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METU ME 307 Machine Elements I Fall 2011

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Prepared by: Ferhat Salam

Room: B-183 Phone: 2557

E-mail: [email protected] Date: 14.12.2011

ME 307 MACHINE ELEMENTS I

TUTORIAL 11

DESIGN OF PERMANENT JOINTS

Problem 1:

A riveted structural connection supports a load of 10 kN as shown in the figure

below. Determine the most heavily loaded rivet and find the force on it. Then find

the maximum shear and bearing stress for the rivets if the diameter of rivets is 15

and 10 mm and thickness of the plate is 12 mm. Consider only the shear and bearingstresses. a=100mm, b=120mm

Solution

Diameter of the rivets: 10 and 15Thickness of the plate: t=12 mm

Load F=10kN

In a riveted connection, all the rivets experience the same primary shear stress

,

and the direct shear force supported by ith

rivet is

5 78.5 7.5 176.7 Direct shear force supported by 10 mm-diameter rivet:

10 5 5 2 7.5 1818Direct shear force supported by 15mm-diameter rivets:

10 7.5 5 2 7.5 4091The centroid of the rivet group

Centroid of the rivet:

2 2 81.8 0

F=10 kN

ba

a/2

a/2

y

x

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The torsion of 10 kN force about the centroid of the rivets: 10 418 1382The radial distances between the centroid of the rivets and each rivet:

2 95.9

2 53.2

The secondary shear force carried by each rivet due to torsion is,

Thus, the secondary shear force supported by 10mm-diamater rivet is

2 6041and the secondary shear force supported by 15mm-diamater rivets is

2 7542The primary and the secondary shear force on the 15-mm diameter rivets are larger

than those on the 10mm-rivet, thus 15mm-diameter rivets are the most heavily

loaded rivets. The resultant forces on rivets are,

2 70

4223 2 9732Then the shear stresses become:

53.7

55.1Therefore, the maximum shear stress occurs in 15mm-diameter rivets.

The bearing stresses:

42231210 35.2

97321215 54.1

Therefore, the maximum bearing stress is 54.1 MPa

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Problem 2

3 plates are connected by 6 rivets as shown in the figure. The first row has 3 rivets

each with 15mm diameter, the second row has a single rivet with 20mm diameter

and the third row has 2 rivets each with 18mm diameter. Find the forces and

stresses acting on the rivets, and determine the safety factor of the joint. (For the

rivets 250, 80 and for the plates 200)

Solution

The shear stresses on the shear areas of the rivets will be the same. It can be seen

clearly from the free body diagram of the main plate that for the rivets in rows 1 and

2 there are 2 shear areas (double shear) for each rivet. In the third row there is only

a single shear area for each rivet. There are totally 10 shear areas.

Then, and where 15.Area of the rivets in the first row:

176.72

Area of the rivet in the second row: 314.16Area of the rivets in the third row: 254.47Then the total shear area: 23 2 2198 15 176.722198 1206 15 314.162198 2144

15 254.472198 1737

Analysis of the rivets in the first row:

Shear stress: . 6.826Bearing stress on plate 1: 10.052Bearing stress on the main plate: 16.083Bearing stress on plate 2:

13.402

Analysis of the rivets in the second row:

Shear stress: same as in the first row.

Bearing stress on plate 1: 13.402Bearing stress on the main plate: 21.444Bearing stress on plate 2: 17.87Analysis of the rivets in the third row:

Shear stress: same as in the first row.

Bearing stress on the main plate: 9.650Bearing stress on plate 2: 16.083The safety factor for the shear failure of the rivets: . 11.72

Plate 2

Plate 1

Main Plate

12015kN

15kN

8

6

10

Row 1 Row 2 Row 3

Plate 2

Plate 1

Main Plate

12015kN

15kN

8

6

10

Row 1 Row 2 Row 3

15kN

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The maximum bearing stress is on the main plate (second row). Then, the safety

factor for rivet bearing stress is . 11.66, the safety factor for platebearing stress is . 9.33Analysis of the main plate:

Thickness of the main plate: 10Row 3:

Cross-sectional area:, 120 2 10120 2 18 840From the figure,

15

Then, the tensile stress on the plate at row 3:, , 15000840 17.857

Row 2:

Cross-sectional area:

,

120

10120 20 1000From the figure, 15 2 11526Then, the tensile stress on the plate at row 2:

, , 115261000 11.526

Row 1:

Cross-sectional area:, 120 3 10120 3 15 750From the figure, 15 2 2 9382Then, the tensile stress on the plate at row 1:

, , 9382750 12.509

Analysis of plate 1:

Thickness of plate 1:

8

Row 1:

Cross-sectional area:, 120 3 8120 3 15 600 3 5763 5763Then, the tensile stress on the plate at row 1:

,

, 5763600 9.605

Row 2:

Cross-sectional area:, 120 8120 20 800 3 2144Then, the tensile stress on the plate at row 2:

, , 2144800 2.680

Analysis of plate 2:

Thickness of plate 2: 6Row 1:

Cross-sectional area:, 120 3 6120 3 15 450 3 2 9237 9237Then, the tensile stress on the plate at row 1:

, , 9237450 20.527

15kN

F

Row 3

F

15kN

Row 2

15kN

F

2

Row 1

P1

F

F

P1

P2

F

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Row 2:

Cross-sectional area:, 120 6120 20 600 3 5618Then, the tensile stress on the plate at row 2:

, , 5618600 9.364

Row 3:Cross-sectional area:, 120 2 6120 2 18 504 3 3474Then, the tensile stress on the plate at row

2:

, , 3474504 6.893

The maximum tensile stress occurs in plate 2 at row 1: , 20.527The safety factor for plate tension:

, 20020.527 9.74Therefore, the plate bearing stress is the most critical.

Then, the safety factorofthe joints 9.33

F

P2

P2

F

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