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THE UNIVERSITY OF CALGARY SCHULICH SCHOOL OF ENGINEERING

ENGG 317: MECHANICS OF MATERIALS

Lab 2: Torsion & Bending

Name or ID number: Lab Section #: Date:

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PART A - TORSION Introduction

In the design of machinery and structures, the problem of transmitting a torque is frequently encountered. The simplest device for accomplishing this is a circular shaft such as that connecting a motor with a pump for example. In steel and reinforced concrete structures torsion rarely occurs alone but is present in combination with transverse shear and bending.

Regardless of the application, knowledge of the behaviour of the material under the influence of torsional forces is necessary for designing structural units subjected to torsion.

As in the last experiment on tension testing, the performance of a relatively ductile material (mild steel) is compared with that of a relatively brittle material (cast iron). Objective

To demonstrate the behaviour of brittle and ductile materials in torsion. Apparatus

Torsion Testing Machine with Troptometer.

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Procedure

A circular bar is gripped in a torsion testing machine, and a twisting moment is applied in increments. Two specimens will be analysed. The first sample will be a cast iron specimen and the second sample with be mild steel.

Please record at every increment the applied torque and the angular deformation in the table below. Cast Iron diameter (mm)= Mild Steel diameter(mm)=

Torque (Nm)

Dial

Gauge (mm)

(mm)

(Radians)

Torque (Nm)

Dial

Gauge (mm)

(mm)

(Radians)

0

0

50

50

100

100

150

150

200

200

250

250

300

300

Failure

Nm Failure

Nm

# of Rotations

Where, (mm) = deformation

Calculate by subtracting each dial gauge reading from the initial dial gauge reading at zero torque.

(radians)= Angle of Twist = deformation measured () arm length

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Summary of Objectives and Methods:

Analysis

The modulus of rigidity, G, is determined using the formula relating torque, angle of twist and specimen geometry,

G = TL/J. where: G = Modulus of rigidity, MPa

J = Polar moment of inertia, mm4

(J = d4 for circular sections) 32 L = Gauge length, mm T = Torque, Nmm

= Angle of twist, radians = deflection measured arm length

1) Plot TL/J versus angle of twist (radians) for each specimen and comment on the differences between the curves for mild steel and cast iron.

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2) From the slope of the graph report the value for G, in GPa, for each specimen.

3) Comment on the differences in the mode of failure between the two materials.

4) Which would you regard as most suitable for the shaft connecting the steering wheel of an automobile to the steering box system and why?

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PART B - BENDING Objective

To determine the load-deflection relationship for a steel beam and compare the results with stresses and strains calculated using the elastic bending formula.

To demonstrate beam behaviour at strains above the elastic limit which produce yielding of the steel. Introduction

In the design of machinery and structures, the problem of bending and the stresses and deflections produced by it must be addressed. Depending on the nature of the application and the properties of the material, bending stress or deflection or both must remain below specified maxima. Consequently, the designer requires knowledge of material bending behaviour to satisfactorily complete the required design. Apparatus

1. A 25.4 x 6 mm mild steel beam subjected to pure bending over the central section in a beam testing frame.

2. A displacement transducer placed at the centre of the beam for deflection

measurements.

3. Two electrical resistance strain gauges mounted longitudinally in the constant bending moment section, one on the tension face and one on the compression face. They are connected to a strain indicator (blue box).

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Procedure

1. Make sure beam is properly centred on test frame.

2. Make sure hangers are in notches on beam. Periodically check to make sure that they do not touch the inside of the frame.

3. Apply loads to each side simultaneously. Be careful not to drop weights or

place hands under weight hangers at any time.

4. Apply loads in increments of 25 N to a maximum of 150 N.

5. Read and record deflection and strain for each load value.

6. Unload weights on each side simultaneously.

7. The instructors will take one setup to yield as a demonstration. Observe and record relevant data for the beam selected by the instructor for loading through the yield point to failure.

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Analysis c = semi-thickness (3 mm) b = width of beam (25.4 mm) h = thickness of beam (6 mm) a = 400mm P = load L = 200mm

Maximum flexural stress (at midspan) I

Mc

Where M = P * a

Moment of Inertia 12

bhI

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Maximum deflection (at midspan) EI8

PaL2

Upper and lower strains E

Radius of curvature

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L2

Where, delta is the deflection E = 200 GPa = 200,000 MPa Summary and Objectives of Methods:

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Analysis

1) Record load, top strain, lower strain, and deflection in the columns in the experimental section in the table below. These are given directly by the data acquisition box (blue box) directly.

2) Calculate the Top Stress and Lower Stess for each of the Loads.

Experimental Theoretical

Load (N)

Top Strain

()

Lower Strain

()

Def

ln

(mm)

Top Stress (MPa)

Lower Stress (MPa)

Calc. Defln (mm)

Calc. Stress (MPa)

Calc. Strain

()

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3) Compute the midspan deflection of the beam for each value of load and record the values in the table in the theoretical section. Provide a sample calculation.

4) Plot a graph of load against deflection using both calculated and experimental

values. Compare the calculated deflections with deflections measured by the transducer.

5) For each value of load for the beam compute the maximum flexural stress using the flexure formula and fill in the columns in the theoretical section. Provide a sample calculation.

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6) Compare the experimental stress to the theoretical stresses. Within what range

would these computed maximum stresses correspond to the actual maximum stress in the beam?

7) Compute the midspan strains of the beam for each displacement and record in the table. Provide a sample calculation.

8) Plot load against strain using both calculated and experimental values. Compare

the calculated strains with the strains measured.

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9) From the deflection and length of beam compute the radius of curvature at the 150 N load level.

10) Compare the graphs you have produced and discuss any errors present in the results.