Flanged bolt couplingsIn shaft connection called flanged bolt couplings (see figure), the torque is transmitted by the shearing force P created in he bolts that is assumed to be uniformly distributed. For any number of bolts n, the torque capacity of the coupling is

If a coupling has two concentric rows of bolts, the torque capacity is

where the subscript 1 refer to bolts on the outer circle an subscript 2 refer to bolts on the inner circle. See figure.For rigid flanges, the shear deformations in the bolts are proportional to their radial distances from the shaft axis. The shearing strains are related by

UsingHooke's lawfor shear, G =/, we have or If the bolts on the two circles have the same area, A1= A2, and if the bolts are made of the same material, G1= G2, the relation between P1and P2reduces to

Problem 326A flanged bolt coupling consists of ten 20-mm-diameter bolts spaced evenly around a bolt circle 400 mm in diameter. Determine the torque capacity of the coupling if the allowable shearing stress in the bolts is 40 MPa.Solution 326HideClick here to show or hide the solution

answerProblem 327A flanged bolt coupling consists of ten steel -in.-diameter bolts spaced evenly around a bolt circle 14 in. in diameter. Determine the torque capacity of the coupling if the allowable shearing stress in the bolts is 6000 psi.Solution 327HideClick here to show or hide the solution

answerProblem 328A flanged bolt coupling consists of eight 10-mm-diameter steel bolts on a bolt circle 400 mm in diameter, and six 10-mm-diameter steel bolts on a concentric bolt circle 300 mm in diameter, as shown inFig. 3-7. What torque can be applied without exceeding a shearing stress of 60 MPa in the bolts?Solution 328HideClick here to show or hide the solutionFor one bolt in the outer circle:

For one bolt in the inner circle:

answerProblem 329A torque of 700 lb-ft is to be carried by a flanged bolt coupling that consists of eight -in.-diameter steel bolts on a circle of diameter 12 in. and six -in.-diameter steel bolts on a circle of diameter 9 in. Determine the shearing stress in the bolts.Solution 329HideClick here to show or hide the solution

bolts in the outer circle answer bolts in the inner circle answerProblem 330Determine the number of 10-mm-diameter steel bolts that must be used on the 400-mm bolt circle of the coupling described inProb. 328to increase the torque capacity to 14 kNmSolution 330HideClick here to show or hide the solution

say 12 bolts answerProblem 331A flanged bolt coupling consists of six -in. steel bolts evenly spaced around a bolt circle 12 in. in diameter, and four -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 Gst= 12 106psi and Gal= 4 106psi.Solution 331HideClick here to show or hide the solution

Equation (1)

Equation (2a) Equation (2b)Equations (1) and (2a)

Equations (1) and (2b)

Use T = 77.75 kipin answerProblem 332In a rivet group subjected to a twisting couple T, show that the torsion formula= T/J can be used to find the shearing stressat the center of any rivet. Let J = A2, where A is the area of a rivet at the radial distancefrom the centroid of the rivet group.Solution 332HideClick here to show or hide the solutionThe shearing stress on each rivet is P/A

Where:

(okay!)This shows that= T/J can be used to find the shearing stress at the center of any rivet.Problem 333A plate is fastened to a fixed member by four 20-mm-diameter rivets arranged as shown inFig. P-333. Compute the maximum and minimum shearing stress developed.

Solution 333HideClick here to show or hide the solution

Where:

Maximum shearing stress (= 120 mm):

answerMinimum shearing stress (= 40 mm):

answerProblem 334Six 7/8-in-diameter rivets fasten the plate inFig. P-334to the fixed member. Using the results ofProb. 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?

Solution 334HideClick here to show or hide the solutionWithout the loads P:

Where:

ShowAnother way to solve for J

answer answerNote:Themaximumis carried by the corner rivets (4 rivets in all) while theminimumis carried by the middle two rivets.With the loads P, two cases will arise:1st case (P )

answerNote:Without the load P = 10 kips, the shear stress at corner rivets is 14 ksi (seemaximum), which is way above 8 ksi. Thus, this minimum value of P is necessary to prevent stressing the corner rivets beyond 8 ksi.2nd case (P > 14 kips)

answerProblem 335The plate shown inFig. P-335is 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 ofProb. 332.)

Solution 335HideClick here to show or hide the solutionSolving for location of centroid of rivets:

Where

ShowAnother way to solve for J

The critical rivets are at distance r1from centroid:

answer