Lab 1 Complex Stresses.docx - MAAE 3202 Lab 1 Experiment A...

This preview shows page 1 - 7 out of 13 pages.

MAAE 3202 Lab 1 Experiment A: Complex Stresses Lab L1 – Group G1 Members: Syed Samdani Sami Tabikh Scott Peterson Julian Becker Li Qixin Kevin Robert Quentin Hogg 101009100 10/17/2019
Quentin Hogg 101009100 Table of Contents Table of Contents .................................................................................................................... 1 1 Objectives ........................................................................................................................ 2 2 Apparatus ........................................................................................................................ 2 2.1 Equipment ............................................................................................................................. 3 2.2 Procedure .............................................................................................................................. 4 3 Theory ............................................................................................................................. 4 4 Experimental Data ........................................................................................................... 5 4.1 Raw Data for Pure Bending .................................................................................................... 5 4.2 Raw Data for Bending and Torsion ......................................................................................... 5 5 Calculations ..................................................................................................................... 5 5.1 Bending ................................................................................................................................. 5 5.1.1 Second Moment of Area ......................................................................................................................... 5 5.1.2 Longitudinal Stress .................................................................................................................................. 6 5.1.3 Plots and Material Properties ................................................................................................................. 6 5.1.4 Principle stress calculations .................................................................................................................... 8 5.2 Bending and Torsion .............................................................................................................. 8 5.2.1 Mohr’s Circle ........................................................................................................................................... 8 5.2.2 Theoretical Principle Stresses ................................................................................................................. 9 5.2.3 Failure due to Maximum Shear ............................................................................................................. 10 6 Discussion ...................................................................................................................... 10 6.1 Results ................................................................................................................................. 10 6.2 Sources of Error ................................................................................................................... 11 7 Conclusion ..................................................................................................................... 12 8 References ..................................................................................................................... 12 1
Quentin Hogg 101009100 1 Objectives The objective of this lab is to use experimental data to determine the material properties of an aluminum cantilever beam. These values will include stress (MPa), strain, Poisson ratio, and stress and strain Mohr’s circles. Values will be compared to expected values through quantitative and theoretical means. This will, furthermore, include a comparison between pure and complex beam bending. 2 Apparatus Figure 1: Schematic of end loaded cantilever beam Figure 2: Side View Figure 3: Section Y-Y 2
Quentin Hogg 101009100 Figure 4: Orientation of the strain gauges 2.1 Equipment 1. Vishays Measuring Group Switch of Balance Unit SB-10 2. Vishays Measuring Group Strain Indicator P-3500 3. Support frame with fixtures for holding a cantilever beam 4. Aluminum beam of hollow circular cross-section 5. Weights and hanger 3 Strain Rosette at point C Strain Rosette at point A Strain Rosette at point B
Quentin Hogg 101009100 2.2 Procedure Refer to the MAAE 3202 Solid Mechanics II Lab Manual - Procedure 1 . 3 Theory The following equations can be found in the Solid Mechanics II Lab Manual 1 . Longitudinal stress on a symmetrical beam under bending follows the formula σ x = My I (1) For a beam of hollow circular cross-section, the second moment of area I is given by I = π 64 ( d 2 4 d 1 4 ) (2) The same beam subjected to a torque about the longitudinal axis will observe a shear stress τ = Tr J (3) The polar moment of area is given by J = π 32 ( d 2 4 d 1 4 ) (4) When the beam is subjected to both bending moment and torque principal stresses are (5) (6) (7) Given this beam is a linear elastic material the principal stresses and strains are related by (8) 1 [ CITATION MAA19 \l 4105 ] 4
Quentin Hogg 101009100 (9) 4 Experimental Data 4.1 Raw Data for Pure Bending Only strains at point A were recorded -

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture