The steel (E = 200GPa, v=0.32) vertical post is loaded to the forces as shown in Figure Q1.If the strain gauges a and b are firmly attached at point A give readings of &a=300μ and =175μ. Determine the magnitudes of P, assuming that P = P2. There is no transverse forceoccurs at point 4. Solve the following problems:(a)Sketch the free body diagram at point 4,(b)Find the moment of inertia of the cross section,(c)Find the normal strains at point A, and(d)Find force P₁.P₂AC2.5 cm60 cmCFigure Q110 cm2.5 cmSection c-c5cm

Answered: Image /qna-images/answer/7bfd7ac0-c5eb-49f6-8837-96de6c3582d3.jpg

The steel (E = 200GPa, v=0.32) vertical post is loaded to the forces as shown in Figure Q1. If the strain gauges a and b are firmly attached at point A give readings of & - 300μ and = 175μ. Determine the magnitudes of P, assuming that P = P2. There is no transverse force occurs at point A. Solve the following problems: (a) Sketch the free body diagram at point A, (b) Find the moment of inertia of the cross section, (c) Find the normal strains at point A, and (d) Find force P₁. 60 cm 2.5 cm 10 cm 2.5 cm Section e-c 5 cm

The steel (E = 200GPa, v=0.32) vertical post is loaded to the forces as shown in Figure Q1. If the strain gauges a and b are firmly attached at point A give readings of & - 300μ and = 175μ. Determine the magnitudes of P, assuming that P = P2. There is no transverse force occurs at point A. Solve the following problems: (a) Sketch the free body diagram at point A, (b) Find the moment of inertia of the cross section, (c) Find the normal strains at point A, and (d) Find force P₁. 60 cm 2.5 cm 10 cm 2.5 cm Section e-c 5 cm

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 7.7.20P: A strain rosette (see figure) mounted on the surface of an automobile frame gives the following...

See similar textbooks

Similar questions

600 strain rosette, or delta rosette, consists of three electrical-resistance strain gagesarranged as shown in the figure. Gage A measures the normal strain e, in the directionof the x axis. Gages Band C measure the strains and e in the inclined directions shown.Obtain the equations for the strains 8. e. and y, associated with the x-v axes.
Two fully loaded tractor trailers travel over the bridge putting substantial loading on the structure. As they pass over the middle of the bridge, one of the vertical supporting pillars, which is fixed at its bottom, deforms as shown below. The weight of the trucks causes point T to move to point T'—a distance of 2.5 cm along the x-axis. If the pillar has an original height of 27 m , find the shear strain at point T.
A set of strain rosette with three strain gauges at 120° apart is attached onto a steel structure surface, point P for strain measurement. The state of stress at point P is then determined from the acquired strain measurement. The orientation of strain rosette is shown in Figure. When the structure is being loaded the readings of the gauges are 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 that direction. c) Find the maximum shear strain value and draw the strain element diagram of that 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 =…
The state of strain at a point on a wrench has components ϵx = 120(10-6), ϵy = -180(10-6), γxy= 150(10-6). Use Mohr's circle to solve the problem. Determine the orientations of the element at which the principal strains occur. θp1= θp2=
v) A delta strain gauge is attached to the member at point ‘X’ as highlighted in the figure. During a particular stage of a lifting process, strain readings are recorded as detailed. Determine the magnitude and nature of the principal stresses acting on the member at point ‘X’, the maximum shear stress, and the angle of the principal planes. Young’s Modulus of elasticity = 205 GN/m2Poisson’s ratio = 0.31
The 45° strain rosette is mounted on the surface of a pressure vessel. The following readings are obtained for each gage: Pa = 475(10-6), Pb = 250(10-6), and Pc = -360(10-6). Determine the in-plane principal strains
The state of strain at a point on the bracket has components of Px = 150(10-6), Py = 200(10-6), gxy = -700(10-6). Use the strain transformation equations and determine the equivalent in-plane strains on an element oriented at an angle of u = 60° counterclockwise from the original position. Sketch the deformed element within the x–y plane due to these strains.
A spherical balloon with an outer diameter of 500 mm and thickness 0.3 mm is filled with a gas. Calculate maximum permissible pressure in the balloon if the allowable normal strain at the outer surface of the balloon is O.h Assume E = 4 MPa and v = 0,45.
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?
A block B is pushed against three springs by a force P (see figure). The middle spring has a stillness K1and the outer springs each have stiffness k^. Initially, the springs are unstressed, and the middle spring is longer than the outer springs (the difference in length is denoted s). (a) Draw a force-displacement diagram with the force P as ordinate and the displacement x of the block as abscissa. (b) From the diagram, determine the strain energy U1 of the springs when x = 2s. (c) Explain why the strain energy E, is not equal to P
The state of strain at the point on the bracket has components Px = 350(10-6), Py = -860(10-6),gxy = 250(10-6). Use the strain transformation equations to determine the equivalent in-plane strains on an element oriented at an angle of u = 45° clockwise from the original position. Sketch the deformed element within the x–y plane due to these strains.
A rectangular aluminum plate of uniform thickness has a strain gauge at the center. It is placed in a test rig which can apply a biaxial force system along the edges of the plate as shown below. If the measured strains are +0.0005 and +0.001 in the x and y directions respectively, a) Determine the corresponding stresses set up in the plate and the strain through the thickness, εz. Take E=72 GPa and ν=0.32. b) Construct the Mohr’s circle for the loaded plate. c) State the values of the principal stresses. d) Determine the maximum shearing stresses and the directions of the planes on which they occur.