Chapter 3. Estimation of Earthquake Load Effects

Transcription

1 Chapter 3. Estmaton of Earthquake Load Effects 3.1 Introducton Sesmc acton on chmneys forms an addtonal source of natural loads on the chmney. Sesmc acton or the earthquake s a short and strong upheaval of the ground. Ths naturally s the cause for loads on any structure. Any structure under sesmc loadng s subjected to cyclcal loadng for a short perod of tme. An earthquake s descrbed by ts ntensty and t epcenter. The ntensty of and earthquake at a place s a measure of the degree of shakng caused durng the earthquake and thus characterzes the effect of the earthquake. Most of the study of earthquakes up to the begnnng of the twenteth century dealt wth the effects of earthquakes and to quanttatvely descrbe these effects a number of ntensty scales were ntroduced. Intally there was the Ross-Forel scale that had ten dvsons. In 1888 Mercall proposed a scale wth 1 subdvsons to permt a clear dstncton n shocks of extreme ntensty. After a number of changes the Modfed Mercall scale or smply the MM scale s generally used by engneers today. Another revson made n 1956 to the MM scale by Rchter s also n use. The focus s the source for the propagaton of sesmc waves. It s also called the hypocenter. The depth of the focus from the surface of the earth drectly above s referred to as the focal depth. The pont on the earth s surface drectly above the focus s known as the epcenter. The structure experences cyclc loadng durng the process of sesmc acton. Ths causes energy to buld up n the system leadng to ts collapse. The frcton wth ar, frcton between partcles that consttute the structure, frcton at junctons of structural elements, yeldng of the structural materal and other processes of energy dsspaton depress the ampltude of moton of a vbratng structure and the vbratons de out n course of tme. When such nternal and or external frcton fully dsspates the energy of the structural system durng ts moton from a dsplaced poston to ts ntal poston of rest, nhbtng oscllatons of the structure, the structure s sad to be crtcally damped. 5

2 Thus the dampng beyond whch moton wll not be oscllatory s called crtcal dampng. The effect of energy dsspaton n reducng successve ampltude of vbratons of a structure from the poston of statc equlbrum s called dampng and s expressed as a percentage of crtcal dampng. There are other terms that are mportant wth respect to sesmc analyss. Durng earthquakes there occurs a sate n saturated coheson less sol where n the effectve shear strength s reduced to a neglgble value, for all engneerng purposes. Un ths condton the sol tends to behave lke a flud mass. A system s sad to be vbratng n ts normal mode or prncpal mode when all ts masses attan maxmum values of dsplacement smultaneously and they also pass through the equlbrum postons smultaneously. When a system s vbratng n ts normal mode, the ampltude of the masses at any partcular tme expressed as a rato of the ampltude of one of the masses s known as the mode shape coeffcent. Durng an earthquake ground vbrated (moves) n all drectons. The horzontal component of the ground moton s generally more ntense than that of the vertcal components durng strng earthquakes. The ground moton s generally random n nature and generally the random peaks of varous drectons may not occur smultaneously. Hence for desgn purposes, at one tme, t s assumed that only the horzontal component acts n any one drecton. All structures are desgned to wthstand ther own weght. Ths could be deemed as though a vertcal acceleraton of 1g s appled to the varous masses of the system. Snce the desgn vertcal forces proposed n the codes are small as compared to the acceleraton of 1 gravty, the same emphass has not been gven to the vertcal forces as compared to the horzontal forces. However for structures where stablty s a crteron t may become necessary to take nto account these vertcal forces. 3. Estmaton of loads The sesmc acton s descrbed by means of a standardzed acceleraton response spectrum. The CICIND code suggests a general response spectra. The response spectra s a relaton between the maxmum effectve peak ground acceleraton at the locaton of the 6

3 chmney. Ths s n relaton wth the natural tme perod of the structure and the sol type exstng at the ste. The movement of the chmney s found by calculatng the frst few mode shapes by modal analyss of the chmney. The result of such a modal analyss wll yeld the values for the deflecton, the shear force and the moment. The modal analyss can determne the functons of the deflecton, shear and the moment only up to a constant factor. Thus f the mode shape calculated s known, then a constant tmes the mode shape too s a possble soluton. Hence the actual value of the shear force or the bendng moment s found by multplyng the normalzed response wth a scalng factor. gven by Hence f u s the value of the normalzed mode shape then the true mode shape s u un (3.1) Where they refer to the th mode of vbraton, and N s the scalng factor. The scalng factor s determned by the followng equaton. N pt 4 a ( T ) s (3.) The a s s the response functon descrbed earler. The value of p s obtaned from p h h u ( z) m( z) dz u ( z) m( z) dz (3.3) The code also assumes the vertcal movements to result n a value of resultants that are.3 tmes the horzontal forces. The ACI code also assumes the vertcal component to be neglgble wth respect to the horzontal one. The code also suggests the spectral values for the values of maxmum ground acceleraton. The followng calculatons are based on the IS code. The code used s the IS:

