T2

‫ﺗﻤﺮﻳﻦ ‪ 2‬ﮔﺮوه ‪1‬‬

‫‪t.m‬‬

‫‪8‬‬

‫‪7‬‬

‫‪5‬‬

‫‪3‬‬

‫‪2‬‬

‫‪1‬‬

‫ﻣﺤﺎﺳﺒﻪ ﻟﻨﮕﺮ ﻣﻘﺎوم‬

‫ﻣﺤﺎﺳﺒﻪ ‪Fv‬‬

‫ﻣﺤﺎﺳﺒﻪ ‪Fb‬‬

‫ﻛﻨﺘﺮل ﻛﻔﺎﻳﺖ ﺗﻜﻴﻪ ﮔﺎه ﺟﺎﻧﺒﻲ‬

‫ﻣﺸﺨﺼﺎت ﻫﻨﺪﺳﻲ ﻣﻘﻄﻊ‬

‫ﻣﺸﺨﺼﺎت ﻣﺼﺎﻟﺢ‬

‫‪=Sx*F'b‬‬

‫ﻟﻨﮕﺮ ﻣﻘﺎوم‬

‫‪223.57‬‬

‫ﻟﻨﮕﺮ ﻣﻘﺎوم‬

‫‪63.7‬‬

‫= ‪3185/eFy‬‬

‫‪-‬‬

‫= )‪Fb (kg/cm 2‬‬

‫ﺗﻜﻴﻪ ﮔﺎه ‪ +‬ﻏﻴﺮ ﻓﺸﺮدﮔﻲ‬

‫‪452‬‬

‫= ‪1400000 / (d/Af) / Fy‬‬

‫= ) ‪Lc2(cm‬‬

‫‪370‬‬

‫= )‪Ag (cm 2‬‬

‫ﻣﺴﺎﺣﺖ ﻣﻘﻄﻊ‬

‫ﺷﺮط ﻛﻔﺎﻳﺖ ﺗﻜﻴﻪ ﮔﺎه ﺟﺎﻧﺒﻲ‬

‫‪125‬‬

‫= )‪Af (cm 2‬‬

‫ﻣﺴﺎﺣﺖ ﺑﺎل‬

‫‪120‬‬

‫= )‪Aw (cm 2‬‬

‫‪290.5‬‬

‫= ) ‪w/l (kg/m‬‬

‫‪1,678,646‬‬

‫= )‪Ix (cm 4‬‬

‫‪2,500‬‬

‫= )‪Fyw (kg/cm 2‬‬

‫ﺗﻨﺶ ﺗﺴﻠﻴﻢ ﺟﺎن‬

‫‪-‬‬

‫‪225.06‬‬

‫ﻟﻨﮕﺮ ﻣﻮﺟﻮد‬

‫‪187.5‬‬

‫=‪hw/tw‬‬

‫‪-‬‬

‫= )‪Fb (kg/cm 2‬‬

‫ﺗﻜﻴﻪ ﮔﺎه ‪ +‬ﻓﺸﺮدﮔﻲ‬

‫‪635‬‬

‫= )‪635 bf / S(Fy‬‬

‫= ) ‪Lc1(cm‬‬

‫‪155‬‬

‫= ) ‪d(cm‬‬

‫ارﺗﻔﺎع ﻛﻠﻲ ﻧﻴﻤﺮخ‬

‫‪2,500‬‬

‫= )‪Fyf (kg/cm 2‬‬

‫ﺗﻨﺶ ﺗﺴﻠﻴﻢ ﺑﺎل‬

‫‪t.m‬‬

‫‪1.007‬‬

‫ﺑﺪون ﺗﻘﻮﻳﺖ ﻛﻨﻨﺪه ﻋﺮﺿﻲ‬

‫‪-‬‬

‫ﻧﺴﺐ ﺗﻨﺶ ﺧﻤﺸﻲ‬

‫‪9‬‬

‫ﻋﺪم ﻛﻔﺎﻳﺖ ﺗﻜﻴﻪ ﮔﺎه‬

‫ﺑﺎ ﺗﻘﻮﻳﺖ ﻛﻨﻨﺪه ﻋﺮﺿﻲ‬

‫‪104.5‬‬

‫‪16.3‬‬

‫=‪Kv‬‬

‫‪0.6‬‬

‫=‪Cv‬‬

‫‪if Cv < .8 then‬‬

‫‪No‬‬

‫)‪Lb < Min( Lc1 , Lc2‬‬

‫= ‪Lb /rT‬‬

‫‪53.7‬‬

‫= )‪S(7200000*Cb /Fy‬‬

‫‪4‬‬

‫‪120.0‬‬

‫= )‪S(36000000*Cb /Fy‬‬

‫ﻛﻨﺘﺮل ﻓﺸﺮدﮔﻲ‬

‫اﺑﻌﺎد ﻣﻘﻄﻊ‬

‫ﻣﺴﺎﺣﺖ ﺟﺎن‬

‫‪150‬‬

‫= ) ‪hw (cm‬‬

‫ارﺗﻔﺎع ﺟﺎن‬

‫وزن واﺣﺪ ﻃﻮل‬

‫‪0.8‬‬

‫= ) ‪tw (cm‬‬

‫ﺿﺨﺎﻣﺖ ﺟﺎن‬

‫ﻣﻤﺎن اﻳﺘﺮﺳﻲ ﻗﻮي‬

‫‪50‬‬

‫= ) ‪bf (cm‬‬

‫ﻋﺮض ﺑﺎل‬

‫‪503.8062284‬‬ ‫ﻣﺤﺎﺳﺒﻪ ﺑﺮش ﻣﻘﺎوم‬

‫‪t‬‬

‫ﺑﺮش ﻣﻮﺟﻮد‬

‫‪60.69‬‬

‫‪=Av*Fv‬‬

‫‪t‬‬

‫ﻣﺴﺎﺣﺖ ﻣﻘﺎوم ﺑﺮﺷﻲ‬

‫‪60.46‬‬

‫‪1.004‬‬

‫‪0.69‬‬

‫‪504‬‬

‫= )‪Fv (kg/cm 2‬‬

‫=‪Cv‬‬

‫‪1,032 if Cv >= .8 then‬‬

‫‪484‬‬

‫‪1,032‬‬

‫= )‪Fb1 (kg/cm2‬‬

‫‪10.0‬‬

‫= ‪(bf/2)/tf‬‬

‫= )‪Fb2 (kg/cm2‬‬

