CE 2313 / MAE 2312 Mechanics of Materials. Examination III

Transcription

1 E 1 / E 1 ecanics of aterials Eamination ril 6, 7 Name: Tere are 4 numered rolems on tis eam. Te relatie eigt of eac rolem is roided in arenteses immediatel after te rolem numer. Time ed for te eam is 8 minutes. Read te rolems carefull and don t aste time doing ork tat is not requested. rolem statements ma include information tat ou do not reall need. roided alues ae at least tree significant digits een en not eressed tat a. ra Free Bod iagrams (or oter diagrams) en aroriate!!!! So eac rolem solution in detail. Test credit ill e ased rimaril on our solution metod rater tan our numerical solution. f ou are filling eac age, ou are roal doing too muc. f ou do need additional sace for a solution ask for a lank seet of aer. On tat seet, rite te digit test in te loer rigt corner and clearl identif te art of te test ou are orking on. Formulas + ' + cos θ + sin θ ' ' sin θ + cos θ tan θ d d E d d d d E V d d d d E 1 1 z z VQ t Q S c Sreq'd Vma Q t V 1.5 Vma e ma a a 6 E 6 E ( + ) ( + ) 4 E

2 1) () oint is in a state of lane stress. Te diagram at te rigt sos te relationsi eteen and to different coordinate sstems, - and -. ' ' a) onsider a stress element at oint oriented as son elo. ssume tat all stress comonents are ositie (ic imlies non-zero). Sketc te stresses on te element, using te orientation tat corresonds to a ositie stress. Gie eac stress a correct, smolic lael (te numeric alues are not knon). s t s t t s t s ) onsider a stress element at oint oriented as son elo. ssume tat all stress comonents are ositie (ic imlies non-zero). Sketc te stresses on te element, using te orientation tat corresonds to a ositie stress. Gie eac stress a correct, smolic lael (te numeric alues are not knon). s' t'' t'' s' s' t'' t'' s'

3 ) () Te diagram sos te state of lane stress of a oint. 1. ksi a) etermine te rincial stresses at te oint and corresonding orientation of te stress element tat sos te rincial stresses. 1. ksi 1. ksi tan θ + 1 tan θ + 1 tan θ θ 9 θ 45 OR ksi 1 t 1. ksi ksi θ 9 θ 45 s s1 s 1 q 1 1. ksi t 1. ksi t ) Sketc te stress element tat sos te rincial stresses. So all te stresses acting on te stress element in tis orientation. So te stresses using teir actual direction and lael tem it teir magnitude. 1 ksi 1 ksi 45 1 ksi 1 ksi

4 ) () eam is to e designed to suort te load as son. Te sear and moment diagrams for te eam are roided. Te ale stresses in te eam material are 1.4 ksi and.5 ksi. Te eam ill ae a rectangular cross section as son in te diagram and it is required tat. B 1 z V (ki) 6 etermine te required eigt,, of te cross section of te eam. (ki-ft) ki-in c S c 4 S 6 S 18 esign for ending stress S req'd in eck sear stress Vma ksi in.5 ksi.15 ksi OK 1. in

5 4) (4) Te continuous, rismatic eam as moment of 4 inertia in and modulus of elasticit E 9 ksi. t is suorted a in at and rollers at and. Te donard, uniforml distriuted load as magnitude 1.8 ki B and te donard, ft a c concentrated load at B as magnitude ki. Te required distances are a 1 ft, 15 ft, and c ft. etermine te ertical reactions at,, and using te etod of Suerosition. Follo te order of stes and utilize te corresonding sace tat is roided elo. a) omlete te diagram to so te rimar structure ou ae cosen. is te redundant reaction. ) etermine te deflection(s) of te rimar structure at te osition(s) of te redundant force(s) due to te alied loads. ' ' ( ) ( ' ' ) E 6 E ( ) ( 45 1 ) E 6 E E E E ' ' ' c) etermine te deflection of te rimar structure at te osition of eac redundant force due to eac redundant force. (f te redundants are and B, calculate te deflection at due to, te deflection at due to B, te deflection at B due to, and te deflection at B due to B. Tis int is not meant to suggest tat tere are to redundants nor tat or B is a suitale coice for a redundant.) ' 6 E 5 ' E ' E '

6 d) Using te results of te first tree stes, gie te suerosition equation(s) and determine te alues of te redundant reactions. + ' E E ki e) etermine te remaining reactions. 1 ft 15 ft ft F + B ( 1.8 ) 1 ( ) ki F ki