# Shearing Stress

## Solution to Problem 338 | Torsion of thin-walled tube

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## Solution to Problem 335 | Flanged bolt couplings

**Problem 335**

The plate shown in Fig. P-335 is fastened to the fixed member by five 10-mm-diameter rivets. Compute the value of the loads P so that the average shearing stress in any rivet does not exceed 70 MPa. (Hint: Use the results of Prob. 332.)

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## Solution to Problem 334 | Flanged bolt couplings

**Problem 334**

Six 7/8-in-diameter rivets fasten the plate in Fig. P-334 to the fixed member. Using the results of Prob. 332, determine the average shearing stress caused in each rivet by the 14 kip loads. What additional loads P can be applied before the shearing stress in any rivet exceeds 8000 psi?

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## Solution to Problem 333 | Flanged bolt couplings

**Problem 333**

A plate is fastened to a fixed member by four 20-mm-diameter rivets arranged as shown in Fig. P-333. Compute the maximum and minimum shearing stress developed.

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## Solution to Problem 332 | Flanged bolt couplings

**Problem 332**

In a rivet group subjected to a twisting couple T, show that the torsion formula τ = Tρ/J can be used to find the shearing stress τ at the center of any rivet. Let J = ΣAρ^{2}, where A is the area of a rivet at the radial distance ρ from the centroid of the rivet group.

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## Solution to Problem 331 | Flanged bolt couplings

**Problem 331**

A flanged bolt coupling consists of six ½-in. steel bolts evenly spaced around a bolt circle 12 in. in diameter, and four ¾-in. aluminum bolts on a concentric bolt circle 8 in. in diameter. What torque can be applied without exceeding 9000 psi in the steel or 6000 psi in the aluminum? Assume G_{st} = 12 × 10^{6} psi and G_{al} = 4 × 10^{6} psi.

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## Solution to Problem 324 Torsion

**Problem 324**

The compound shaft shown in Fig. P-324 is attached to rigid supports. For the bronze segment AB, the maximum shearing stress is limited to 8000 psi and for the steel segment BC, it is limited to 12 ksi. Determine the diameters of each segment so that each material will be simultaneously stressed to its permissible limit when a torque T = 12 kip·ft is applied. For bronze, G = 6 × 10^{6} psi and for steel, G = 12 × 10^{6} psi.

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## Solution to Problem 323 Torsion

**Problem 323**

A shaft composed of segments AC, CD, and DB is fastened to rigid supports and loaded as shown in Fig. P-323. For bronze, G = 35 GPa; aluminum, G = 28 GPa, and for steel, G = 83 GPa. Determine the maximum shearing stress developed in each segment.

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## Solution to Problem 322 Torsion

**Problem 322**

A solid steel shaft is loaded as shown in Fig. P-322. Using G = 83 GPa, determine the required diameter of the shaft if the shearing stress is limited to 60 MPa and the angle of rotation at the free end is not to exceed 4 deg.

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## Solution to Problem 320 Torsion

**Problem 320**

In Prob. 319, determine the ratio of lengths b/a so that each material will be stressed to its permissible limit. What torque T is required?

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