Course: Higher Diploma in Civil Engineering Unit: Structural Analysis I Experiment: Expected Duration: 1.25 Hours Objective: 1. To determine the shear modulus of the metal specimens. 2. To determine the shear stress at the limit of proportionality of the test specimens. 3. To study the different failure modes of ductile and brittle specimens. Apparatus 1. TecQuipment ing Machine as shown in Fig. 1. 2. specimens as shown in Fig. 2 3. Steel rule and micrometer. Theory From the general torsion theory of a circular specimen: T J Gθ τ = = l r where T = Applied Torque (Nm). J = Polar moment of inertia (mm 4 ) = πd 4 /32 G = Shear Modulus (Nmm -2 ). θ = Angle of twist (over length) in radians. l = Gauge length (mm). τ = Shear stress at radius r (Nmm -2 ). r = Radius (mm). Experimental Procedures 1. Measure the overall length (l) and diameter (d) of the test section of the specimen before and after testing. Pg. 1
2. Draw a line down the length of the test specimen with a pencil; this serves as a visual aid to the degree of twist being put on the specimen during loading. 3. Mount the specimen firmly in the ing Machine and use the levelling wheel to reset the dial gauge reading to its original value at the start of the experiment. For each increment of angle of twist record the following to destruction:- a) angle of twist of the specimen in degrees (θ). (later convert to radian) b) applied torque (T). Suggested Increment of Twist Angle To ensure that an adequate number of values are obtained from the test, particularly during the elastic region of strain, the following is recommended:- Specimen Code Angular Increment 0.15% carbon steel (as drawn) MT15 3 o Cast Iron MCI 2 o Remark: Two specimens of MT15 and MCI will be used for the experiment. Results: 1. Dimensions of the specimens before and after testing: Dimensions of the specimens (mm) Type of specimen 0.15% Carbon Steel (MT15) Cast Iron (MCI) Initial diameter (mm) Final diameter (mm) Gauge length (mm) Initial overall length (mm) Final overall length (mm) Pg. 2
2. Test data for the torsion test: Mild Steel (MT15) 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90 93 96 99 Cast Iron (MCI) 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 Pg. 3
3. Graphical Presentation for the Test Data: a) Plot a graph of applied torque T (Nm) against the angle of twist θ (in radian) of each specimen for the complete test to destruction. Hints: T as y-axis and θ as x-axis. b) Calculate the slope of the graph of the elastic region in order to determine the values of the shear modulus of each specimen. Hints: By using the given formula c) From the graphs, determine the torque and then calculate the shear stress at the limit of proportionality for each specimen. Hints: By using the given formula. 4. Observation of the Modes of Failure Record and sketch the modes of failure of each specimen. Discussion of Results 1. Comment on the modes of failure of the test specimens. 2. State and comment upon the values (shear moduli, shear stresses at the limit of proportionality) obtained from the test. 3. Discuss the errors involved in this experiement and make suggestions for the improvement. Laboratory Report 1. Each student shall submit his / her laboratory report which includes the following items: (a) (b) (c) (d) (e) (f) Name of Test Objectives of Test Test Data Test Data presented in Graphical Form. Shear moduli and torsional shear stresses at the limit of proportionality of specimens obtained in (d). Report and explain the modes of failures of specimens. 2. Hand in the report on / before. Pg. 4