Laboratory work # 8 (14) EXPERIMENTAL ESTIMATION OF CRITICAL STRESSES IN STRINGER UNDER COMPRESSION

Transcription

1 Laboratory wor # 8 (14) XPRIMNTAL STIMATION OF CRITICAL STRSSS IN STRINGR UNDR COMPRSSION At action of comprssing ffort on a bar (column, rod, and stringr) two inds of loss of stability ar possibl: 1) Local loss of stability; ) Gnral loss of stability. At local loss of stability on of flangs of a bar (stringr) is bucld (loss of stability). Th gnral loss of stability corrsponds to bucling of whol bar, i.. th structur is bnt in a dirction, prpndicular to an axis of th minimal inrtia momnt of oss sction. Th ach ind of loss of stability has th corrsponding maning of itical strss. At comprssion of a bar that ind of loss of stability will appar to which th minimal itical strss corrsponds. Thrfor purpos of wor is th dfinition of a ind of stability loss and comparison of itical strsss which found thortically and from xprimnt. Th itical strss is gnrally dtrmind by th mpirical formula, fair both for lastic, and for lasto-plastic aras of straind stat: 1 ν. (1) 1 ν ν whr ν, At local loss of stability w calculat local itical strsss by ulr s formula: () whr b is th width of a flang of oss sction in mm; - thicnss of a flang in mm, l ulr s local itical strss, =7GPa lasticity modulus. Thos itical strsss you should calculat for ach flang from your stringr is consistd. Th ach flang you should considr as a plat. Th maning of th attaching factor for plats of your stringr is dtrmind by th diagram on fig. 1 that dpnds from grip conditions. Thortically plat can hav thr inds of grip conditions: fr dg, pinning and fixd support. You should dtrmin a ind of grip conditions on four sids of a plat. You should discount th rlation of lngth to width. In cas of gnral loss of stability w can calculat itical strsss by ulr s formula: min g (3) С π I F l 1

2 whr F - ara of oss sction of a bar in m ; Imin - th minimal momnt of inrtia in m 4, g ulr s gnral itical strss in Pa, l- is lngth in m fr sid pinnd sid fixd sid Fig. 1. Attaching factor for plats. If lp it is ncssary rcalculat by formula (1). Th factor C is dtrmind according to grip conditions of a bar, fig.. At xprimnt th stringr bass on whol oss sction. In this cas C= 14. In safty factor it is usual strssman accpts th minimal maning C=1.

3 Fig.. Attaching factor C for column in global instability. Squnc of ralization of wor 1. You should writ down hading of this laboratory wor, your surnam, dat, draw stringr with dimnsions and grip condition for its flangs.. Calculat itical strsss of local and gnral losss of stability, having tan advantag th formulas accordingly (1), () and (3). Maning for th formula () you should choos by th diagram on fig.1, having provd choic of thos or othr grip conditions. You should ta two thortical grip conditions clos to ral grip condition. Similarly indpndntly you should ma choic th factor C for (3) according to fig... On givn by th data of tsts you should plot th diagram of dpndnc of ffort of comprssion of a bar P from displacmnt l (fig. 3). Р[g] l[mm] 3. Dtrmin th itical strsss rcivd from xprimnt of a bar and to prov its charactr (gnral or local form of loss of stability): P max F. (4) whr P max is maximal load in N, F is ara of stringr s oss sction in m. 4. If from xprimnt you stablishd, that th local loss of stability prcds gnral, b th manings t and dtrmind on th formulas (1) and (), do not coincid, it is ncssary to find maning, that appropriat. You must solv th quation (1) rathr (itical strss by ulr s formula). In this quation w hav that = (from xprimnt), and w shall rciv: ( ) 0. (5) 3

4 Valu which dtrmind from (5) is ncssary to substit in () and from last to dtrmin. 5. Issu th rport. P P l For quation (5) th solv is: whr (5) has viw In this quation w hav a=1, b=,, Fig. 3. Klapyron s diagram b b 4ac x1 (6) a 1,, ax bx c 0, x 1, =. с In this formula strsss ar positiv and must b positiv. Upon valu from formula (6) you should calculat xprimntal valu of attaching factor : b ( ) (7) 4

5 You should compar th xprimntal valu of attaching factor thortical valu from fig.1 and stimat rlativ rror: by (7) with 100 (%) Rquirmnts to th contnts of th rport Th rport should contain: 1. Hading (numbr and th nam of laboratory wor, numbr of group and a surnam of th studnt, dat, th purposs and tass of wor).. You should plot drawings of spcimn. 3. Rsults of thortical calculation for all itical strsss- local and gnral. 4. You should plot th xprimntal diagram and stimat xprimntal valu of itical strss. 5. You should compar xprimntal and thortical valus of itical strss and calculat xprimntal valu of attaching factor. 6. You should compar th xprimntal valu of attaching factor with thortical valu and stimat rlativ rror. 5