Cross section of a beam is as shown in Figure Q1(a),determine; (i) center of gravity with respect to bottom edge AB; (ii) second moment of area of the section about AB.
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Q: Cross section of a beam is as shown in Figure Q1(a),determine; (1i) center of gravity with respect…
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- Figure (a) shows the cross-sectional dimensions for the structural steel section known as C1020 (channel with a nominal depth of 10 in., weighing 201b/ft). The American Institute of Steel Construction Structural Steel Handbook lists the following properties for the cross section: A=5.88in.2,Ix=78.9in.4, and Iy=2.81in.4. If two of these channels are welded together as shown in Fig. (b), find Ix and Iy for the resulting cross section.For the area below, evaluate 1. The (x,y) coordinates of the centroid (please mark your origin or reference point on the diagram) 2. The 2nd moments and product of area in centroidal-based xy (horizontal-vertical) coordinates 3. The principal 2nd moments of area, and the direction of the first principal axis relative to the horizontal (x) axis (anticlockwise positive) 50 75 30 150 60 50 15 Figure 1: Cross section (all dimensions in mm) Quantity Xc (please mark your origin on the diagram) Yc (please mark your origin on the diagram) Ix ly Ixv I₁ I₂ a1 (please show the direction) Value 30 UnitsA simply supported beam has a symmetrical rectangular cross-section. If thesecond moment of area (I) of a beam with a rectangular cross-section is 11.50 x 106 mm4 about its centroidal x-axis and the depth dimension (d) of the rectangular section is 180 mm, determine the breadth dimension (b) for this beam section. Give your answer in millimetres (mm) and to 2 decimal places. Assume the beam section material is homogeneous. (show all work)
- A simply supported beam has a symmetrical rectangular cross-section. If the second moment of area (I) of a beam with a rectangular cross-section is 11.50 x 106 mm4 about its centroidal x-axis and the depth dimension (d) of the rectangular section is 180 mm, determine the breadth dimension (b) for this beam section. Give your answer in millimetres (mm) and to 2 decimal places. Assume the beam section material is homogeneous.For the beam l-section below, calculate the second moment of area about its centroidal x-axis (Ixxcentroid), where b1 = 10.50 mm, b2 = 2.50 mm, b3 = 38.50 mm, d1 = 1.50 mm, d2 = 36.50 mm and d3 = 12.50 mm. %3D Give your answer in mm4 to two decimal places. b1 d2 -+ b2 d3 b3For the beam I-section below, calculate the second moment of area about its centroidal x-axis (Ixxcentroid), where b1 = 10.50 mm, b2= 2.50 mm, b3 = 38.50 mm, d1 = 1.50 mm, d2 = 36.50 mm and d3 = 12.50 mm. %3D Give your answer in mm4 to two decimal places. b1 di dz + b2 b3 Answer:
- For the beam I-section below, calculate the second moment of area about its centroidal x-axis (Ixxcentroid), where b1 = 10.50 mm, b2 = 2.50 mm, b3 = 38.50 mm, d1 = 1.50 mm, d2 = 36.50 mm and d3 = 12.50 mm. Give your answer in mm4 to two decimal places.For the beam I-section below, calculate the second moment of area about its centroidal x-axis (Ixxcentroid), where b1 = 12.50 mm, b2= 2.50 mm, b3 = 25.00 mm, d1 = 4.25 mm, d2 = 19.50 mm and d3= 6.50 mm. Give your answer in mm4 to two decimal places. b1 d2 ➜ → b₂ b3 d₁Q1(a) Cross section of a beam is as shown in Figure Q1(a),determine; (i) center of gravity with respect to bottom edge AB; (ii) second moment of area of the section about AB. 200 300 100 A B Figure Q1(a) (take all dimensions in milli meters) (b) If a concentric hole of diameter100 mm drilled on the circular section in Q1(a), explain its effect on the center of gravity with respect to 'AB'.
- A force F of 10 N is applied in the direction indicated, per meter depth (into page). The 300 mm long triangular beam is Aluminum, 1100 series, and extends 2 meters into the page. What is the moment about point A, per meter of depth? The system is on Earth, at sea level, gravity acts in the direction of F. 40 Note: The centroid of a triangle is located at h/3. 300 A) 16 Nm / m B) 19 Nm / m C) 24 Nm/ m D) 27 Nm / mQUESTION 1 An I-section is shown in the figure. All dimensions are in mm The centroidal axis X' is located as shown. Live 20 20 200 300 150 20 185 x' The second moment of area Ixx about the x-axis passing through the centroid is most nearly equal to: Ⓒa. 56.6x105 mm4 b.28.3 x106 mm O 328x106 mm4 O d. 58.2 x106 mm e. 13.6 x105 mm14. Form the Fig.(2) The second moment of area Iyy is then given by; 50mm Imm 120mm 2mm Fig. (2) 2mm 100mm a. Iyy = 4.50* 105mm* b. Iyy = 5.41 * 105mm* c. Iyy d. Iyy = 3.65* 105mmt %3D 1.49 * 10°mm 4 %3D