solving transportation problems using modi method[Linear Programming]
Description : Skrill Method
Full description
Descripción: DUDUK FLUTE ARMENIAN METHOD
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RANKINE¶S THEORY FOR FAILURE OF COLUMNS OF ANY LENGTH p
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(21.27) n wh h 0 a cons an ha depends upon he ma era of he coumn. The faures ress n compresson, , of a coumn of any eng h s hen, from Eq. (21.27) (21.28)
No e ha for a coumn of a g en ma era s a func on of he senderness ra o, e.
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E E TED W T P T L7 ÷oowng are he man concep s and heores whch are assoca ed w h hs prac ca c c c c c c c c
oumn V ru Ydea and rea coumn assfca on of coumns ond ons of equbrum Buckng of coumn fference be ween coapse and s ab y Euer¶s heory of buckng for ong coumns
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Ê 6 or n arch ec ure and s ruc ura engneerng s a ver ca s ruc ura eemen ha ransm s, hrough compresson, he wegh of he s ruc ure above o o her s ruc ura eemen s beow. ÷or he purpose of wnd or ear hquake engneerng, coumns may be desgned o ress a era forces.
oumns
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Ê s a s ruc ura componen desgned o ress ong udna compresson. V ru s provde ou wards-facng suppor n her eng hwse drec on, whch can be
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used o keep wo o her componen s separa e, performng he oppos e func on of a × . They are commony used n arch ec ure and engneerngc c
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Ê coumn whch does no show any defec on a he cr ca oad for ha coumn .e. Pcr s known as an dea coumn. Yn our rea fe no coumn s an dea coumn. Ênd a coumn whch shows some defec on even a mnor one when cr ca oad s apped o s caed a rea coumn.
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When comes o he cassfca on of coumns, we have 3 dfferen s andards on he bass of whch we can cassfy and ds ngush he coumns. c *c cLDc Yn hs ra o Le represen s he effec ve eng h of he coumn and represen s he eas dmenson of he par. On he bass of hs ra o coumns are o be dvded n hree ca egores. ñc Vhor coumns (LDcra o s ess han 4) ñc Yn ermeda e coumns (LDcra o s n be ween 4 & 30) ñc Long coumns (LDc ra o s grea er han 30) c *c cc Venderness ra o s he ra o be ween effec ve eng h and radus of gyra on of he coumn. Usuay eas radus of gyra on s used for hs equa on as he coumn bucke aong he axs where here s eas vaue of r and maxmum vaue of senderness ra o. Ths ra o can be ma hema cay expressed as cccccccccccccccccccccccccccccccc Vc
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On he bass of hs ra o coumns are dvded n hree ca egores whch are gven as under. ñc Vhor coumn (senderness ra o s ess han 30) ñc Long coumn (senderness ra o s grea er han c) ñc Yn ermeda e coumn (senderness ra o may vary from 30-100 or c) Where he genera formuae for c = ë
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6 c *c c66 6 c c On he bass of hs s andard coumns are o be dvded n 2 ca egores ñc oumn w h concen rc oadng ñc oumn w h eccen rc oadng
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Yn he coumns w h concen rc oadng oad ac s a he cen rod of he coumn and hence ony norma s ress s produced n he coumn. Whe n coumns w h eccen rc oadng oad ac s a any o her pon ra her han he cen rod of he coumn and hence no ony causes norma s ress bu aso causes momen due o eccen rc y.
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Thc c6 c c:c ccc Thc6 c6 c c:c cc c When bo h of hese cond ons are sa sfed n s a c sys ems a forces and orques sum o zero c When appyng he second cond on we are free o choose any axs abou whch o compu e orques. Y s bes o choose an axs ha emna es one or more forces ha have nes of force ha pass hrough .
º c *LY c ccLc c When a perfec coumn s subjec ed o a compressve axa force as shown n ÷gure 1, he ony deforma on ha akes pace s a shor enng of he coumn. ÷or ow vaues of ÷, f he coumn were o be defec ed a eray by a force perpendcuar o he coumn, and he a era force hereaf er removed, he coumn woud re urn o s s ragh pos on, even w h he force ÷ remanng n pace. Ths ndca es a cond on of s ab y. Yf he oad ÷ were ncreased, here s a vaue of ÷ for whch, when he a era oad s removed, he coumn woud reman n he deformed shape. Ths cond on s referred o as buckng and he coumn s sad o have faed from a s ruc ura s andpon . Ên exampe s gven n ÷gure 1, where he coumn faure was due o an ear hquake. Buckng can aso be descrbed n smpe erms as bendng or bowng of a coumn due o a compressve oad. Ths s us ra ed n ÷gure 2.
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To 6 means break down suddeny n s reng h and hereby cease o func on. ÷or a s ruc ure foowng may be he reasons of coapse of a s ruc ure. Jc Jc Jc Jc Jc Jc
Bad esgn ÷au y ons ruc on ÷ounda on ÷aure Ex raordnary Loads Unexpec ed ÷aure Modes ombna on of auses
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ERIVATION OF EULER¶S FORMULAE
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ENERGY METHO FOR THE CALCULATION OF *UCKLING LOAS IN COLUMNS (RAYLEIGH±RITZ METHO ! ' ' Y : 3
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