,. 'UTIS. i,i I Univcnity of Technology, Sydney TO BE RETURNED AT THE END OF EXAMINATION. THIS PAPER MUST NOT BE REMOVED FROM THE EXAM CENTRE. SURNAME: FIRST NAME: STUDENT NUMBER: COURSE: Tutor's name: Tutorial class day & time: Spring Semester 2011 SUBJECT NAME MECHANICS OF SOLIDS SUBJECT NO 48331 DAYIDATE TIME ALLOWED Monday/21 st of November 3 Hours 10 Min START/END TIME: 9:30 12:40 NOTESIINSTRUCTIONS TO CANDIDATES There are eight (8) questions. All questions are to be attempted. Show your work clearly. The value ofeach question is as indicated on the question paper. THIS IS A CLOSED BOOK EXAMINATION. Non-programmable calculators and drawing instruments may be used. Formulas are listed on the last page. Write your tutor's name on the answer booklet. 1
Question 1 - Multiple choice (6 Marks per question) Total of30 Marks Write your choices on the solution booklet. For example write "Question la-answer (c)". 1.1 For a material with the stress-strain diagram shown in the figure, which point represents the initiation ofmaterial yielding? c D (a) B (b) A (c) C Cd) D 1.2 What is the shape factor of the rectangular section shown in the figure? h (a) 1.5 (b) 1.17 (c) 1.7 (d) 1.8 1.3 -Which one of the following general statements is not correct? (a) Location of the shear centre for an open thin-walled mono-symmetric section is only a function ofsection geometry. (b) Shape factor ofa section is only a function ofsection geometry. (c) Location of the shear centre for an open thin-walled mono-symmetric section is always independent of section wall thickness. (d) Plastic bending moment capacity of a cross-section made of steel, depends on section geometry and yield stress of steel 1.4 - For the prismatic, elastic cantilever beam under bending moment M at the tip as shown in the figure, which one ofthe following statements is not correct? M (a) Maximum rotation (slope) occurs at enda. (b) Rotation (slope) at fixed support B is zero. Q B~ (c) Maximum deflection occurs at end A. (d) Curvature varies linearly along the entire beam length. L I~ ~I 'Over/... ' 2
1.5 Which one of the Mohr circles is properl y expressing the stress state for the element shown in the figure? (element is under pure shear stress state) (J /-----t_ (a) (b) (c) (d) Question 2 (TotalS Marks) For the state of stress given in Figure-2, determine the magnitude and orientation of the principal stresses. Show the results on a properly oriented element. Note: You may use either the Mohr's circle or the Jormula. Figure-2 Question 3 (Total 10 Marks) The T-beam has dimensions as shown in Figure-3. If the section is made of an elastic perfectly plastic material with yield stress of O'y = 200MPa (in tension and compression), determine the plastic moment and the bending moment corresponding with the occurrence of first yield in the section. Hint: In the first step, position ojneutral axis (NA.) should be determined. NA. Figure-3 'Over!... ' 3
Question 4 (Total 10 Marks) Detennine the required diameter d l for the segment AB of the shaft, shown in Figure-4, if the pennissible (allowable) shear stress for is 1"all =160 MPa and the total angle of twist between A and C is not to exceed t/jac =0.02 rad. The loading is TB = 2.5 kj'j.m and Tc = 1.0 kj'j.m, shear modulus ofaluminium and brass is G G b =50GPa. LI 3m and L2 =lm and 30mm. a d 2, Figure-4 Question 5 (Total 15 Marks) Find the distance e from the web to the shear centre of the section shown in Figure-5. The section has a constant thickness t=20 mm. Note: in your calculations you have to take the thickness ofthe elements into consideration. V!oE::-<----,e==----:>;;o.. 200mm 1< >1 L tr~ ~.._._.-.. _._._._._._._._. Shear centre,--------,i t: 1< 200mm >1 Figure-5 Question 6 (Total 10 Marks) Find the deflected shape (elastic curve) ofthe cantilever beam shown in Figure-6 and detennine the deflection and the rotation at the tip of the cantilever (point A). The cross-section of the beam has a moment ofinertia ofi and the material modulus of elasticity is E. o o N 'Over!... ' 4
Question 7 (Total 10 Marks) The tube shown in Figure-7 is of constant t=20 mm thickness. Detennine the maximum pennissible (allowable) load P, assuming that d=30 mm. The load P is applied on the outer edge of the tube. The maximum allowable stress of the material in compression is (O"c )allowable =120 MPa and the maximum allowable stress of material in tension is (0"/ ) allowable = 80 MPa. z Figure-7 Question 8 (Total 10 Marks) Two round aluminium and steel bars are supported between rigid walls, as shown in Figure-8. Ifthe temperature is increased from 20 C to 50 C, detennine the stress in each bar. Data for the aluminium are aa = 20x10-6 rc, Ea = 70GPa and data for the steel are as = loxl0-6 rc, Es = 200GPa. 50mm 30mm f-o----- 3 m ----+~- Figure-8 'Over!... ' 5
FORMULAS Axial load and bending: Shear: q 1 1 N (j= A VQ T=- Ib Torsion: T G T -=-= J L P J Jrd 4 32 (d=diameter) tan28 p =-~ (jx -(jy (j Txv e - rx},:::oc or =aa.tl Z I Y max M S=_P (jy k PL EA My Z b F= Iqds 0 Moment of inertia of the rectangle (about the z axis) bh 3 I zz - 12 Effective length factor K 1[2EI P=- e (kl)2 p l.,.::: 0.51. I ",,0:71. Pinned ends Fixed ends Pinned and fixed ends f-1,.u.trn<l r"",.rub, 1:l;:'~() {5J IK~2'1