnitude of 15.5 MPa act in the directions shown. Determine the stresses acting on an element oriented at a clockwise angle of 40g from the horizontal. Show these stresses on a sketch of an element oriented at this angle.
.4-2 An element in uniaxial stress is subjected to tensile stresses sx= 57 MPa. as shown in the figure. Using Mohr’s circle, determine the following. (a) The stresses acting on an clement oriented at an angle 0 = 33° from the x axis (minus means clockwise). (b) The maximum shear stresses and associated normal stresses. Show all results on sketches of properly oriented elements.
At a point on the surface of an elliptical exercise machine, the material is in biaxial stress with t = 1400 psi and trv = —900 psi, as shown in the figure part a. The figure part b shows an inclined plane aa cut through the same point in the material but oriented at an angle ft Determine the value of the angle 6 between zero and 90° such that no normal stress acts on plane aa. Sketch a stress clement having plane aa as one of its sides and show all stresses acting on the clement
During a test of an airplane wing, the strain gage readings from a 45° rosette (see figure) are as follows: gage A, 520 × l0-6; gage B. 360 × l0-6; and gage C,-80 × 10-6. Determine the principal strains and maximum shear strains, and show them on sketches of properly oriented elements.
The polyethylene liner of a settling pond is subjected to stresses ax= 350 psi. a = 112 psi. and = -120 psi, as shown by the plalte-stress element in the figure part a. Determine the normal and shear stresses acting on a seam oriented at an angle 01300 to the element, as shown in the figure part b. Show these stresses on a sketch of an element having its sides parallel and perpendicular to the seam.
Show all steps
The principal tensile stress at a point across two mutually perpendicular planes are 100 N/mm2 and 40 N/mm2. The normal, tangential and resultant stresses on a plane inclined at 20° to the axis of the minor principal stress by analytical method is
Ox+0y , Ox-Oy Plane-stress transformation: 0x, = 2 -cos20 + TxySin20 Txryı 2 sin20 + TxyCos20 2 Ox+0y Ox-Oy Oyi у -cos20 – Txysin20 2 2 The state of plane stress at a point is represented on the element shown in the figure below. Determine the state of stress at this point on another element oriented 28° clockwise from the position shown. Show your work. 25 ksi 12 ksi