Please Do solution step by step and correct
Posted: Sun May 15, 2022 9:12 pm
Please Do solution step by step and correct
For the section shown in the figure below: a. b. Calculate the distance of its centroid from the left-hand side of the section; and (10 marks) Calculate the second moment of area with respect to the horizontal X-X axis passing through the centroid as shown. (10 marks) 15 cm 2 cm X х 30 cm 2 cm 2 cm T
LIST OF CENTROIDS, AREAS, AND SECOND MOMENTS OF AREA Shape Figure Centroid 3 4 h x Rectangle A-2=-2 A = b 12 12 y = 2 N b y triangle 2b te=3 h A 1 X bh3 Ixx = 36 In = 36 Y= bh ** b Filled circular area Ixx HD AT Iyy = centre of circle = A = ar? х Filled semi- circular area y A X = 0 y =ỹ 4r 311 Ixx 8 8 977 = 0.109874 ir Iyy = 8 C X r2 T x Filled quarter- circular area Xc = x 4r Зп YA A 1 = Ixx = 0.0549 r4 Түү = 0.0549 r4 х 19 Tr2 y =ỹ 4r Зп X
. = = FORMULA SHEET • Weight: W = mg = P gV [N] [ Hydrostatic pressure: p = pgh [N m-2] Force on plane surfaces: F = pgh-AN] Depth of centre of pressure (vertical plane surface): Ic hp = hc + HA • Location of centre of pressure along an inclined plane surface: Ic Lp = Lc + LÇA Centroid formula: XyA ΣΑ, • Second moment of area formula: Ix = Elxi + XAYi - y.)2 Metacentric height MB = Iws/Vwd = = . Yc .
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LIST OF CENTROIDS, AREAS, AND SECOND MOMENTS OF AREA Shape Figure Centroid 3 4 h x Rectangle A-2=-2 A = b 12 12 y = 2 N b y triangle 2b te=3 h A 1 X bh3 Ixx = 36 In = 36 Y= bh ** b Filled circular area Ixx HD AT Iyy = centre of circle = A = ar? х Filled semi- circular area y A X = 0 y =ỹ 4r 311 Ixx 8 8 977 = 0.109874 ir Iyy = 8 C X r2 T x Filled quarter- circular area Xc = x 4r Зп YA A 1 = Ixx = 0.0549 r4 Түү = 0.0549 r4 х 19 Tr2 y =ỹ 4r Зп X
. = = FORMULA SHEET • Weight: W = mg = P gV [N] [ Hydrostatic pressure: p = pgh [N m-2] Force on plane surfaces: F = pgh-AN] Depth of centre of pressure (vertical plane surface): Ic hp = hc + HA • Location of centre of pressure along an inclined plane surface: Ic Lp = Lc + LÇA Centroid formula: XyA ΣΑ, • Second moment of area formula: Ix = Elxi + XAYi - y.)2 Metacentric height MB = Iws/Vwd = = . Yc .