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Mizzou ENGINR 2200 - Exam1_solution

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University of Missouri - Columbia ENGR 2200 - Intermediate Strength of Materials Civil and Environmental Engineering Exam I - Summer, 20 II Name: KJ?-:/ Student No. ----------------Short Answer Problems: (10 pts) Q1. (6 points) Sketch the typical stress-strain diagram for steel when subjected to axial loading in tension. Label the axis, show the correct shape of the curve, and label any important values. ~L"~ 0::; rt--,;V (7K \ Q2. (2 points) How could Young's Modulus (modulus of elasticity) be determined from your sketch in Question I? Q3. (2 points) What are the SI units of Young's modulus? s s---h-~ ?c s c e--\S ..J Answer the [allowing questions by circling the correct answer (10 pts) Q4. (2 points) Axial strain is expressed in units of force per area. (T) cEJ Q5. (2 points) An isotropic material has properties that are independent of the direction of loading @J (F) Q6. (2 points) Necking behavior in axial loading of a ductile material occurs before the yield stress has been reached. (T) ® Q7. (2 points) If a ductile material fails during tensile testing, the failure surface is on the cross-section perpendicular to the axis of loading. (T) ® Q8. (2 points) A ductile material can experience a brittle-type failure under repeated loading @ (F) July 8,2011 Intermediate Strength of MaterialsUniversity of Missouri - Columbia ENGR 2200 - Intermediate Strength of Materials Civil and Environmental Engineering Exam 1 - Summer, 20 II Q9. (6 points) Bars A and B are made of the same material and have the same circular cross-section (same diameter). Bar A is twice as long as bar B. (a) If a load P i~~aXiallY to both bars, the stress in bar A will be (higher than, lower than, am a ) the stress in bar B (b) If a load P is applied axially to both bars, the strain in bar A will be (higher than, lower than same as the strain in bar B (c) I~load Pis app Ie axially to both bars, the deformation in bar A will b ~ lower than, same as ) the deformation in bar B an Quantitative Section: Work out each ofthe problems below and show all o(your work. Q7. (14 points). A 50-ft length ofO.50-in diameter steel wire stretches 0.25 inch when a tensile force P is applied. Knowing that E = 29 X 106 psi, determine (a) the magnitude of the force P, (b) the corresponding normal stress in the wire. 0 , 2 '5 /'L O-Obo 4-/1.:,7~ = 1"'-2-7 C I I o = L ccL 203 7.2 1£ 5J A Q8. (20 pts) A horizontal bar CBD having a length of2.4 m is supported and loaded as shown in the figure. The vertical member AB has a cross-sectional area of 550 mm2. Determine the magnitude of the load P so that it produces a normal stress equal to 40 MPa in member AB. /"';;-----;... D t--~--2.4m--"----_ .. ", .2 ~(C'-= - r ( ? 4 vYj") 1-\j) X p (' 2_4-\ I I . C; J d-' G A / / 2_ (l:)<;U x / iJ ~ Gr;J,j '"2/FAB ::: 10 x/O 'VI M I S J 7 5V NJ L-----July8,2011 Intermediate Strength of Materials 2University of Missouri - Columbia ENGR 2200 - Intermediate Strength of Materials Civil and Environmental Engineering Exam 1 - Summer, 20 II Q9. (20 pts) Three steel plates are joined by two rivets as shown in the figure. If the rivets have diameters of 20 mm and the ultimate shear stress in the rivets is~O MPa, what force P is required to cause the rivets to fail in shear? 2A-I =[2 (IT ) (Q, C I ~ ) 'L] " Jt -+u~ CA 1'l 2 rlVltr b=4-f.u,,,,, o p o LILlI - ~i{ - 2 iD 'K/Q ~ A (j.It Vi1 . / vi./-LP I Q50 A bar is subjected to loads as shown in the figure below. The bar is made of steel with modulus of elasticity E=200 GPa and cross sectional area A=225 mm2• Determine the deflection at the lower end ofthe bar due to the loads PI, P2, and P3. Does the bar elongate or shorten? s PL \ = ~ \lx = ~ 2 ~N C-1-6\AS l ~)CD YCD PI == 0 kN ~~ PeD '!:" 4-D -iN (-hIASIJ'A ) ~~ --:;2 ~tV C~dl~V'-) ~ t< s -L EA o ' . ( ~ :2) 00" f 4o} 0 0 0 ~"" ( 2--oD ~I 0 q) (L 2 5 )I \ D (VI. + 1 7)00a ) July 8, 2011 Intermediate Strength of Materials


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