‫‪187.5‬‬

‫= ‪hw /tw‬‬

‫‪10.9‬‬

‫= ‪545 / SFy‬‬

‫ﻣﺮز ﻓﺸﺮدﮔﻲ ‪ -‬ﻏﻴﺮ ﻓﺸﺮدﮔﻲ ﺑﺎل‬

‫‪107.3‬‬

‫= ‪5365 / SFy‬‬

‫ﻣﺮز ﻓﺸﺮدﮔﻲ ‪ -‬ﻏﻴﺮ ﻓﺸﺮدﮔﻲ ﺟﺎن ‪11.87‬‬

‫= )‪Fb (kg/cm 2‬‬

‫ﺑﺮش ﻣﻘﺎوم‬

‫ﻧﺴﺐ ﺗﻨﺶ ﺑﺮﺷﻲ‬

‫‪6‬‬

‫‪6370/SFb‬‬

‫‪10‬‬

‫وزن واﺣﺪ ﻃﻮل‬

‫‪290.5‬‬

‫‪187.5‬‬

‫= ‪hw /tw‬‬

‫‪198‬‬

‫= ‪6370 / SFb‬‬

‫‪-‬‬

‫> ‪hw/tw‬‬

‫ﻻﻏﺮي ﻃﻮل آزاد ﺑﺎل‬

‫‪21,660‬‬

‫= )‪Sx (cm 3‬‬

‫ﻻﻏﺮي ﺟﺎن‬

‫‪67.36‬‬

‫= ) ‪rx (cm‬‬

‫ﺷﻌﺎع ژﻳﺮاﺳﻴﻮن ﻗﻮي‬

‫‪52,090‬‬

‫= )‪Iy (cm 4‬‬

‫ﻣﻤﺎن اﻳﺘﺮﺳﻲ ﺿﻌﻴﻒ‬

‫= ) ‪ry (cm‬‬

‫ﻣﺪول ﻣﻘﻄﻊ ﻗﻮي‬

‫= ) ‪tf (cm‬‬

‫‪2.5‬‬

‫ﺷﺮاﻳﻂ ﺗﻜﻴﻪ ﮔﺎﻫﻲ‬

‫= ) ‪Lb (cm‬‬

‫‪1,400‬‬

‫ﺷﻌﺎع ژﻳﺮاﺳﻴﻮن ﺿﻌﻴﻒ ‪if required‬‬

‫‪11.4‬‬

‫= )‪795 / S(Fy/Kc‬‬

‫ﻣﺮز ﻏﻴﺮ ﻓﺸﺮدﮔﻲ ‪ -‬ﻻﻏﺮي ﺑﺎل‬

‫‪26,043‬‬

‫= )‪IT (cm 4‬‬

‫ﻣﻤﺎن اﻳﺘﺮﺳﻲ‪T‬‬

‫‪198.3‬‬

‫= ‪6370 / SFb‬‬

‫ﻣﺮز ﻏﻴﺮ ﻓﺸﺮدﮔﻲ ‪ -‬ﻻﻏﺮي ﺟﺎن‬

‫‪145‬‬

‫= )‪AT (cm 2‬‬

‫ﻣﺴﺎﺣﺖ ﻣﻘﻄﻊ ‪T‬‬

‫ﺳﺮاﺳﺮي‬

‫ﻓﺸﺮدﮔﻲ‬

‫‪13.40‬‬

‫= ) ‪rT (cm‬‬

‫ﺷﻌﺎع ژﻳﺮاﺳﻴﻮن ‪T‬‬

‫ﺳﺎده‬

‫ﻏﻴﺮ ﻓﺸﺮدﮔﻲ‬

‫‪1.13‬‬

‫= ‪r T /r y‬‬

‫‪0.51‬‬

‫= ‪Kc‬‬

‫‪Ok‬‬

‫= )‪Fb ' (kg/cm 2‬‬

‫ﻧﺴﺒﺖ ‪ rT‬ﺑﻪ ‪ry‬‬

‫ﺿﺨﺎﻣﺖ ﺑﺎل‬

‫اﻟﺰام اﺳﺘﻔﺎده از ﺳﺨﺖ ﻛﻨﻨﺪه )‪(hw/tw> 260‬‬

‫= ) ‪a (cm‬‬

‫‪100.0‬‬

‫ﻓﺎﺻﻠﻪ دو ﺗﻜﻴﻪ ﮔﺎه ﺟﺎﻧﺒﻲ‬

‫)ﺳﺮاﺳﺮي‪/‬ﻣﻨﻘﻄﻊ(‬

‫)ﺳﺎده‪/‬ﻣﻀﺎﻋﻒ(‬

‫ﻓﺎﺻﻠﻪ ﺧﺎﻟﺺ دو ﺳﺨﺖ ﻛﻨﻨﺪه‬

‫اﺗﺼﺎل ﺑﺎل و ﺟﺎن‬

‫اﻧﺤﻨﺎي ﻋﻀﻮ‬

‫‪-‬‬

‫= |‪|M1‬‬

‫ﻟﻨﮕﺮ ﻛﻮﭼﻚ در ﺗﻜﻴﻪ ﮔﺎه‬

‫‪216.80‬‬

‫= |‪|M2‬‬

‫ﻟﻨﮕﺮ ﺑﺰرگ در ﺗﻜﻴﻪ ﮔﺎه‬

‫ﻻﻏﺮي‬

‫= ‪a/hw‬‬

‫‪0.67‬‬

‫‪325.6‬‬

‫=)‪985000/ S((Fy+1160)Fy‬‬

‫‪335.4‬‬

‫= ‪16770 / SFy‬‬

‫ﻧﺪارد ﻳﺎ ‪a/hw>1.5‬‬

‫‪a/hw <= 1.5‬‬

‫‪hw/tw < 16770/sqrt‬‬ ‫)‪q (Fyy‬‬

‫‪335.4‬‬

‫<‬

‫‪187.5‬‬

‫‪1.00‬‬

‫= ‪Cb‬‬

‫)ﺑﻠﻪ ‪ /‬ﺧﻴﺮ(‬

‫ﺑﻠﻪ‬

‫‪t.m‬‬ ‫‪t‬‬

‫ﻟﻨﮕﺮ ﺑﺰرﮔﺘﺮ ﻣﻴﺎﻧﻲ‬

‫‪225.06‬‬

‫ﻟﻨﮕﺮ ﻣﻮﺟﻮد‬

‫‪60.69‬‬

