UNIVERSITY OF PRETORIA DEPT SlVlELE INGENIEURSWESE / DEPT OF CIVIL ENGINEERING

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1 1 UNIVERSCTEIT VAN PRETORIA I UNIVERSITY OF PRETORIA DEPT SlVlELE INGENIEURSWESE / DEPT OF CIVIL ENGINEERING STRENGTH OF MATERIALS SWK210 STERKTELEER SWK210 FINAL EXAMINATION - EiNDEKSAMEN VAN en VOORLETTERS HANDTEKENlNG STUDENTENOMMER SURNAME and INITIALS SIGNATURE STUDENT NUMBER Volpunte l Full Marks: 80 Tyd 1 Time: 2 ure 1 hours June 2009 INSTRUCTIONS... READ: + Answer all questions in the provided spaces. + The invigilators will supply no additional or loose pages. + Rough work may be done on the final blank page but this page will not be marked. c3 Answers in pencil will not be marked. * Tippex or any other similar product may not be used. * No highlighter may be used. + Students may ask no questions for whatever reason during the exam or test. If you are of the opinion that you need additional information, make assumptions and state these assumptions. d The relevant units must substantiate all answers. + All aspects as described in the EXAMINATION REGULATIONS are applicable. + All calculations to reach an answer must be shown. INSTRUKSIES..... LEES: c3 Beanfwoord alle vrae in die spasies voorsien. + Die toesighouers sal geen addisionele of 10s bladsye voorsien nie. d Rofwerk mag op die laaste blanko bladsy gedoen word en hierdie bladsy word nie gemerk nie. + Antwoorde in potlood w ~rd nie gemerk nis. Tippex of enige soortgelyke produk mag nie gebruik word nie. d Geen glimpen [ "highlighter"] mag gebruik word nie. Q Srudenfe msg nie tydens die eksarnen vrae vra nie - om waiter rede ookal, lndien u van mening is dat addisionele inligting benodig w~rd, maak aannames en stel di, aannames. c3 Alle anfiiooide moet deur die nodige eenhede bevestig word. G AAl aspekte soos ~~ervat in die EKSAMENREGULASiES is van foepassing. c3 Alle berekeninge om antwoorde fe bepaal moet getoon ward. Dosente 1 Lecturers: Prof L Maree Prcf C Roth Mr F van Graan I Eksterne Eksarninator I Extemzl Examiner: Prof BVVJ VAN RENSBURG SWKZIO FINAL EXAMINATION

2 QUESTION 1 1 VRAAG 1 2 The support cable AB of the building frame RSTV is originally ilnstretched. The two columns RT and SV each tilts 2 clockwise from the vertical about their basis as a result of an earth tremor. Calculate the normal strain in the cable. Die ondersteuningskabel AB van die bouraam RSTV is aanvanklik onuitgerek. SWi21G li2009 FINAL EXAMINATION

3 ,,, SWK21D FINAL EXAMINATION

4 A copper sleeve [C] with outside diameter equal to 30 mm and inside diameter equal to 20 rnm surrounds a 20 mm diameter steel bolt [A]. The yield stress for steel is equal to 650 MPa and the yield stress for copper is equal to 500 MPa. ESteel = 200 GPa and EcoPper= 70 GPa. 'n Koperhuls [C] met buitediameter gelyk aan 30 rnm en binnediameter gelyk aan 20 mrn omhul 'n 20 mm diameter staal bout. Die vloeispanning van die staal 650 MPa en die vloeispanning van koper gelyk is aan 500 MPa. Estaal = 2 00 GPa en. Ekoper = 7.0 GPa. A = 20 mm 0 Steel bolt I staal bout B = Thin washer/ ~ u wasser n C = Copper sleeve / Koper huls 2[a] Determine the largest elastic load P that can be applied to the assembly [6].. if the load P is administered by an external loading. Bepaal'die grootste elastiese las P wat op die samestelling aangewend kan word,indien P toegepas word deur 'n eksterne belasting. 0 - s, = 4 * I- 0 I - FS SVG'( FINAL EXAM!bIATION

5 2[b] Determine the largest elastic load P that can be applied to the assembly [4] if the load P is administered by tightening the bolt. Bepaal die grootste elastiese las P wat op die samestelling aangewend kan word indien P toegepas word deur die bout vas te draai.

6 QUESTION 3 1 VRAAG 3 6 Light beam ABC is supported by a roller at A and a hinge at C. The cross-section of the beam is also given: Ligte balk ABC word ondersteun deur 'n roller by A en 'n skarnier by C..Die dwarssnit is ook gegee. 3[a] Determine all the reactions. Bepaal a1 die reaksies'. 3[b] Determine themagnitude and sense of the bending moment at point D [31 - which is 3 metres from A. Bepaal die groote en aard van die buigmoment by punt D - v~at 3 meter vanaf punt A gelee is.

7 3[c] Draw a diagram [with vabes] depicting the bending stress in ~lrnm* [I21 at D from the top to the bottom of the section. Teken 'n diagram [met waardesl wat die buigspanning in ~ /rnrn~ by D vanaf die bokant tot die onderkant van die dwarsdeursnit weergee. SWK210 1/2009 FINAL EXAMINATION

8 Light beam ABC is supported by a roller at A and a hinge at C. The cross-section of the beam is also given. Ligte balk ABC word ondersteun deur 'n roller by A en 'n skarnier by C. Die dwarssnit is ook gegee. 4[a] Determine the shear force at point D - which is 3 metres from A. Bepaal die skuifkrag by punt D - wat 3 meter vanaf punt A geleg.is. I 4[b] Draw a diagram [with values] depicting the shear stress at D from j [I01 the top to the bottom of the section. Teken 'n diagram [met waardesl wat die skuifspanning by D vanaf die bokant tot die onderkant van die dwarsdeursnit weergee. i

9 I " 0 Yb =-. doook zoo (40j-$ a/Lz..-&-..~~D.D~ - ' //o WP & ;ZD -. D D D D -. _.... r 4[c] To construct the beam the web is fixed to the flange by means of metal bolts. 161 Check cross-section. The capacity per bolt in single shear is 20 kn. Determine the number of bolts that should be placed along section AB of the beam. Om die balk saam te stel is die web met behulp van metaalboute aan die f lens geheg, Si-en dwarsdeursnit. Die vermoe per metaalbout in enkelskuif is 20 kn. Bepaal die aantal boute nodig in gebied AB van die balk.

10 Light beam ABC is supported by a hinge at A and a roller at B. Ligte balk ABC word ondersteun deur 'n skarnier by A en 'n roller by B. FIG 1 5[a] Draw the deflected form of the beam on FIG 1. Teken die gedeflekteerde form van die balk op FIG 1. 5[b] Develop an equation [in x] that gives the Bending Moment for [21 section AB of the beam Ontwikkel 'n vergelyking [in x] wat die Buigmoment vir gebied AB van die balk weergee. 5[c] Determine the maximum deflection of the beam in mm. Bepaal die maksimum defleksie van die balk in mm.

11 5[6] Determine the slope of the deflection curve at point B of the beam. [31 Bepaal die helling van die defleksiekromme by punt B van die balk. 5[e] Determine the deflection at point C of the beam in mm. Bepaal die defleksie by punt C van die balk in mm.

Universiteit van Pretoria

Universiteit van Pretoria Departement Siviele Ingenieurswese Department of Civil Engineering Struktuuranalise SIN 311 Structural analysis SIN 311 Eerste Semestertoets 2010 Volpunte = 60 First Semester