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1 Department of Civil and Environmental Engineering School of Mining and Petroleum Engineering 3-33 Markin/CNRL Natural Resources Engineering Facility Tel: Edmonton, Alberta, Canada T6G 2W2 Fax: Please complete the following information: Surname: I.D. Number: Date: Given Names: No. of Booklets Student s Signature: ********************************************************************** Very Important NOTE: the Exam consists of 24 Multiple Choice Questions Version Clearly indicate your chosen answer in the supplied General Answer Sheet (No other forms of solution will be accepted) according to the following instructions: - Please use HB pencil - Mark ONLY ONE answer in the provided General Purpose Answer Sheet - Make heavy black marks that fill the circle completely. - Mark the version of your exam on the box Special Codes in your General Purpose Answer Sheet as shown in the box below. **********************************************************************

2 University of Alberta Department of Civil and Environmental Engineering CivE 398: Mid Term Exam II Time allowed: hour and 20 minutes Date: November 6 th 204. The position function of a continuum follows the relationship Then, the component of the infinitesimal strain matrix is: a b c d The position function of a continuum follows the same relationship as in question. Then, the component is: a b c d The stress at a point is given by the following matrix Where,,,. If is the deviatoric stress tensor then: a. /3 b. /3 /3 2/3 c. 2/3 2/3 0 d

3 4. The shown figure represents a specimen under a confined compression test. The vertical stress is 200MPa while the confining pressure is kept at 00MPa. 200MPa 00MPa 00MPa 200MPa The maximum shear stress inside the specimen is: a. Zero b. 50 MPa c. 00 MPa d. 200 MPa 5. The shown figure represents a specimen under a confined compression test. The vertical stress is where is a positive real number while the confining pressure is applied by ensuring that the specimen does not expand or contract laterally. The specimen is isotropic linear elastic with Young s modulus and Poisson s ratio. Confining pressure Confining pressure The confining pressure is equal to: a. b. c. d. 3

4 6. Let :, be defined such that : sin. Then, the following is true about : a. is surjective but not injective b. is injective but not surjective c. is bijective d. None of the above 7. In a tensile test of a steel specimen, the engineering stress was measured at 350MPa while the corresponding engineering strain was measured at 0.. The true stress is equal to: a. 38MPa b. 350MPa c. 385MPa d. None of the above 8. If the stress matrix in a three dimensional state of stress is represented by where,0. Then the normal stress on a plane perpendicular to the direction of the vector,, is: a. b. c. d The longitudinal engineering strains on the surface of a test specimen were measured using a strain rosette to be 0.02, 0.0 and 0.0 along the three directions:, and respectively, where,0,, and 0,. If the material is assumed to be in a small strain state, then the strain component is equal to: a. 0.0 b c. 0.0 d In a uniaxial tension test, a specimen is pulled with a positive (tensile) normal stress while the remaining stress components are zero. If the material is linear elastic and isotropic with Young s modulus and Poisson s ratio, then, the following statement is true: a. The volumetric strain is positive b. If 0, then the volumetric strain is negative c. If 0, then the volumetric strain is negative d. None of the above 4

5 . In a linear elastic isotropic material with Young s modulus and Poisson s ratio, the stress matrix is: Where,. Then, the strain matrix is: 2 0 a b c /2 0 d. / The stress matrix at point A on the outside wall of the shown pipe expressed using the coordinate system indicated in the figure is: A a b c d

6 3. Let, (i.e., is the set of vectors which have the form,, ). Then set represents the geometry of: a. a line in 3D space b. a plane in 3D space c. a cube of unit length in 3D space d. None of the above 4. An object expanded such that if the original position is,,, then the final position vector is.. The Green Strain matrix associated with this deformation is:. 0 0 a b c d The stress matrix as a function of the position in a continuum has the following form: Where, and. If the body forces vector applied to the continuum is equal to,0,0 units, then for the stress matrix to satisfy the differential equation of static equilibrium: a. 0, 3, 6 b. 0, 3, 3 c. 5, 0, 0 d. 6, 0, 0 6. Let be a rotation matrix such that If,,,,, and,, then, the following is a correct statement regarding the vectors, and : a. b. c. d. Both a and b are correct 6

7 7. Before any deformation is applied, the cuboid has the dimensions shown in the figure below. A deformation described by the following small strain matrix is applied to the cube: The length of after deformation is: a. 2.0 units b units c..99 units 2 d..98 units 8. Before any deformation is applied, the cuboid has the dimensions shown in the figure below. A deformation described by the following small strain matrix is applied to the cube: The length of the line after deformation is: a units 2 b units c units d units 9. Before any deformation is applied, the cuboid has the dimensions shown in the figure below. The cuboid is subjected to a stress state described by the following stress matrix: The cuboid is made out of a linear elastic material with Young s modulus 2 and a negative Poisson s ratio of value 0.. The length of the vector after deformation is: a units 2 b units c..07 units d..03 units 7

8 20. A possible position function describing the shown two dimensional deformation is: Reference configuration Deformed configuration ( is a small angle) a. / / b. 0 c. 0 d. 2. The shown beam has a constant width units and a height that varies according to the equation The beam is subjected to a horizontal body forces that is equal to units of force/unit volume and a horizontal boundary force of value. If is the only nonzero stress component, then the following is the differential equation of equilibrium written in terms of : a. 2 b. 2 2 c. 2 2 d. 2 8

9 22. The following relationship between the uniaxial engineering (small) strain and the uniaxial Green strain measures is true (where is the stretch): a. b. c. d. None of the above 23. The stress matrix representing the stress at a point inside a continuum is symmetric as a result of: a. The strain matrix being symmetric b. The law of the balance of moments c. The body is a linear material d. The material conserving energy 24. In a linear elastic structure, the matrix of coefficients relating the stresses and the strains is symmetric as a result of: a. The strain matrix being symmetric b. The stress matrix being symmetric c. Both the strain and the stress matrix being symmetric d. The material conserving energy 9

10 b 2d 3d 4b 5a 6a 7c 8a 9b 0 a a 2 d 3 a 4 d 5 c 6 c 7 b 8 a 9 b 20 d 2 c 22 b 23 b 24 d

PURE BENDING. If a simply supported beam carries two point loads of 10 kn as shown in the following figure, pure bending occurs at segment BC.

PURE BENDING. If a simply supported beam carries two point loads of 10 kn as shown in the following figure, pure bending occurs at segment BC. BENDING STRESS The effect of a bending moment applied to a cross-section of a beam is to induce a state of stress across that section. These stresses are known as bending stresses and they act normally