‫ﺑﺮش ﻣﻮﺟﻮد‬

‫ﺗﻤﺮﻳﻦ ‪ 2‬ﮔﺮوه ‪2‬‬

‫‪t.m‬‬

‫‪8‬‬

‫‪7‬‬

‫‪5‬‬

‫‪3‬‬

‫‪2‬‬

‫‪1‬‬

‫ﻣﺤﺎﺳﺒﻪ ﻟﻨﮕﺮ ﻣﻘﺎوم‬

‫ﻣﺤﺎﺳﺒﻪ ‪Fv‬‬

‫ﻣﺤﺎﺳﺒﻪ ‪Fb‬‬

‫ﻛﻨﺘﺮل ﻛﻔﺎﻳﺖ ﺗﻜﻴﻪ ﮔﺎه ﺟﺎﻧﺒﻲ‬

‫ﻣﺸﺨﺼﺎت ﻫﻨﺪﺳﻲ ﻣﻘﻄﻊ‬

‫ﻣﺸﺨﺼﺎت ﻣﺼﺎﻟﺢ‬

‫‪=Sx*F'b‬‬

‫ﻟﻨﮕﺮ ﻣﻘﺎوم‬

‫‪300.79‬‬

‫ﻟﻨﮕﺮ ﻣﻘﺎوم‬

‫‪63.7‬‬

‫= ‪3185/eFy‬‬

‫‪-‬‬

‫= )‪Fb (kg/cm2‬‬

‫ﺗﻜﻴﻪ ﮔﺎه ‪ +‬ﻏﻴﺮ ﻓﺸﺮدﮔﻲ‬

‫‪452‬‬

‫= ‪1400000 / (d/Af) / Fy‬‬

‫= )‪Lc2(cm‬‬

‫‪370‬‬

‫= )‪Ag (cm2‬‬

‫ﻣﺴﺎﺣﺖ ﻣﻘﻄﻊ‬

‫ﺷﺮط ﻛﻔﺎﻳﺖ ﺗﻜﻴﻪ ﮔﺎه ﺟﺎﻧﺒﻲ‬

‫‪125‬‬

‫= )‪Af (cm2‬‬

‫ﻣﺴﺎﺣﺖ ﺑﺎل‬

‫‪120‬‬

‫= )‪Aw (cm2‬‬

‫‪290.5‬‬

‫= )‪w/l (kg/m‬‬

‫‪1,678,646‬‬

‫‪2,500‬‬

‫= )‪Fyw (kg/cm2‬‬

‫ﺗﻨﺶ ﺗﺴﻠﻴﻢ ﺟﺎن‬

‫‪-‬‬

‫‪300.32‬‬

‫ﻟﻨﮕﺮ ﻣﻮﺟﻮد‬

‫‪187.5‬‬

‫=‪hw/tw‬‬

‫‪-‬‬

‫= )‪Fb (kg/cm2‬‬

‫ﺗﻜﻴﻪ ﮔﺎه ‪ +‬ﻓﺸﺮدﮔﻲ‬

‫‪635‬‬

‫= )‪635 bf / S(Fy‬‬

‫= )‪Lc1(cm‬‬

‫‪155‬‬

‫= )‪d(cm‬‬

‫ارﺗﻔﺎع ﻛﻠﻲ ﻧﻴﻤﺮخ‬

‫‪2,500‬‬

‫= )‪Fyf (kg/cm2‬‬

‫ﺗﻨﺶ ﺗﺴﻠﻴﻢ ﺑﺎل‬

‫‪t.m‬‬

‫‪0.998‬‬

‫‪-‬‬

‫ﺑﺪون ﺗﻘﻮﻳﺖ ﻛﻨﻨﺪه ﻋﺮﺿﻲ‬

‫ﻧﺴﺐ ﺗﻨﺶ ﺧﻤﺸﻲ‬

‫‪9‬‬

‫ﻋﺪم ﻛﻔﺎﻳﺖ ﺗﻜﻴﻪ ﮔﺎه‬

‫ﺑﺎ ﺗﻘﻮﻳﺖ ﻛﻨﻨﺪه ﻋﺮﺿﻲ‬

‫‪89.5‬‬

‫‪No‬‬

‫)‪Lb < Min( Lc1 , Lc2‬‬

‫= ‪Lb /rT‬‬

‫اﺑﻌﺎد ﻣﻘﻄﻊ‬

‫ﻣﺴﺎﺣﺖ ﺟﺎن‬

‫‪150‬‬

‫= )‪hw (cm‬‬

‫ارﺗﻔﺎع ﺟﺎن‬

‫وزن واﺣﺪ ﻃﻮل‬

‫‪0.8‬‬

‫= )‪tw (cm‬‬

‫ﺿﺨﺎﻣﺖ ﺟﺎن‬

‫= )‪Ix (cm4‬‬

‫ﻣﻤﺎن اﻳﺘﺮﺳﻲ ﻗﻮي‬

‫‪50‬‬

‫= )‪bf (cm‬‬

‫ﻋﺮض ﺑﺎل‬

‫= )‪Fb1 (kg/cm2‬‬

‫‪10.0‬‬

‫= ‪(bf/2)/tf‬‬

‫ﻻﻏﺮي ﻃﻮل آزاد ﺑﺎل‬

‫‪21,660‬‬

‫= ) ‪Sx (cm‬‬

‫ﻣﺪول ﻣﻘﻄﻊ ﻗﻮي‬

‫= )‪tf (cm‬‬

‫ﺿﺨﺎﻣﺖ ﺑﺎل‬

‫= )‪Fb2 (kg/cm2‬‬

‫‪187.5‬‬

‫= ‪hw /tw‬‬

‫ﻻﻏﺮي ﺟﺎن‬

‫‪67.36‬‬

‫= )‪rx (cm‬‬

‫ﺷﻌﺎع ژﻳﺮاﺳﻴﻮن ﻗﻮي‬

‫‪10.9‬‬

‫= ‪545 / SFy‬‬

‫ﻣﺮز ﻓﺸﺮدﮔﻲ ‪ -‬ﻏﻴﺮ ﻓﺸﺮدﮔﻲ ﺑﺎل‬

‫‪52,090‬‬

‫= )‪Iy (cm4‬‬

‫ﻣﻤﺎن اﻳﺘﺮﺳﻲ ﺿﻌﻴﻒ‬

‫‪107.3‬‬

‫= ‪5365 / SFy‬‬

‫ﻣﺮز ﻓﺸﺮدﮔﻲ ‪ -‬ﻏﻴﺮ ﻓﺸﺮدﮔﻲ ﺟﺎن‬

‫‪11.87‬‬

‫= )‪ry (cm‬‬

