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Structural Analysis (I) ex

# Structural Analysis (I) ex - Structural Analysis(I Sheet...

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Structural Analysis (I) Sheet No. (3) Prepared by Amr A. El-Sayed, Civil Eng. Dept., El-Minia Univ., Eg. 1 A 1 3 A 2 A X Problems: 1 - Two equal and opposite couples of magnitude M=25.0 kN.m are applied to the channel- shaped beam AB . Observing that the couples causes the beam to bend in a horizontal plane, determine the stress: (a) at point C , (b) at point D , (c) at point E . D C E M M B A Solution Data: M = 25.0 kN.m (the moment causes the beam to bend in a horizontal plan, i.e. M Y ) Required: The stresses at points C, D, and E 1- Properties of the section: all dimensions are in m Area = 0.030*0.120*2 + 0.040*0.120 = 0.012 m 2 ﻞѧﺛﺎﻤﺗ رﻮѧﺤﻣ ﻪѧﻟ نأ ﺪѧﺠﻧ ﻞﻜﺸѧﻟا ﻞѧﻘﺛ ﺰѧآﺮﻣ دﺎѧﺠﻳﻹو ) ﻢﺴѧﻘﻳ ًﺎﻣﺎﻤﺗ ﻦﻴﻠﺛﺎﻤﺘﻣ ﻦﻴﻤﺴﻗ ﻰﻟإ ﻞﻜﺸﻟا ( رﻮﺤﻣ ﻮهو X ﻰﻟﺎﺘﻟﺎﺑو ، رﻮﺤﻣ دﺎﺠﻳإ ﻮه بﻮﻠﻄﻤﻟﺎﻓ Y ﻰѧﻟإ ﻞﻜﺸѧﻟا ﻢﻴﺴѧﻘﺘﺑ ﻚѧﻟذ ﻢﺘѧﻳو ، 3 ﻰѧﻓ ﺖѧﺑﺎﺛ ﻂѧﺧ لﻮѧﺣ تﺎﺣﺎﺴѧﻤﻟا موﺰѧﻋ ﺬѧﺧأو ،تﻼﻴﻄﺘﺴѧﻣ ،ﻞﻜﺸﻟا ) ﺔﻬﺟ ﻦﻣ ﻞﻜﺸﻟﺎﺑ ﺮﻤﻳ ﻂﺧ ﺮﺧﺁ ﻦﻜﻴﻟو رﺎﺴﻴﻟا ( - ﺖѧﺑﺎﺛ ﻂѧﺧ لﻮѧﺣ تﺎﺣﺎﺴѧﻤﻟا ﻦѧﻣ ﺔѧﻋﻮﻤﺠﻣ موﺰѧﻋ = مﺰѧﻋ ﻂﺨﻟا ﺲﻔﻧ لﻮﺣ ﺔﻴﻠﻜﻟا ﺔﺣﺎﺴﻤﻟا . A 1 *X 1 + A 2 *X 2 + A 3 *X 3 = A total * X (0.03*0.12*0.06)*2 + 0.04*0.12*0.02 = 0.012* X

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Structural Analysis (I) Sheet No. (3) Prepared by Amr A. El-Sayed, Civil Eng. Dept., El-Minia Univ., Eg. 2 3 A X 2 A A 1 Y X = 0.044 m …. (44 mm) أ رﻮﺤﻣ نأ ى Y رﻮﺤﻣ ﻰﻠﻋ ﺪﻣﺎﻌﺘﻳو ﻞﻜﺸﻟا ﻞﻘﺛ ﺰآﺮﻤﺑ ﺮﻤﻳ ىﺬﻟا X ﺪﻌﺒﻳ 44 رﺎﺴѧﻴﻟا ﻦѧﻣ ﻞﻜﺸѧﻟﺎﺑ ﺮѧﻤﻳ ﻂѧﺧ ﺮѧﺧﺁ ﻦﻋ ﻢﻣ ﻰﻤﺴﻳ ﺎﻣ ﻮهو (Datum Line) .
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