Problem C-2 [Average Normal and Average Shear Stresses]A structure is under an external loading of P achievingequilibrium, as shown in the figure. Member AC has atransverse cross-section of 0.2×0.2 in.². The cross-sectiona-a is along the vertical direction. Top view of pin B isshown to the bottom of the figure. The diameter of the pinat B is 0.1 in.-0.2 in.4 in.2 in.(1) Determine the average normal and average shearstresses developed in the member AC at cross-section a-a.ВCD(2) Determine the shear stress developed in pin B.|- 3 in.H+ 2 in.P= 6 kipsBNote: the problem has two parts: (1) and (2). Solutions toboth must be correct to validate this problemUploadChoose a File

To normal and average stress at section aa

Problem C-2 [Average Normal and Average Shear Stresses] A structure is under an external loading of P achieving equilibrium, as shown in the figure. Member AC has a transverse cross-section of 0.2x0.2 in.?. The cross-section a-a is along the vertical direction. Top view of pin B is shown to the bottom of the figure. The diameter of the pin at B is 0.1 in. A 0.2 in. 4 in. 2 in. (1) Determine the average normal and average shear stresses developed in the member AC at cross- section a-a. B C D (2) Determine the shear stress developed in pin B. 3 in. 2 in. P 6 kips B Note: the problem has two parts: (1) and (2). Solutions to both must be correct to validate this problem Upload Choose a File

Problem C-2 [Average Normal and Average Shear Stresses] A structure is under an external loading of P achieving equilibrium, as shown in the figure. Member AC has a transverse cross-section of 0.2x0.2 in.?. The cross-section a-a is along the vertical direction. Top view of pin B is shown to the bottom of the figure. The diameter of the pin at B is 0.1 in. A 0.2 in. 4 in. 2 in. (1) Determine the average normal and average shear stresses developed in the member AC at cross- section a-a. B C D (2) Determine the shear stress developed in pin B. 3 in. 2 in. P 6 kips B Note: the problem has two parts: (1) and (2). Solutions to both must be correct to validate this problem Upload Choose a File

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 7.2.8P: An element in plane stress on the fuselage of an airplane (figure part a) is subjected to...

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Plastic bar of diameter d = 32 mm is compressed in a testing device by a Force P = 190 N that is applied as shown in the figure. (a) Determine the normal and shear stresses acting: on all faces of stress elements oriented at (1 ) an angle 8 = 00, (2) an angle ?? = 22.5s, and (3) an angle ?? = 45°. In each case, show the stresses on a sketch of a properly oriented element. What are smaxtmax (b) Find smax and tmax in the plastic bar if a re-cantering spring of stiffness k is inserted into the testing device, as shown in the figure. The spring stillness is 1/6 of the axial stiffness of the plastic bar.
An element on the gusset plate in Problem 7.2-23 in uniuxial stress is subjected to compressive stresses of magnitude 6750 psi. as shown in the figure. Using Mohr’s circle, determine the following. (a) The stresses acting on an element oriented at a slope of 1 on 2 (see figure). (b) The maximum shear stresses and associated normal stresses. Show all results on sketches of properly oriented elements. s
A bar AB of length L and weight density y hangs vertically under its awn weight (see figure). The stress-strain relation forth? Material is given by the Romberg-Osgood equation [Eq. (2-71)]: Derive the formula For the elongation of the bar.
Solve the preceding problem for a plate of dimensions 100 mm × 250 mm subjected to a compressive stress of 2.5 MPa in the long direction and a tensile stress of 12.0 MPa in the short direction (see figure).
A circle of a diameter d = 200 mm is etched on a brass plate (see figure). The plate has dimensions of 400 x 400 x 20 mm. Forces are applied to the plate, producing uniformly distributed normal stressescr^ =59 MPaander^ = —17 MPa. Calculate the following quantities: (a) the change in length Aac of diameter at: (b) the change in length Abd of diameter bd; (c) the change At in the thickness of the plate; (d) the change AV in the volume of the plate; (e) the strain energy U stored in the plate; (f) the maximum permissible thickness of the plate when strain energy £/must be at least 784 J; and (g) the maximum permissible value of normal stress axwhen the change in volume of the plate cannot exceed 0.015% of the original volume. (Assume E = 100 GPa and v = 0.34
Solve the preceding problem for sx= 11 MPa and ??y= -20 MPa (see figure).
A double-decker bicycle rack made up of square steel tubing is fixed at A (figure a). The weight of a bicycle is represented as a point load applied at B on a plane frame model of the rack (figure b). (a)Find the state of plane stress on an element C located on the surface at the left side of the vertical tube at the base A. Include the weight of the framing system. (Assume weight density y = 77 kN/m .) (b) Find the maximum shear stresses on an element at C and show them on a sketch of a properly oriented element. Assume that element C is a sufficient distance from support A so that stress concentration effects are negligible
Acting on the sides of a stress element cut from a bar in uniaxial stress are tensile stresses of 10,000 psi and 5000 psi, as shown in the figure. (a) Determine the angle 0 and the shear stress T and show all stresses on a sketch of the element. (b) Determine the maximum normal stress amaxand the maximum shear stress Tmax in the material.
A sign is supported by a pipe (see figure) having an outer diameter 110 mm and inner diameter 90 mm. The dimensions of the sign are 2.0 m X 1.0 m, and its lower edge is 3.0 m above the base. Note that the center of gravity of the sign is 1.05 m from the axis of the pipe. The wind pressure against the sign is 1.5 kPa. Determine the maximum in-plane shear stresses due to the wind pressure on the sign at points /I, B, and C, located on the outer surface at the base of the pipe.
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.
The state of stress on an element of material is shown in the figure. Calculate the unit volume change of the element if the stresses x and y. are -20 ksi and 10 ksi, respectively. Assume E = 10,600 ksi and v = 0.33.
A simply supported beam is subjected to point load P at mid-span. The normal stress on an element at mid-span is known to be ??x= 1.5 ksi. Determine the element stresses lilt is rotated through angle ? = 450• Show these stresses on a sketch of an element oriented at that angle.