‫ﺷﻌﺎع ژﻳﺮاﺳﻴﻮن ﺿﻌﻴﻒ‬

‫‪11.4‬‬

‫= )‪795 / S(Fy/Kc‬‬

‫ﻣﺮز ﻏﻴﺮ ﻓﺸﺮدﮔﻲ ‪ -‬ﻻﻏﺮي ﺑﺎل‬

‫‪26,043‬‬

‫= )‪IT (cm4‬‬

‫ﻣﻤﺎن اﻳﺘﺮﺳﻲ‪T‬‬

‫‪170.2‬‬

‫= ‪6370 / SFb‬‬

‫ﻣﺮز ﻏﻴﺮ ﻓﺸﺮدﮔﻲ ‪ -‬ﻻﻏﺮي ﺟﺎن‬

‫‪145‬‬

‫= )‪AT (cm2‬‬

‫ﻣﺴﺎﺣﺖ ﻣﻘﻄﻊ ‪T‬‬

‫ﺳﺮاﺳﺮي‬

‫ﻓﺸﺮدﮔﻲ‬

‫‪13.40‬‬

‫= )‪rT (cm‬‬

‫ﺷﻌﺎع ژﻳﺮاﺳﻴﻮن ‪T‬‬

‫ﺳﺎده‬

‫ﻏﻴﺮ ﻓﺸﺮدﮔﻲ‬

‫‪1.13‬‬

‫= ‪rT /ry‬‬

‫‪0.51‬‬

‫= ‪Kc‬‬

‫‪16.3‬‬

‫=‪Kv‬‬

‫‪71.0‬‬

‫= )‪S(7200000*Cb /Fy‬‬

‫‪4‬‬

‫‪0.6‬‬

‫=‪if Cv < .8 then Cv‬‬

‫‪158.7‬‬

‫= )‪S(36000000*Cb /Fy‬‬

‫ﻛﻨﺘﺮل ﻓﺸﺮدﮔﻲ‬

‫‪503.8062284‬‬ ‫ﻣﺤﺎﺳﺒﻪ ﺑﺮش ﻣﻘﺎوم‬

‫‪t‬‬

‫ﺑﺮش ﻣﻮﺟﻮد‬

‫‪58.41‬‬

‫‪=Av*Fv‬‬

‫‪t‬‬

‫ﻣﺴﺎﺣﺖ ﻣﻘﺎوم ﺑﺮﺷﻲ‬

‫‪60.46‬‬

‫‪0.69‬‬

‫‪504‬‬

‫= )‪Fv (kg/cm2‬‬

‫=‪Cv‬‬

‫‪1,400 if Cv >= .8 then‬‬

‫‪988‬‬

‫‪1,400‬‬

‫= )‪Fb (kg/cm2‬‬

‫ﺑﺮش ﻣﻘﺎوم‬

‫‪0.966‬‬

‫ﻧﺴﺐ ﺗﻨﺶ ﺑﺮﺷﻲ‬

‫‪6‬‬

‫‪6370/SFb‬‬

‫‪10‬‬

‫وزن واﺣﺪ ﻃﻮل‬

‫‪290.5‬‬

‫‪187.5‬‬

‫= ‪hw /tw‬‬

‫‪170‬‬

‫= ‪6370 / SFb‬‬

‫‪1,389‬‬

‫= )‪Fb ' (kg/cm2‬‬

‫> ‪hw/tw‬‬

‫‪3‬‬

‫ﻧﺴﺒﺖ ‪ rT‬ﺑﻪ ‪ry‬‬

‫‪2.5‬‬

‫ﺷﺮاﻳﻂ ﺗﻜﻴﻪ ﮔﺎﻫﻲ‬

‫= )‪Lb (cm‬‬

‫‪1,200‬‬

‫‪if required‬‬

‫اﻟﺰام اﺳﺘﻔﺎده از ﺳﺨﺖ ﻛﻨﻨﺪه )‪(hw/tw> 260‬‬

‫= )‪a (cm‬‬

‫‪100.0‬‬

‫ﻓﺎﺻﻠﻪ دو ﺗﻜﻴﻪ ﮔﺎه ﺟﺎﻧﺒﻲ‬

‫)ﺳﺮاﺳﺮي‪/‬ﻣﻨﻘﻄﻊ(‬

‫)ﺳﺎده‪/‬ﻣﻀﺎﻋﻒ(‬

‫ﻓﺎﺻﻠﻪ ﺧﺎﻟﺺ دو ﺳﺨﺖ ﻛﻨﻨﺪه‬

‫اﺗﺼﺎل ﺑﺎل و ﺟﺎن‬

‫اﻧﺤﻨﺎي ﻋﻀﻮ‬

‫‪-‬‬

‫= |‪|M1‬‬

‫ﻟﻨﮕﺮ ﻛﻮﭼﻚ در ﺗﻜﻴﻪ ﮔﺎه‬

‫‪300.32‬‬

‫= |‪|M2‬‬

‫ﻟﻨﮕﺮ ﺑﺰرگ در ﺗﻜﻴﻪ ﮔﺎه‬

‫ﻻﻏﺮي‬

‫= ‪a/hw‬‬

‫‪0.67‬‬

‫‪325.6‬‬

‫=)‪985000/ S((Fy+1160)Fy‬‬

‫‪335.4‬‬

‫= ‪16770 / SFy‬‬

‫ﻧﺪارد ﻳﺎ ‪a/hw>1.5‬‬

‫‪a/hw <= 1.5‬‬

‫)‪hw/tw < 16770/sqrt(Fy‬‬

‫‪335.4‬‬

‫<‬

‫‪187.5‬‬

‫ﺟﺎن ﺗﻴﺮ ﻻﻏﺮ اﺳﺖ‪.‬‬

‫‪1.75‬‬

‫= ‪Cb‬‬

‫)ﺑﻠﻪ ‪ /‬ﺧﻴﺮ(‬

‫ﺧﻴﺮ‬

‫‪t.m‬‬ ‫‪t‬‬

‫ﻟﻨﮕﺮ ﺑﺰرﮔﺘﺮ ﻣﻴﺎﻧﻲ‬

‫‪300.32‬‬

‫ﻟﻨﮕﺮ ﻣﻮﺟﻮد‬

‫‪58.41‬‬

