Soluzioni di travi elementari variamente caricate

SOLUZIONI DI TRAVI ELEMENTARI VARIAMENTE CARICATEABTravi con doppio incastrolCARICHI ESTERNIPABMAMBVAVBab22Pb= (l 2a) ; PaVB = (l + 2b)3ll22PabMA= − ; Pa bM2 B=2llVA +3ATravi con incastro e cernieralCARICHI ESTERNIPABM A11V A= P ; 5V B= P16 16V A V B3M A= Pl16l/2l/2BMAAVAl/2Pl/2VBBMBV = VA B=MA= MB=P2Pl8q5ABV A= ql; 3V B= qlM A8 82qlV A V BMA =8MAqAVAVBBMBV = VA B=MA= MB=ql22ql12q2AB V A= ql ; qlV B=M A5 102qlV A V BMA =15M AMAMAMAMAMAMAqAV AaAVAAVAaAVAl/2AAAVAVAMttbMl/2bV BqVBVBVBBBBBBM BMBMBMBMB2 3qa ⎛ 2a a ⎞ ;V = ⎜ +⎟A2-2 32 ⎝ l l ⎠3AMBqa ⎛ a ⎞V = ⎜2 -MB 2⎟A 9 MV2l ⎝ lA= −VB=⎠8 lV2A V B2⎛1 2a a ⎞;MM = −⎜ +⎟Aqa -M2A=⎝ 2 3l 4l ⎠l/2 l/2822⎛a a ⎞M = −⎜ −⎟Bqa2⎝ 3l 4l ⎠3V A= ql ; 7AM B3 MV B= qlM A VA = −VB=20 202 l1 2MA= ql ; 1 2MB= qlV A V BMM A=30 2026MabVA= −VB= −3lA B3 α∆tEJMAtb ⎛ bVA= −VB=⎞ ;M A= M ⎜ 2 − 3 ⎟2 lhtl ⎝ l ⎠VAVB3 α∆tEJMa ⎛ aA=⎞2 hM B= −M⎜2− 3 ⎟l ⎝ l ⎠DISTORSIONI VINCOLARI3 MVA = −VB=AB3ϕEJ2 lMAVA= −VB=2MlMA = MB=VAVB3ϕEJ4M A=lMA= −MBα∆tEJ=hDISTORSIONI VINCOLARIB6ϕEJVMB A= −VB=2lVB4ϕEJM A= ; 2ϕEJM B=llB12∆EJMBVA= −VB=3lVB6∆EJMA= MB=2lMAAVAVBB3∆EJVA= −VB=3l3∆EJMA=2lAB3∆EJM AVA= −VB=3lV A V B3∆EJMA=2l

Travi con incastro e doppiopendoloAlBMAAVAl/2Pl/2CARICHI ESTERNIBMBV A= P3M A= Pl ; PlM B=8 8MAADISTORSIONI VINCOLARIBMBMA= −MBϕEJ=lMAAVAPBMBV A= PMA = MB=Pl2ABMAqAVABMBV A= ql2qlM = ;AM3B =ql62MAMAqAAVAl/2Ml/2BBqlV A=MB 22qlM = ;A8MBMA = MB=MM2B =2ql24MAAttBMBM = −MABα∆tEJ=h