JUT!SI I I I 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 2013 SUBJECT NAME MECHANICS OF SOLIDS SUBJECT NO 48331 DAY/DATE TUESDAY, 24th SEPTEMBER 2013 TIME ALLOWED START/END TIME 2 Hours 30 Minutes plus 10 Min. reading time 6:00 pm- 8:40 pm NOTES/INSTRUCTIONS TO CANDIDATES There are six ( 6) questions. All questions are to be attempted. Show your work clearly. The value of each 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.
Question 1 -Multiple choice (Total 30 Marks) Write your choices on the solution booklet._for example write "Question 2.7-Answer (e)". 1.1 - Referring to the figure below, at which points is the bending moment zero? ( 6 Marks) (.~M--P~*----~C~~2P~~---E---ji~F AAO B " HH9 r- L -r--- 2L --T-- L -7-- L --r-- L --T' (a) A,DandF (b) D,EandF (c) A and D (d) C and F 1.2 - Referring to the figure below, which of the following represents the correct distribution of the shear stresses under the applied distributed load q? (6 Marks) (a) (b) ~ k (c) ~T (d) ~ r 2
1.3- Which of the following is a true statement? (6 Marks) (a) For a beam under bending moment, the normal strain distribution is linear across the section of the beam only when the material is elastic. (b) For a composite beam under bending moment, the normal strain distribution is linear across the section of the beam. (c) For a beam under pure bending moment, shear stress distribution on a rectangular section of the beam is linear across the section. (d) For a beam under bending moment, the normal stress distribution is quadratic across the section of the beam. 1.4- Which of the following is not a true statement? (6 Marks) (a) Shear stress distribution is linear across the section of the beam (b) Internal shear force is zero if bending moment is constant along the beam axis (c) In reality shear stresses cause warping of a cross section (d) Warping effect due to shear stress is negligible for slender beams 1.5 The moment of inertia of the rectangle about the x -axis equals ( 6 Marks) 4mml 2. 3
Question 2 (Total 10 Marks) Two flat bars loaded in tension by forces P=20kN are spliced using two rectangular splice plates and two 15mm dian1eter rivets. Determine the shear stress in the rivets. Disregard the friction between the plates. Fig.2. Spliced connection Question 3 (Total 20 Marks) A plastic bar ACB having two different solid circular sections is held between rigid supports as shown in the figure. The diameters in the left- and right-hand parts are 50mm and 75mm, respectively. The corresponding lengths are 225mm and 300mm. The modulus of elasticity E is 6 GPa and the coefficient of thermal expansion a is 1 o- 4 I C. The bar is subjected to uniform temperature increase of 30 C. Calculate a) the compressive force in the bar (10 marks) b) the maximum compressive stress in the bar (5 marks) and c) the displacement 8c of point C (5 marks). Fig.3. Bar between rigid supports Question 4 (Total 1 0 Marks) Determine the maximum compressive and tensile stresses that occur in the beam shown in the figure below. Note that the moment of inertia and the location of the neutral axis are given in the figure. M=50kNm ==="==============If r=20kn P=40 kn 0 ~A B cf?); / 2m / 4m / / 7 7 65mm 125mm Fig.4. a) Overhanging beam under load b) Cross-section of the beam 4
Question 5 (Total15 Marks) A welded steel girder having the cross-section shown in the figure is fabricated of two 280 mm x 25 mm flange plates and a 600 mm X 15 mm web plate. The plates are joined by four fillet welds that run continuously for the length of the girder. Each weld can carry shear flow of9-kn/m. Calculate the maximum allowable shear force for the girder considering the strength of the welds. y z 0 15 mm... _ Fig.5. Welded steel!-section Question 6 (Total 15 Marks) A wood beam 150 mm wide and 200 mm deep is reinforced on top and bottom by 10 mm thick steel plates. Wood has the modulus of elasticity Ew = 1 OGPa and steel has the modulus of elasticity Est = 200GPa. Find the allowable bending moment M max about the z axis if the allowable stress in the wood is 50 MPa and in the steel is 80 MPa. y 5
FORMULAS Hooke's Law for axial stress-strain Hooke's Law for shear stress-strain a-=e& Generalized Hooke's Law r=gy Deflection of a rod of span L under axial load 8= J P(x) dx EA(x) 0 Deflection of a uniform rod of span L under uniform load 8 =PL EA Thermal expansion of a uniform rod of span L 8T =ai1tl Axial stress under axial load N CJ=- A Axial stress under bending moment M (J=--y I Moment of inertia of the rectangle (about the z axis) bh 3 I=zz 12 Shear stress VQ r=- Ib Shear flow VQ q=- I 2 Area for circle A = tr D 4 where D is the diameter 6