1. Given are Plane Composite Geometric Figure and their basic dimensions.Solve for the following:• Total Area AICentroid about the x - axis y• Centroid about the y - axis i• Moment of Inertia About the x - axis Ix• Moment of Inertial About the y - axis ly• Polar moment of Inertia about the axes Jo• Moment of Inertia About the centroidal x - axis IxMoment of Inertial About the centroidal y – axis Iy• Polar moment of Inertia about the centroidal axes Jo 40301010D=1515305540

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Answered: 1. Given are Plane Composite Geometric…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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H= 3 R= 1 Inputs: • Center of Circle is the SAME as the Rectangle. • H= Height in cm (From Table) ● R = Radius of Circle in cm (From Table) Required: For the composite area: 1. Locate the centroid in x and y. 2. Draw the Centroidal Axis. 3. Find the Moment of Inertia around centroidal x axis only. ↑A А D 8 cm R 16 cm 3 cm B C E H cm F X
3. An A36 Steel Cantilever Beam is shown below, also showing its cross section. Determine the following: Given the formula of the Maximum allowable bending stress of steel, fb = 0.66Fy. Where Fy is the Yield Stress of Steel. Where the bending stress for a beam is (fb) = Mc/I, where c is the distance of the centroid to the extreme most fiber of the beam (either top-most or bottom-most distance). Does the Steel fail under the loading given? Use Fy = 450 Mpa. Use the Moment in (a) and the moment of inertia in (c).
A prestressed beam is given in the figure below. Aps = 720 mm² H = 600 mm B = 400 mm y = 100 mm If the initial prestress is fps,i = 1,208 MPa, calculate the stress at the top fiber, at midspan section due to prestress only. Input the answer in MPa, wtih 2 decimal places including the sign. + for tensi for compression. Aps mm B (mm) II (mm) y (mm) L (m)
Example Problem Solution Find: Centroid of composite Solution: Divide into simple areas Find centroid of each section Find moment areas Sum areas and moment areas Compute centroid locations Section A, mm² 1 5,000 2 2,500 3 3,927 4 -1,963 Σ 9,463.5 x y = x, mm 50 66.67 121.2 70 Σ*A ΣΑ ΣÿA ΣΑ ỹ, mm 25 66.67 50 40 Show the table and complete solution. Example above. 1. Determine the moment of inertia of the composite area about the centroidal y axis. XA, mm³ A, mm³ 250,000 125,000 166,667 166,667 476,032 196,350 -137,445 -78,540 755,254 409,476 2. Locate the centroid y of the composite area, then determine the moment of inertia of this area about the x' axis. -15 -50-50- Dimensions in mm 150 BYU IDAHO
A composite assembly consisting of a steel [G = 80 GPa] core (2) connected by rigid plates at the ends of an aluminum [G = 28 GPa] tube (1) is shown. The cross-sectional dimensions of the assembly are shown in the second figure. Assume L = 340 mm, D1 = 53, d = 37 mm, d2 = 19 mm. If a torque of T = 1200 N-m is applied to the composite assembly, determine (a) the maximum shear stress in the aluminum tube and in the steel core. (b) the rotation angle of end B relative to end A. (1) T T B L (1) d2 di DI Answers: (a) Talum = i 53.839 MPa Tsteel i 891.026 MPa (b) PB - PA = i 0.02467 rad (2)
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Find the centroid of the composite shape below. Then, find the lx, ly, rx, ry, and J for the shape about its own center. 12" X- 24" 12 in. radius X
A wooden beam is fabricated by nailing together three pieces of dimension lumber as shown. The cross-sectional dimensions of the beam are also shown. The centroid is 3.4 in. below the top surface of the beam, and the moment of inertia about the z axis is 230.9 in.4. The beam must support an internal shear force of V = 365 Ib. If each nail can provide 120 Ib of horizontal resistance, determine the maximum spacing sfor the nails. 2 in. 4 in. 2 in. 2 in. 8 in. O 4.86 in. 8.32 in. O 7.91 in. 9.36 in. O 5.59 in.
Determine the location of the centroid of the symmetrical composite section, as shown in the following figure. 150 mm 15 mm 150 mm 50 mm @ 15 mm C 3
The following are properties of the reinforced concrete beam shown, f, = 60,000 psi and Sc = 4,000 psi . Determine the distance from the top 12 in 3 in. of the beam the centroid of the effective area of the concrete subjected to the compressive stress 0.85 f. . 27 in. 33 in 30 in. 4 #11 3 in. 18 in. O 3.47 in. O 7.43 in. 4.73 in. O 3.74 in.
a. Determine the centroid of the composite figure.b. Calculate the moment of inertia with respect to the red horizontal axis.c. Calculate the moment of inertia with respect to the red vertical axis. given : L5 = 6 L6 = 4 L7 = 6
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1. Given are Plane Composite Geometric Figure and their basic dimensions. Solve for the following: • Total Area AI Centroid about the x - axis ỹ Centroid about the y - axis š