4 Snce the earthquakes occur wthout any warnng, t s very necessary to avod constructon practces that cause sudden falure or brttle falure. The current phlosophy reles heavly on the acton of members to absorb all the vbratonal energy resultng from strong ground moton by desgnng the member to behave n a ductle manner. In ths manner even f an earthquake occurs that s stronger than that whch has been foreseen, total collapse of the buldng can be avoded. Earthquake resstant desgns are generally performed by pseudo-statc analyss, the earthquake loads on the foundatons are consdered as statc loads and hence capable of producng settlement as dead loads. Therefore as the footngs are generally desgned for equal stresses under them, the footngs for exteror columns wll have to be made wder. Permssble ncrease n safe bearng pressure wll have to depend n the solfoundaton system. Where small settlements are lkely to occur larger ncrease can be allowed and vce versa Desgn sesmc coeffcents for dfferent zones The force attracted by any structure durng an earthquake s dynamc n nature and s a functon of the ground moton and the propertes of the structure tself. the domnant effect s equvalent to a horzontal force varyng over the heght of the structure. Therefore the assumpton of a unform force to be appled along one axs at a tme s an oversmplfcaton whch can be justfed for reasons of savng effort n dynamc analyss. However a large number of structures desgned on ths bass have wthstood earthquake shocks n the past. Ths s a justfcaton of a unform sesmc coeffcent n sesmc desgn. In the code, therefore, t s consdered adequate to provde unform sesmc coeffcents to ordnary structures. The IS code suggests two methods for the purpose of evaluaton of the earthquake loads. Ths s smlar to the two methods suggested for the calculaton of across-wnd loads. Both methods calculate the desgn value of the horzontal coeffcent. Sesmc coeffcent method The value of the horzontal sesmc desgn coeffcent shall be calculated usng the followng expresson. 8

5 h I (3.4) 1.5. Where s a coeffcent dependng on the sol type. Ths value vares between 1. and I s the mportance factor. s the basc horzontal sesmc coeffcent. The response spectrum method The response acceleraton s frst obtaned for the natural tme perod and dampng of the structure and the desgn value of horzontal sesmc coeffcent s computed usng the followng expresson. S IF a h g (3.5) Here F s a sesmc zone factor. S a /g s the average acceleraton coeffcent dependng on the natural perod and dampng of the structure. 3.3 Calculatons for a typcal case The calculaton of the earthquake load for a typcal chmney s gven below. The assumptons made are also specfed. The weght data for the case has been taken from the STRAP model of the chmney. Perod of vbraton Dameter of the base =.7 m Base Thckness =.649m Inner dameter at the base s 1.4m Area of cross secton at the base s A d out d n 4 (3.6) 9

6 A = 45. m The moment of nerta at the base s calculated by The value of I = 74.5 m 4 Radus of gyraton r s gven by r = 7.86 I 4 4 (3.7) 64 d out d n Hence the slenderness raton l/r s gven by I r (3.8) A l r 3. (3.9) The coeffcent C T C T 57.8 (3.1) Weght of the chmney Wt D mean TH t (3.11) Weght = kg The perod of vbraton s now gven by Wh t ' T C (3.1) T EAg Substtutng the values the value of T = 15.6 Desgn sesmc coeffcent Usng the Response Spectrum method and the equaton ** a h =.3975 the value assumed are = 1. (assumng a hard/medum sols) I = 1. (mportance factor) 3

7 F =.5 (assumng the chmney to be n the zone IV) Shear force and Bendng moments The desgn shear force at a dstance of X from the top s gven by V 5X ' X ' C W (3.13) V h t 3h' 3h' Where the value of C V has been found to be. for the very large tme perod obtaned. Varyng the value of X from to 5 the profle of the shear force has been calculated kn Fgure 3.1 Shear force due to sesmc loads The bendng moment can be calculated usng the formula M 1 4 X ' X ' hwh t.6.4 h' h' (3.14) 31

8 Agan the value of X s vared and the expresson evaluated. The resultant graph s gven below MNm Fgure 3. Bendng Moment due to sesmc loads As can be seen from the graph, the maxmum moment at the base of the chmney s about 8 MNm. 3.4 Conclusons The reasons and assumptons nvolved n the evaluaton of earthquake loads have been studed. The codal provsons for the calculaton of the same have been understood. A sample calculaton has been done to calculate the shear force and bendng moment caused due to earthquake loadng on chmneys. The loads n ths case have been found to be sgnfcantly lower that those obtaned n the wnd analyss. Hence earthquake loads do not normally form the man loads to be consdered for desgn. 3