‫ﺑﺮش ﻣﻮﺟﻮد‬

‫ﺗﻤﺮﻳﻦ ‪ 2‬ﮔﺮوه ‪3‬‬

‫‪t.m‬‬

‫‪8‬‬

‫‪7‬‬

‫‪5‬‬

‫‪3‬‬

‫‪2‬‬

‫‪1‬‬

‫ﻣﺤﺎﺳﺒﻪ ﻟﻨﮕﺮ ﻣﻘﺎوم‬

‫ﻣﺤﺎﺳﺒﻪ ‪Fv‬‬

‫ﻣﺤﺎﺳﺒﻪ ‪Fb‬‬

‫ﻛﻨﺘﺮل ﻛﻔﺎﻳﺖ ﺗﻜﻴﻪ ﮔﺎه ﺟﺎﻧﺒﻲ‬

‫ﻣﺸﺨﺼﺎت ﻫﻨﺪﺳﻲ ﻣﻘﻄﻊ‬

‫ﻣﺸﺨﺼﺎت ﻣﺼﺎﻟﺢ‬

‫‪=Sx*F'b‬‬

‫ﻟﻨﮕﺮ ﻣﻘﺎوم‬

‫‪349.61‬‬

‫ﻟﻨﮕﺮ ﻣﻘﺎوم‬

‫‪63.7‬‬

‫= ‪3185/eFy‬‬

‫‪-‬‬

‫= )‪Fb (kg/cm2‬‬

‫ﺗﻜﻴﻪ ﮔﺎه ‪ +‬ﻏﻴﺮ ﻓﺸﺮدﮔﻲ‬

‫‪412‬‬

‫= ‪1400000 / (d/Af) / Fy‬‬

‫= )‪Lc2(cm‬‬

‫‪382‬‬

‫= )‪Ag (cm2‬‬

‫ﻣﺴﺎﺣﺖ ﻣﻘﻄﻊ‬

‫ﺷﺮط ﻛﻔﺎﻳﺖ ﺗﻜﻴﻪ ﮔﺎه ﺟﺎﻧﺒﻲ‬

‫‪125‬‬

‫= )‪Af (cm2‬‬

‫ﻣﺴﺎﺣﺖ ﺑﺎل‬

‫‪132‬‬

‫= )‪Aw (cm2‬‬

‫‪299.9‬‬

‫= )‪w/l (kg/m‬‬

‫‪2,053,121‬‬

‫‪2,500‬‬

‫= )‪Fyw (kg/cm2‬‬

‫ﺗﻨﺶ ﺗﺴﻠﻴﻢ ﺟﺎن‬

‫‪-‬‬

‫‪349.62‬‬

‫ﻟﻨﮕﺮ ﻣﻮﺟﻮد‬

‫‪206.3‬‬

‫=‪hw/tw‬‬

‫‪-‬‬

‫= )‪Fb (kg/cm2‬‬

‫ﺗﻜﻴﻪ ﮔﺎه ‪ +‬ﻓﺸﺮدﮔﻲ‬

‫‪635‬‬

‫= )‪635 bf / S(Fy‬‬

‫= )‪Lc1(cm‬‬

‫‪170‬‬

‫= )‪d(cm‬‬

‫ارﺗﻔﺎع ﻛﻠﻲ ﻧﻴﻤﺮخ‬

‫‪2,500‬‬

‫= )‪Fyf (kg/cm2‬‬

‫ﺗﻨﺶ ﺗﺴﻠﻴﻢ ﺑﺎل‬

‫‪t.m‬‬

‫‪1.000‬‬

‫‪-‬‬

‫ﺑﺪون ﺗﻘﻮﻳﺖ ﻛﻨﻨﺪه ﻋﺮﺿﻲ‬

‫ﻧﺴﺐ ﺗﻨﺶ ﺧﻤﺸﻲ‬

‫‪9‬‬

‫ﻋﺪم ﻛﻔﺎﻳﺖ ﺗﻜﻴﻪ ﮔﺎه‬

‫‪No‬‬

‫)‪Lb < Min( Lc1 , Lc2‬‬

‫ﻣﺴﺎﺣﺖ ﺟﺎن‬

‫‪165‬‬

‫= )‪hw (cm‬‬

‫ارﺗﻔﺎع ﺟﺎن‬

‫وزن واﺣﺪ ﻃﻮل‬

‫‪0.8‬‬

‫= )‪tw (cm‬‬

‫ﺿﺨﺎﻣﺖ ﺟﺎن‬

‫= )‪Ix (cm4‬‬

‫ﻣﻤﺎن اﻳﺘﺮﺳﻲ ﻗﻮي‬

‫‪50‬‬

‫= )‪bf (cm‬‬

‫ﻋﺮض ﺑﺎل‬

‫‪1,479 if Cv >= .8 then‬‬

‫= )‪Fb1 (kg/cm2‬‬

‫‪10.0‬‬

‫= ‪(bf/2)/tf‬‬

‫ﻻﻏﺮي ﻃﻮل آزاد ﺑﺎل‬

‫‪24,154‬‬

‫= ) ‪Sx (cm‬‬

‫ﻣﺪول ﻣﻘﻄﻊ ﻗﻮي‬

‫= )‪tf (cm‬‬

‫ﺿﺨﺎﻣﺖ ﺑﺎل‬

‫‪1,081‬‬

‫= )‪Fb2 (kg/cm2‬‬

‫‪206.3‬‬

‫= ‪hw /tw‬‬

‫ﻻﻏﺮي ﺟﺎن‬

‫‪73.31‬‬

‫= )‪rx (cm‬‬

‫ﺷﻌﺎع ژﻳﺮاﺳﻴﻮن ﻗﻮي‬

‫‪10.9‬‬

‫= ‪545 / SFy‬‬

‫ﻣﺮز ﻓﺸﺮدﮔﻲ ‪ -‬ﻏﻴﺮ ﻓﺸﺮدﮔﻲ ﺑﺎل‬

‫‪52,090‬‬

‫= )‪Iy (cm4‬‬

‫ﻣﻤﺎن اﻳﺘﺮﺳﻲ ﺿﻌﻴﻒ‬

‫‪107.3‬‬

‫= ‪5365 / SFy‬‬

‫ﻣﺮز ﻓﺸﺮدﮔﻲ ‪ -‬ﻏﻴﺮ ﻓﺸﺮدﮔﻲ ﺟﺎن‬

‫‪11.68‬‬

‫= )‪ry (cm‬‬

‫ﺷﻌﺎع ژﻳﺮاﺳﻴﻮن ﺿﻌﻴﻒ‬

‫‪11.1‬‬

