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I. OBJECTIVES

1.1 To become familiar with torsion tests of rods with solid circularcross sections.

1.2 To observe the relation between shear stress (ττττ) and shear strain (γγγγ).

1.3 To experimentally determine the shear modulus (G) of three differentcircular metal rods.

II. INTRODUCTION AND BACKGROUND

The stress distribution in a torsion member such as a transmission shaft isnon-uniform; it varies from zero at the centroidal longitudinal axis to amaximum at the outer fibers.

In many engineering applications, such as torque transmission and insprings, the torsional behavior critically governs the design. In many casesthe maximum torsional stress is the limiting factor in design while inothers, it may be the maximum permissible angle of twist.

III. EQUIPMENT

3.1 TERCO. Twist and Bend Machine, MT210.

3.2 3-8 mm diameter round rods of Steel, Aluminum, and Brass.

3.3 Tools: dial gauge, a micrometer, dead-weights, and othermiscellaneous equipment.

IV. PROCEDURE

4.1 Measure the actual diameters of the three rods, calculate the polarmoment of inertia of each rod and record the results on the datasheet.

4.2 For a torque of 1.75 N-m (17.5 N at a radius of 100 mm), determinethe Factor of Safety with respect to yield for shear stress. The Factorof Safety is the yield stress divided by the calculated stress.Assume the following properties:

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Material Shear Yield Stress(MN/m2)

Structural Steel (A36) 145Aluminum Alloy (2024-T3) 207Brass 165

REF: Stevens, Karl K., Statics and Strength of Materials, 2nd Edition,Prentice Hall.

4.3 Check your results with the Laboratory Instructor before continuingand obtain the rod gage length to be used in the tests.

4.4 Insert the first rod through the torsional fastening components of thebearers and lock rod into the fixed bearer first. Adjust the distancebetween the bearers to match the desired rod gauge length. The rodshould then be fastened into the free bearer with the lever close tothe upper limit pin.

NOTE: 5 to 10 in-lbs of torque on each Allen screw is sufficient tolock each bearer. DO NOT OVER TORQUE THESE SCREWS.Remember, the replacement cost of all damaged components will bededucted from your laboratory fee refund.

4.5 Locate the dial gauge support so that the gauge shaft is aligned withthe small groove at the center of the flat spot on the lever. Carefullylower the gauge until the small hand reads 10. The large hand maybe set to zero by carefully rotating the outer ring of the dial face.

NOTE: The dimension between the groove on the lever and the axisof the rod is 57.3 mm., thus, one revolution of the gauge correspondsto one degree of twist in the rod.

4.6 Torque is applied to the rod by placing the knife edges of the weightpan in the groove near the tip of the lever. The weight of the pan is2.5N. Adding three 5N weights produces the maximum allowabletorque. Before recording the lever deflections as a function of theapplied load, exercise the setup three or four times by applying andremoving the full 17.5N weight. This will allow minute slippages tooccur at the contact surfaces. You will be ready to record data whenthe large hand of the dial gauge returns to the exact location (+ or -1.0 unit) it was at prior to applying the load.

Apply torque to the rod in the increments indicated on the data sheetand record the corresponding angle of twist. Record data during

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both the loading and unloading cycle and note the amount ofhysterisis for each material.

4.7 Repeat steps 4.4 through 4.6 for the second and third rods.

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V. REPORT

5.1 Make a plot of shear stress vs. shear strain for each rod. Each curveshould be approximately linear. Calculate the slope of the beststraight line fit through each set of data points. The slope of theshear stress vs shear strain curve is the shear modules (G). using aconstant for each rod, derived from the following expressions:

ττττ = TR/J shear stress

γ γ γ γ = Rθθθθ/L shear strain

G = ττττ / γ γ γ γ shear modulus

where:

T = torque applied to rodR = radius of rod

J = Polar moment of inertia of rod (J= ππππr4/2)L = gage length of rod

θ θ θ θ = maximum rotation of rod (radians)

A linear regression analysis, using spreadsheet program or a handcalculator, is an acceptable alternative to drawing a best fit curve throughthe data points for each rod. The regression analysis will use a leastsquares fit to find the slope and y-intercept of a line through each set ofdata points. The slope is the shear modules G.

5.2 Also discuss the following:

a. The linearity of the data for each material.

b. The amount of hysterisis observed.

c. Compare the shear moduli obtained by this experiment withvalues given in appendices of two Strength of Materials texts.Some references are:

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Reference:

Stevens, A.R., Statics and Strength of Materials, Prentice Hall,1987.

Higdon, A. Ohlsen, E.H., Stiles, W.B., Weese, J.A., & Riley,W.F., Mechanics of Materials, Wiley, 1985.

Popov, E.P., Engineering Mechanics of Solids, Prentice Hall.1990.

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AM 317 MECHANICS LABORATORY

DATA SHEET #1 FOR EXPERIMENT #4

STUDENT NAME________________________GROUP #_______________

INSTRUCTOR NAME______________________DATE OF EXP.__________

TABLE 1 ROD DIMENSIONS AND MAXIMUM STRESS

SPECIMEN #1 #2 #3MATERIAL

DIAMETER (mm)

POLAR MOMENT OFINERTIA (J) mm4

MAX TORSIONAL STRESS

F.S. SHEAR YIELD

TABLE 2 ROD TWIST vs APPLIED LOAD

SPECIMEN #1 #2 #3 MATERIAL

LOAD0

2.5

7.5

12.5

17.5

12.5

7.5

2.5

0

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TABLE 3COMPARISON OF RESULTS WITHVALUES FROM TWO TEXT BOOKS

SPECIMEN ROD 1 ROD 2 ROD 3MATERIAL

G from Experiment (GN/m2)

G from referece text 1

_________________(GN/m2)

G from reference text 2

_________________(GN/m2)

Maximum % Deviation