Explanation The following diagram shows the dimensions of the section A − A of the crane hook. Figure (1) Write the radius of the centroidal axis. r c = r i + h 2 (I) Here, the radius of inner fiber is r i and the length of the section A − A is h . Write the area of the section A − A of the crane hook. A = ( r o − r i − d ) ( b ) (II) Here, the radius of the outer fiber is r o , the diameter of the hole in the center of the critical section is d . Write the radius of the neutral axis of the crane hook as shown in the Figure (1). r n = A ∫ d A r = A ∫ r i r o ( b d r r ) = A 0.75 ( ln 3.625 2 ) + 0.75 ( ln 6 4.375 ) (III) Write the distance from the centroidal axis to neutral axis. e = r c − r n (IV) Write the distance from the neutral axis to inner fiber of the lever. c i = r n − r i (V) Write the distance from the neutral axis to outer fiber of the lever. c o = r o − r n (VI) Write the bending moment on the eyebolt. M = F × r c (VII) Here, the load applied on the crane hook is F . Calculate the stess at the inner surface of the crane hook at section A − A . σ i = F A + M c i A e r i (VIII) Calculate the stess at the outer surface the crane hook at section A − A . σ o = F A − M c o A e r o (IX) Conclusion: Substitute 2 in for r i and 4 in for h in Equation (I). r c = 2 in + 4 in 2 = 4 in Substitute 6 in for r o , 2 in for r i , 0.75 in for d and 0.75 in for b in Equation (II). A = ( 6 in − 2 in − 0.75 in ) ( 0.75 in ) = ( 3.25 in ) ( 0.75 in ) = 2.4375 in 2 Substitute 2.4375 in 2 for A in Equation (III). r n = 2.4375 in 2 0.68292 in = 3.56923 in Substitute 4 in for r c and 3.56923 in for r n in Equation (IV). e = 4 in − 3.56923 in ≈ 0.43077 in Substitute 2 in for r i and 3.56923 in for r n in Equation (V). c i = 3.56923 in − 2 in = 1.56923 in Substitute 6 in for r o and 3.56923 in for r n in Equation (VI)

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

Videos

Question

Chapter 3, Problem 130P

To determine

The stess at the inner surface of the crane hook at the critical section.

The stess at the outer surface of the crane hook at the critical section.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 3, Problem 129P

Chapter 3, Problem 131P

Students have asked these similar questions

5: The structure shown was designed to support a30-kN load. It consists of a boom AB with a 30 x 50-mmrectangular cross section and a rod BC with a 20-mm-diametercircular cross section. The boom and the rod are connected bya pin at B and are supported by pins and brackets at A and C,respectively.1. Calculate the normal stress in boom AB and rod BC,indicate if in tension or compression.2. Calculate the shear stress of pins at A, B and C.3. Calculate the bearing stresses at A in member AB,and in the bracket.

4: The boom AC is a 4-in. square steel tube with a wallthickness of 0.25 in. The boom is supported by the 0.5-in.-diameter pinat A, and the 0.375-in.-diameter cable BC. The working stresses are 25ksi for the cable, 18 ksi for the boom, and 13.6 ksi for shear in the pin.Neglect the weight of the boom.1. Calculate the maximum value of P (kips) based on boom compression and the maximum value of P (kips) based on tension in the cable.2. Calculate the maximum value of P (kips) based on shear in pin.

3: A steel strut S serving as a brace for a boat hoist transmits a compressive force P = 54 kN to the deck of a pier as shown in Fig. STR-08. The strut has a hollow square cross section with a wall thickness t =12mm and the angle θ between the strut and the horizontal is 40°. A pin through the strut transmits the compressive force from the strut to two gusset plates G that are welded to the base plate B. Four anchor bolts fasten the base plate to the deck. The diameter of the pin is 20mm, the thickness of the gusset plates is 16mm, the thickness of the base plate is 8mm, and the diameter of the anchor bolts is 12mm. Disregard any friction between the base plate and the deck.1. Determine the shear stress in the pin, in MPa and the shear stress in the anchor bolts, in MPa.2. Determine the bearing stress in the strut holes, in MPa.

Chapter 3 Solutions

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

Ch. 3 - 31 to 34 Sketch a free-body diagram of each...Ch. 3 - 31 to 34 Sketch a free-body diagram of each...Ch. 3 - Sketch a free-body diagram of each element in the...Ch. 3 - 3-1 to 3-4 Sketch a free-body diagram of each...Ch. 3 - 35 to 38 For the beam shown, find the reactions at...Ch. 3 - 35 to 38 For the beam shown, find the reactions at...Ch. 3 - 35 to 38 For the beam shown, find the reactions at...Ch. 3 - For the beam shown, find the reactions at the...Ch. 3 - For the beam shown, find the reactions at the...Ch. 3 - Repeat Prob. 36 using singularity functions...

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 stess at the inner surface of the crane hook at the critical section. The stess at the outer surface of the crane hook at the critical section.

Solution Summary: The author compares the stess at the inner and outer surfaces of the crane hooks.

Videos

The stess at the inner surface of the crane hook at the critical section. The stess at the outer surface of the crane hook at the critical section.

Want to see the full answer?

Chapter 3 Solutions

The stess at the inner surface of the crane hook at the critical section.

The stess at the outer surface of the crane hook at the critical section.