‫= )‪795 / S(Fy/Kc‬‬

‫ﻣﺮز ﻏﻴﺮ ﻓﺸﺮدﮔﻲ ‪ -‬ﻻﻏﺮي ﺑﺎل‬

‫‪26,043‬‬

‫= )‪IT (cm4‬‬

‫ﻣﻤﺎن اﻳﺘﺮﺳﻲ‪T‬‬

‫‪165.6‬‬

‫= ‪6370 / SFb‬‬

‫ﻣﺮز ﻏﻴﺮ ﻓﺸﺮدﮔﻲ ‪ -‬ﻻﻏﺮي ﺟﺎن‬

‫‪147‬‬

‫= )‪AT (cm2‬‬

‫ﻣﺴﺎﺣﺖ ﻣﻘﻄﻊ ‪T‬‬

‫ﺳﺮاﺳﺮي‬

‫ﻓﺸﺮدﮔﻲ‬

‫‪13.31‬‬

‫= )‪rT (cm‬‬

‫ﺷﻌﺎع ژﻳﺮاﺳﻴﻮن ‪T‬‬

‫ﺳﺎده‬

‫ﻏﻴﺮ ﻓﺸﺮدﮔﻲ‬

‫‪1.14‬‬

‫= ‪rT /ry‬‬

‫‪0.49‬‬

‫= ‪Kc‬‬

‫ﺑﺎ ﺗﻘﻮﻳﺖ ﻛﻨﻨﺪه ﻋﺮﺿﻲ‬

‫‪75.1‬‬

‫= ‪Lb /rT‬‬

‫اﺑﻌﺎد ﻣﻘﻄﻊ‬

‫‪18.6‬‬

‫=‪Kv‬‬

‫‪71.0‬‬

‫= )‪S(7200000*Cb /Fy‬‬

‫‪4‬‬

‫‪0.6‬‬

‫=‪if Cv < .8 then Cv‬‬

‫‪158.7‬‬

‫= )‪S(36000000*Cb /Fy‬‬

‫ﻛﻨﺘﺮل ﻓﺸﺮدﮔﻲ‬

‫‪476.9023993‬‬ ‫ﻣﺤﺎﺳﺒﻪ ﺑﺮش ﻣﻘﺎوم‬

‫‪t‬‬

‫ﺑﺮش ﻣﻮﺟﻮد‬

‫‪60.89‬‬

‫‪=Av*Fv‬‬

‫‪t‬‬

‫ﻣﺴﺎﺣﺖ ﻣﻘﺎوم ﺑﺮﺷﻲ‬

‫‪62.95‬‬

‫‪0.67‬‬

‫‪477‬‬

‫= )‪Fv (kg/cm2‬‬

‫=‪Cv‬‬

‫‪1,479‬‬

‫= )‪Fb (kg/cm2‬‬

‫ﺑﺮش ﻣﻘﺎوم‬

‫‪0.967‬‬

‫ﻧﺴﺐ ﺗﻨﺶ ﺑﺮﺷﻲ‬

‫‪6‬‬

‫‪6370/SFb‬‬

‫‪10‬‬

‫وزن واﺣﺪ ﻃﻮل‬

‫‪299.9‬‬

‫‪206.3‬‬

‫= ‪hw /tw‬‬

‫‪166‬‬

‫= ‪6370 / SFb‬‬

‫‪1,447‬‬

‫= )‪Fb ' (kg/cm2‬‬

‫> ‪hw/tw‬‬

‫‪3‬‬

‫ﻧﺴﺒﺖ ‪ rT‬ﺑﻪ ‪ry‬‬

‫‪2.5‬‬

‫ﺷﺮاﻳﻂ ﺗﻜﻴﻪ ﮔﺎﻫﻲ‬

‫= )‪Lb (cm‬‬

‫‪1,000‬‬

‫‪if required‬‬

‫اﻟﺰام اﺳﺘﻔﺎده از ﺳﺨﺖ ﻛﻨﻨﺪه )‪(hw/tw> 260‬‬

‫= )‪a (cm‬‬

‫‪100.0‬‬

‫ﻓﺎﺻﻠﻪ دو ﺗﻜﻴﻪ ﮔﺎه ﺟﺎﻧﺒﻲ‬

‫)ﺳﺮاﺳﺮي‪/‬ﻣﻨﻘﻄﻊ(‬

‫)ﺳﺎده‪/‬ﻣﻀﺎﻋﻒ(‬

‫ﻓﺎﺻﻠﻪ ﺧﺎﻟﺺ دو ﺳﺨﺖ ﻛﻨﻨﺪه‬

‫اﺗﺼﺎل ﺑﺎل و ﺟﺎن‬

‫اﻧﺤﻨﺎي ﻋﻀﻮ‬

‫‪-‬‬

‫= |‪|M1‬‬

‫ﻟﻨﮕﺮ ﻛﻮﭼﻚ در ﺗﻜﻴﻪ ﮔﺎه‬

‫‪349.62‬‬

‫= |‪|M2‬‬

‫ﻟﻨﮕﺮ ﺑﺰرگ در ﺗﻜﻴﻪ ﮔﺎه‬

‫ﻻﻏﺮي‬

‫= ‪a/hw‬‬

‫‪0.61‬‬

‫‪325.6‬‬

‫=)‪985000/ S((Fy+1160)Fy‬‬

‫‪335.4‬‬

‫= ‪16770 / SFy‬‬

‫ﻧﺪارد ﻳﺎ ‪a/hw>1.5‬‬

‫‪a/hw <= 1.5‬‬

‫)‪hw/tw < 16770/sqrt(Fy‬‬

‫‪335.4‬‬

‫<‬

‫‪206.3‬‬

‫ﺟﺎن ﺗﻴﺮ ﻻﻏﺮ اﺳﺖ‪.‬‬

‫‪1.75‬‬

‫= ‪Cb‬‬

‫)ﺑﻠﻪ ‪ /‬ﺧﻴﺮ(‬

‫ﺧﻴﺮ‬

‫‪t.m‬‬ ‫‪t‬‬

‫ﻟﻨﮕﺮ ﺑﺰرﮔﺘﺮ ﻣﻴﺎﻧﻲ‬

‫‪349.62‬‬

‫ﻟﻨﮕﺮ ﻣﻮﺟﻮد‬

‫‪60.89‬‬

‫ﺑﺮش ﻣﻮﺟﻮد‬

