Explanation Write the expression for the moment of inertia of the shaft. I = π d 4 64 (I) Here, the diameter of the shaft is d and the moment of inertia is I . Draw the free body diagram of the beam. Figure (1) Write the expression for the deflection equation for section B C for beam 6 using Table A-9. y A = F B a 1 ( l − x ) 6 E I l ( x 2 + a 1 2 − 2 l x ) (II) Here, the deflection of the beam is y A , the net force at point B is F B , the location of point B from left end is a 1 , the total length of the beam is l , the Young modulus of the material is E and the moment of inertia of the beam is I . Write the expression for the slope at point C . ( θ B C ) C = d d x [ F B a 1 ( l − x ) 6 E I l ( x 2 + a 1 2 − 2 l x ) ] x = l = [ F B a 1 6 E I l ( 6 l x − 3 x 2 − a 1 2 − 2 l 2 ) ] x = l = F B a 1 6 E I l ( l 2 − a 1 2 ) (III) Here, the slope of the beam at point C is ( θ B C ) C and the force on the beam at point B is F B . Write the expression for the deflection for beam 10 using Table A-9. y ′ A = − F A a 2 2 3 E I ( l + a 2 ) (IV) Here, the location of point C from right end is a 2 . Write the expression for the deflection at A using superposition principle. y A = [ ( θ B C ) C a 2 ] b e a m 6 + [ y ′ A ] b e a m 10 (V) Substitute F B a 1 6 E I l ( l 2 − a 1 2 ) for ( θ B C ) C and − F A a 2 2 3 E I ( l + a 2 ) for y ′ A in Equation (V). y A = [ F B a 1 6 E I l ( l 2 − a 1 2 ) a 2 ] + { − F A a 2 2 3 E I ( l + a 2 ) } = [ F B a 1 6 E I l ( l 2 − a 1 2 ) a 2 ] − { F A a 2 2 3 E I ( l + a 2 ) } (VI) Write the expression for the slope at A relative to the z-axis. ( θ A ) z = F B a 1 6 E I l ( l 2 − a 1 2 ) + d d x [ F A ( x − l ) 6 E I ( ( x − l ) 2 − a 2 ( 3 x − l ) ) ] x = l + a 2 = F B a 1 6 E I l ( l 2 − a 1 2 ) − F A 6 E I ( 3 a 2 2 + 2 l a 2 ) (VII) Here, the slope at A relative to the z-axis is ( θ A ) z . Conclusion: Substitute 30 mm for d in Equation (I). I = π ( 30 mm ) 4 64 = 2544690.049 64 mm 4 = 39.76 × 10 3 mm 4 Substitute − 3312 N for F B , 230 mm for a 1 , 510 mm for l , 207 × 10 3 MPa for E , 39

Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)

10th Edition

ISBN: 9780073398204

Author: Richard G Budynas, Keith J Nisbett

Publisher: McGraw-Hill Education

See similar textbooks

Concept explainers

Torsion

In mechanical engineering, torque, torsion, and twisting moment are three of the most important concepts which have different meanings. Torque is the consequence of a moment of a force that produces an angular acceleration in a body or induces rotational…

Videos

Question

Chapter 4, Problem 24P

To determine

The deflection of the shaft at point A.

The slope of the shaft at point A.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4, Problem 23P

Chapter 4, Problem 25P

Students have asked these similar questions

- | العنوان In non-continuous dieless drawing process for copper tube as shown in Fig. (1), take the following data: Do-20mm, to=3mm, D=12mm, ti/to=0.6 and v.-15mm/s. Calculate: (1) area reduction RA, (2) drawing velocity v. Knowing that: ti: final thickness V. Fig. (1) ofthre

A direct extrusion operation produces the cross section shown in Fig. (2) from an aluminum billet whose diameter 160 mm and length - 700 mm. Determine the length of the extruded section at the end of the operation if the die angle -14° 60 X Fig. (2) Note: all dimensions in mm.

For hot rolling processes, show that the average strain rate can be given as: = (1+5)√RdIn(+1)

Chapter 4 Solutions

Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)

Ch. 4 - The figure shows a torsion bar OA fixed at O,...Ch. 4 - For Prob. 41, if the simple support at point A...Ch. 4 - A torsion-bar spring consists of a prismatic bar,...Ch. 4 - An engineer is forced by geometric considerations...Ch. 4 - A bar in tension has a circular cross section and...Ch. 4 - Prob. 6P Ch. 4 - Prob. 7P Ch. 4 - Derive the equations given for beam 2 in Table A9...Ch. 4 - Derive the equations given for beam 5 in Table A9...Ch. 4 - The figure shows a cantilever consisting of steel...

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.

The deflection of the shaft at point A . The slope of the shaft at point A .

Solution Summary: The author explains the deflection of the shaft at point A, the moment of inertia, and the free body diagram for beam 6.

Concept explainers

Videos

The deflection of the shaft at point A.

The slope of the shaft at point A.

Want to see the full answer?

Chapter 4 Solutions

The deflection of the shaft at point A . The slope of the shaft at point A .

Solution Summary: The author explains the deflection of the shaft at point A, the moment of inertia, and the free body diagram for beam 6.

Concept explainers

Videos

The deflection of the shaft at point A. The slope of the shaft at point A.

Want to see the full answer?

Chapter 4 Solutions

The deflection of the shaft at point A.

The slope of the shaft at point A.