Question: A prismatic bar of diameter d0 = 20 mm is being compared with a stepped bar of the same diameter (d1 = 20 mm) that

A prismatic bar of diameter d0 = 20 mm is being compared with a stepped bar of the same diameter (d1 = 20 mm) that is enlarged in the middle region to a diameter d2 = 25 mm (see figure). The radius of the fillets in the stepped bar is 2.0 mm.
(a) Does enlarging the bar in the middle region make it stronger than the prismatic bar? Demonstrate your answer by determining the maximum permissible load P1 for the prismatic bar and the maximum permissible load P2 for the enlarged bar, assuming that the allowable stress for the material is 80 MPa.
(b) What should be the diameter d0 of the prismatic bar if it is to have the same maximum permissible load as does the stepped bar?

Pi P2 di do

Step by Step Solution

★★★★★

3.33 Rating (153 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

d 0 20 mm d 1 20 mm d 2 25 mm Fillet radius R 2 mm Allowable str... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

836-P-M-S (109).docx

120 KBs Word File

Students Have Also Explored These Related Mechanics Questions!

A prismatic bar of length L = 1.8 m and cross-sectional area A = 480 mm2 is loaded by forces P1 = 30 kN and P2 = 60 kN (see figure). The bar is constructed of magnesium alloy having a stress-strain...

The normal stress on plane pq of a prismatic bar in tension (see figure) is found to be 7500 psi. On plane rs, which makes an angle Î² = 30° with plane pq, the stress is found to be...

A prismatic bar in tension has length L = 2.0 m and cross-sectional area A = 249 mm2. The material of the bar has the stressstrain curve shown in the figure. Determine the elongation Î´...

A round brass bar of diameter d1 = 20 mm has upset ends of diameter d2 = 26 mm (see figure). The lengths of the segments of the bar are L1 = 0.3 m and L2 = 0.1 m. Quarter-circular fillets are used at...

Explain in brief the terms: stress concentration and notch sensitivity, and their significance in design of machine element. A round straight bar with a diameter of d, = 20 mm is being compared with...

A tapered bar AB of solid circular cross section is twisted by torques T (see figure). The diameter of the bar varies linearly from dA at the left-hand end to dB at the right-hand end. For what ratio...

Problem 6 a . The vertical post in the figure consists of two solid cylindrical rods. The upper rod is 3 0 c m diameter, while the lower rod is 1 0 c m diameter. Both rods are made of steel with...

PROBLEMS For the following problems, unless noted otherwise, refer to Appendices F and/or G for necessary mechanical prop- erties. Section 4-1 Poisson's Ratio A 1. A 2 in. diameter AISI 1020 steel...

The elongation of a conical bar under its own weight is equal to a ) that of a prismatic bar of same length b ) one half that of a prismatic bar of same length c ) one third that of a prismatic bar...

A prismatic bar AB of length 378mm is held between immovable supports. The temperature of the bar is raised uniformly by an amount 31. Assume the bar is made of steel E=200GPa;a=11.7\\\\times...

Light bulbs are tested for their luminance, with the intensity of brightness desired to be within a certain range. Random samples of five bulbs are chosen from the output, and the luminance is...

P Corporation paid $420,000 for 70% of S Corporation's $10 par common stock on December 31, 2016, when S Corporation's stockholders' equity was made up of $300,000 of Common Stock, $90,000 of Other...

El 1 8 de marzo de 2 0 2 5 , una sociedad de inversi n de Estados Unidos desea invertir USD 2 0 0 , 0 0 0 , 0 0 0 en certificados burs tiles con vencimiento en 9 0 d as del Banco Afirme cuando el...

53. Dr. Susan Benner is an industrial psychologist. She is currently studying stress among executives of Internet companies. She has developed a questionnaire that she believes measures stress. A...

The bar has a cross-sectional area of 400(10 6 ) m 2 . If it is subjected to a uniform axial distributed loading along its length of 9 kN/m, and to two concentrated loads as shown, determine the...

The two members used in the construction of an aircraft fuselage are joined together using a 30° fish-mouth weld. Determine the average normal and average shear stress on the plane of each weld....

The 2-Mg concrete pipe has a center of mass at point G. If it is suspended from cables AB and AC, determine the average normal stress in the cables. The diameters of AB and AC are 12 mm and 10 mm,...

show work please Show HOW YOU Calcuni wc Hum JUU WUJ computations, you will not receive a full score (and will miss the opportunity of partial credits). Note that the points from the bonus question...

The DuPont equation shows the relationships among asset management, debt management, and profitability ratios. Management can use the DuPont equation to analyze ways of improving the firm's...

What is the present value of $3,100 per year, at a discount rate of 9 percent, if the first payment is received 5 years from now and the last payment is received 15 years from now? (Do not round...