‫ﺗﻤﺮﻳﻦ ‪ 2‬ﮔﺮوه ‪4‬‬

‫‪t.m‬‬

‫‪8‬‬

‫‪7‬‬

‫‪5‬‬

‫‪3‬‬

‫‪2‬‬

‫‪1‬‬

‫ﻣﺤﺎﺳﺒﻪ ﻟﻨﮕﺮ ﻣﻘﺎوم‬

‫ﻣﺤﺎﺳﺒﻪ ‪Fv‬‬

‫ﻣﺤﺎﺳﺒﻪ ‪Fb‬‬

‫ﻛﻨﺘﺮل ﻛﻔﺎﻳﺖ ﺗﻜﻴﻪ ﮔﺎه ﺟﺎﻧﺒﻲ‬

‫ﻣﺸﺨﺼﺎت ﻫﻨﺪﺳﻲ ﻣﻘﻄﻊ‬

‫ﻣﺸﺨﺼﺎت ﻣﺼﺎﻟﺢ‬

‫‪=Sx*F'b‬‬

‫ﻟﻨﮕﺮ ﻣﻘﺎوم‬

‫‪407.73‬‬

‫ﻟﻨﮕﺮ ﻣﻘﺎوم‬

‫‪63.7‬‬

‫= ‪3185/eFy‬‬

‫‪-‬‬

‫= )‪Fb (kg/cm2‬‬

‫ﺗﻜﻴﻪ ﮔﺎه ‪ +‬ﻏﻴﺮ ﻓﺸﺮدﮔﻲ‬

‫‪359‬‬

‫= ‪1400000 / (d/Af) / Fy‬‬

‫= )‪Lc2(cm‬‬

‫‪402‬‬

‫= )‪Ag (cm2‬‬

‫ﻣﺴﺎﺣﺖ ﻣﻘﻄﻊ‬

‫ﺷﺮط ﻛﻔﺎﻳﺖ ﺗﻜﻴﻪ ﮔﺎه ﺟﺎﻧﺒﻲ‬

‫‪125‬‬

‫= )‪Af (cm2‬‬

‫ﻣﺴﺎﺣﺖ ﺑﺎل‬

‫‪152‬‬

‫= )‪Aw (cm2‬‬

‫‪315.6‬‬

‫= )‪w/l (kg/m‬‬

‫‪2,773,413‬‬

‫‪2,500‬‬

‫= )‪Fyw (kg/cm2‬‬

‫ﺗﻨﺶ ﺗﺴﻠﻴﻢ ﺟﺎن‬

‫‪-‬‬

‫‪404.13‬‬

‫ﻟﻨﮕﺮ ﻣﻮﺟﻮد‬

‫‪237.5‬‬

‫=‪hw/tw‬‬

‫‪-‬‬

‫= )‪Fb (kg/cm2‬‬

‫ﺗﻜﻴﻪ ﮔﺎه ‪ +‬ﻓﺸﺮدﮔﻲ‬

‫‪635‬‬

‫= )‪635 bf / S(Fy‬‬

‫= )‪Lc1(cm‬‬

‫‪195‬‬

‫= )‪d(cm‬‬

‫ارﺗﻔﺎع ﻛﻠﻲ ﻧﻴﻤﺮخ‬

‫‪2,500‬‬

‫= )‪Fyf (kg/cm2‬‬

‫ﺗﻨﺶ ﺗﺴﻠﻴﻢ ﺑﺎل‬

‫‪t.m‬‬

‫‪0.991‬‬

‫‪-‬‬

‫ﺑﺪون ﺗﻘﻮﻳﺖ ﻛﻨﻨﺪه ﻋﺮﺿﻲ‬

‫ﻧﺴﺐ ﺗﻨﺶ ﺧﻤﺸﻲ‬

‫‪9‬‬

‫ﻋﺪم ﻛﻔﺎﻳﺖ ﺗﻜﻴﻪ ﮔﺎه‬

‫‪No‬‬

‫)‪Lb < Min( Lc1 , Lc2‬‬

‫ﻣﺴﺎﺣﺖ ﺟﺎن‬

‫‪190‬‬

‫= )‪hw (cm‬‬

‫ارﺗﻔﺎع ﺟﺎن‬

‫وزن واﺣﺪ ﻃﻮل‬

‫‪0.8‬‬

‫= )‪tw (cm‬‬

‫ﺿﺨﺎﻣﺖ ﺟﺎن‬

‫= )‪Ix (cm4‬‬

‫ﻣﻤﺎن اﻳﺘﺮﺳﻲ ﻗﻮي‬

‫‪50‬‬

‫= )‪bf (cm‬‬

‫ﻋﺮض ﺑﺎل‬

‫‪1,500 if Cv >= .8 then‬‬

‫= )‪Fb1 (kg/cm2‬‬

‫‪10.0‬‬

‫= ‪(bf/2)/tf‬‬

‫ﻻﻏﺮي ﻃﻮل آزاد ﺑﺎل‬

‫‪28,445‬‬

‫= ) ‪Sx (cm‬‬

‫ﻣﺪول ﻣﻘﻄﻊ ﻗﻮي‬

‫= )‪tf (cm‬‬

‫ﺿﺨﺎﻣﺖ ﺑﺎل‬

‫‪1,047‬‬

‫= )‪Fb2 (kg/cm2‬‬

‫‪237.5‬‬

‫= ‪hw /tw‬‬

‫ﻻﻏﺮي ﺟﺎن‬

‫‪83.06‬‬

‫= )‪rx (cm‬‬

‫ﺷﻌﺎع ژﻳﺮاﺳﻴﻮن ﻗﻮي‬

‫‪10.9‬‬

‫= ‪545 / SFy‬‬

‫ﻣﺮز ﻓﺸﺮدﮔﻲ ‪ -‬ﻏﻴﺮ ﻓﺸﺮدﮔﻲ ﺑﺎل‬

‫‪52,091‬‬

‫= )‪Iy (cm4‬‬

‫ﻣﻤﺎن اﻳﺘﺮﺳﻲ ﺿﻌﻴﻒ‬

‫‪107.3‬‬

‫= ‪5365 / SFy‬‬

‫ﻣﺮز ﻓﺸﺮدﮔﻲ ‪ -‬ﻏﻴﺮ ﻓﺸﺮدﮔﻲ ﺟﺎن‬

‫‪11.38‬‬

‫= )‪ry (cm‬‬

‫ﺷﻌﺎع ژﻳﺮاﺳﻴﻮن ﺿﻌﻴﻒ‬

‫‪10.7‬‬

‫= )‪795 / S(Fy/Kc‬‬

‫ﻣﺮز ﻏﻴﺮ ﻓﺸﺮدﮔﻲ ‪ -‬ﻻﻏﺮي ﺑﺎل‬

‫‪26,043‬‬

‫= )‪IT (cm4‬‬

‫ﻣﻤﺎن اﻳﺘﺮﺳﻲ‪T‬‬

‫‪164.5‬‬

‫= ‪6370 / SFb‬‬

‫ﻣﺮز ﻏﻴﺮ ﻓﺸﺮدﮔﻲ ‪ -‬ﻻﻏﺮي ﺟﺎن‬

‫‪150‬‬

‫= )‪AT (cm2‬‬

‫ﻣﺴﺎﺣﺖ ﻣﻘﻄﻊ ‪T‬‬

‫ﺳﺮاﺳﺮي‬

‫ﻓﺸﺮدﮔﻲ‬

‫‪13.16‬‬

‫= )‪rT (cm‬‬

‫ﺷﻌﺎع ژﻳﺮاﺳﻴﻮن ‪T‬‬

‫ﺳﺎده‬

‫ﻏﻴﺮ ﻓﺸﺮدﮔﻲ‬

‫‪1.16‬‬

‫= ‪rT /ry‬‬

‫‪0.45‬‬

‫= ‪Kc‬‬

‫ﺑﺎ ﺗﻘﻮﻳﺖ ﻛﻨﻨﺪه ﻋﺮﺿﻲ‬

‫‪68.4‬‬

‫= ‪Lb /rT‬‬

‫اﺑﻌﺎد ﻣﻘﻄﻊ‬

‫‪21.4‬‬

‫=‪Kv‬‬

‫‪71.0‬‬

‫= )‪S(7200000*Cb /Fy‬‬

‫‪4‬‬

‫‪0.5‬‬

‫=‪if Cv < .8 then Cv‬‬

‫‪158.7‬‬

‫= )‪S(36000000*Cb /Fy‬‬

‫ﻛﻨﺘﺮل ﻓﺸﺮدﮔﻲ‬

‫‪412.9792702‬‬ ‫ﻣﺤﺎﺳﺒﻪ ﺑﺮش ﻣﻘﺎوم‬

‫‪t‬‬

‫ﺑﺮش ﻣﻮﺟﻮد‬

‫‪59.81‬‬

‫‪=Av*Fv‬‬

‫‪t‬‬

‫ﻣﺴﺎﺣﺖ ﻣﻘﺎوم ﺑﺮﺷﻲ‬

‫‪62.77‬‬

‫‪0.62‬‬

‫‪413‬‬

‫= )‪Fv (kg/cm2‬‬

‫=‪Cv‬‬

‫‪1,500‬‬

‫= )‪Fb (kg/cm2‬‬

‫ﺑﺮش ﻣﻘﺎوم‬

‫‪0.953‬‬

‫ﻧﺴﺐ ﺗﻨﺶ ﺑﺮﺷﻲ‬

‫‪6‬‬

‫‪6370/SFb‬‬

‫‪10‬‬

‫وزن واﺣﺪ ﻃﻮل‬

‫‪315.6‬‬

‫‪237.5‬‬

‫= ‪hw /tw‬‬

‫‪164‬‬

‫= ‪6370 / SFb‬‬

‫‪1,433‬‬

‫= )‪Fb ' (kg/cm2‬‬

‫> ‪hw/tw‬‬

‫‪3‬‬

‫ﻧﺴﺒﺖ ‪ rT‬ﺑﻪ ‪ry‬‬

‫‪2.5‬‬

‫ﺷﺮاﻳﻂ ﺗﻜﻴﻪ ﮔﺎﻫﻲ‬

‫= )‪Lb (cm‬‬

‫‪900‬‬

‫‪if required‬‬

‫اﻟﺰام اﺳﺘﻔﺎده از ﺳﺨﺖ ﻛﻨﻨﺪه )‪(hw/tw> 260‬‬

‫= )‪a (cm‬‬

‫‪105.0‬‬

‫ﻓﺎﺻﻠﻪ دو ﺗﻜﻴﻪ ﮔﺎه ﺟﺎﻧﺒﻲ‬

‫)ﺳﺮاﺳﺮي‪/‬ﻣﻨﻘﻄﻊ(‬

‫)ﺳﺎده‪/‬ﻣﻀﺎﻋﻒ(‬

‫ﻓﺎﺻﻠﻪ ﺧﺎﻟﺺ دو ﺳﺨﺖ ﻛﻨﻨﺪه‬

‫اﺗﺼﺎل ﺑﺎل و ﺟﺎن‬

‫اﻧﺤﻨﺎي ﻋﻀﻮ‬

‫‪-‬‬

‫= |‪|M1‬‬

‫ﻟﻨﮕﺮ ﻛﻮﭼﻚ در ﺗﻜﻴﻪ ﮔﺎه‬

‫‪404.13‬‬

‫= |‪|M2‬‬

‫ﻟﻨﮕﺮ ﺑﺰرگ در ﺗﻜﻴﻪ ﮔﺎه‬

‫ﻻﻏﺮي‬

‫= ‪a/hw‬‬

‫‪0.55‬‬

‫‪325.6‬‬

‫=)‪985000/ S((Fy+1160)Fy‬‬

‫‪335.4‬‬

‫= ‪16770 / SFy‬‬

‫ﻧﺪارد ﻳﺎ ‪a/hw>1.5‬‬

‫‪a/hw <= 1.5‬‬

‫)‪hw/tw < 16770/sqrt(Fy‬‬

‫‪335.4‬‬

‫<‬

‫‪237.5‬‬

‫ﺟﺎن ﺗﻴﺮ ﻻﻏﺮ اﺳﺖ‪.‬‬

‫‪1.75‬‬

‫= ‪Cb‬‬

‫)ﺑﻠﻪ ‪ /‬ﺧﻴﺮ(‬

‫ﺧﻴﺮ‬

‫‪t.m‬‬ ‫‪t‬‬

‫ﻟﻨﮕﺮ ﺑﺰرﮔﺘﺮ ﻣﻴﺎﻧﻲ‬

‫‪404.13‬‬

‫ﻟﻨﮕﺮ ﻣﻮﺟﻮد‬

‫‪59.81‬‬

‫ﺑﺮش ﻣﻮﺟﻮد‬