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engineering
civil engineering

Engineering Mechanics Statics 11 Edition Russell C. Hibbeler - Solutions

The arched surface AB is shaped in the form of a quarter circle. If it has a length L, determine the horizontal and vertical components of the resultant force caused by the water acting on the surface.The density of water is ρw.Units Used:Mg = 103 kgkN = 103 NGiven:L = 8 mρw = 1.0Mg/m3a = 3 mb =
The rectangular bin is filled with coal, which creates a pressure distribution along wall A that varies as shown, i.e. p = p0(z/b)3. Determine the resultant force created by the coal and specify its location measured from the top surface of the coal.Units used:kip = 103 lbGiven:a = 4 ftb = 10 ftp0
The semicircular drainage pipe is filled with water. Determine the resultant horizontal and vertical force components that the water exerts on the side AB of the pipe per foot of pipe length; water has density γ.Given:γ = 62.4lb/ft3r = 2 ft
The load over the plate varies linearly along the sides of the plate such that p = k y (a-x). Determine the magnitude of the resultant force and the coordinates (xc, yc) of the point where the line of action of the force intersects the plate.Given:a = 2 ftb = 6 ftk = 10lb/ft4
The drum is filled to its top (y = a) with oil having a density γ. Determine the resultant force of the oil pressure acting on the flat end of plate A of the drum and specify its location measured from the top of the drum.Given:a = 1.5 ftγ = 55lb/ft3
The gasoline tank is constructed with elliptical ends on each side of the tank. Determine the resultant force and its location on these ends if the tank is half full.Given:a = 3 ftb = 4 ftγ = 41lb/ft3
The loading acting on a square plate is represented by a parabolic pressure distribution. Determine the magnitude of the resultant force and the coordinates (xc, yc) of the point where the line of action of the force intersects the plate. Also, what are the reactions at the rollers B and C and the
The tank is filled with a liquid which has density ρ. Determine the resultant force that it exerts on the elliptical end plate, and the location of the center of pressure, measured from the x axis.Units Used:kN = 103 NGiven:a = 1 mb = 0.5 mρ = 900kg/m3g = 9.81m/s2
A circular V-belt has an inner radius r and a cross-sectional area as shown. Determine the volume of material required to make the belt.Given:r = 600 mma = 25 mmb = 50 mmc = 75 mm
A circular V-belt has an inner radius r and a cross-sectional area as shown. Determine the surface area of the belt.Given:r = 600 mma = 25 mmb = 50 mmc = 75 mm
Locate the center of mass of the homogeneous rod.Given:a = 200 mmb = 600 mmc = 100 mmd = 200 mmθ = 45 deg
Locate the centroid of the solid
Locate the centroid (xc, yc) of the thin plate.Given:a = 6 in
Determine the weight and location (xc, yc) of the center of gravity G of the concrete retaining wall.The wall has a length L, and concrete has a specific gravity of γ.Units Used:kip = 103 lbGiven:a = 12 ft f = 1 ftb = 9 ft g = 2 ftc = 1.5 ft L = 10 ftd = 5.5 ft γ = 150lb/ft3e = 1.5 ft
The hopper is filled to its top with coal. Determine the volume of coal if the voids (air space) are a fraction p of the volume of the hopper.Given:a = 1.5 mb = 4 mc = 1.2 md = 0.2 mp = 0.35
Locate the centroid (xc, yc) of the shaded area.Given:a = 16 ftb = 4 ftc = (√a − √b)2
The rectangular bin is filled with coal, which creates a pressure distribution along wall A that varies as shown, i.e., p = p0(z/b)1/3. Compute the resultant force created by the coal, and its location, measured from the top surface of the coal.Given:p0 = 8lb/ft2a = 3 ftb = 8 ft
The load over the plate varies linearly along the sides of the plate such that p = 2/3x (4 − y) kPa. Determine the resultant force and its position (xc, yc) on the plate.
The pressure loading on the plate is described by the function p = {-240/(x + 1) + 340} Pa. Determine the magnitude of the resultant force and coordinates of the point where the line of action of the force intersects the plate.
Determine the moment of inertia for the shaded area about the x axis.Given:a = 2 mb = 4 m
Determine the moment of inertia for the shaded area about the y axis.Given:a = 2 mb = 4 m
Determine the moment of inertia for the thin strip of area about the x axis. The strip is oriented at an angle θ from the x axis. Assume that t
Determine the moment for inertia of the shaded area about the x axis.Given:a = 4 inb = 2 in
Determine the moment for inertia of the shaded area about the y axis.Given:a = 4 inb = 2 in
Determine the moment of inertia for the shaded area about the x axis.
Determine the moment of inertia for the shaded area about the x axis.
Determine the moment of inertia for the shaded area about the y axis.
Determine the moment of inertia for the shaded area about the x axis.Given:a = 4 inb = 2 in
Determine the moment of inertia for the shaded area about the y axis.Given:a = 4 inb = 2 in
Determine the moment of inertia for the shaded area about the x axisGiven:a = 8 inb = 2 in
Determine the moment of inertia for the shaded area about the x axisGiven:a = 2 mb = 1 m
Determine the moment of inertia for the shaded area about the y axisGiven:a = 2 mb = 1 m
Determine the moment of inertia for the shaded area about the x axis.Given:a = 4 in b = 4 in
Determine the moment of inertia for the shaded area about the y axis.Given:a = 4 inb = 4 in
Determine the moment of inertia of the shaded area about the x axis.Given:a = 2 inb = 4 in
Determine the moment of inertia for the shaded area about the y axis.Given:a = 2 inb = 4 ine
Determine the moment of inertia for the shaded area about the x axis.Given:a = 4 inb = 2 in
Determine the moment of inertia for the shaded area about the y axis.Given:a = 4 inb = 2 in
Determine the moment for inertia of the shaded area about the x axis.Given:a = 2 inb = 4 inc = √12 in
Determine the moment for inertia of the shaded area about the y axis.Given:a = 2 inb = 4 inc = 12 in
Determine the moment of inertia for the shaded area about the x axis.Given:a = 2 mb = 2 m
Determine the moment of inertia for the shaded area about the y axis. Use Simpson's rule to evaluate the integral.Given:a = 1 mb = 1 m
Determine the moment of inertia for the shaded area about the x axis. Use Simpson's rule to evaluate the integral.Given:a = 1 mb = 1 m
The polar moment of inertia for the area is IC about the z axis passing through the centroid C. The moment of inertia about the x axis is Ix and the moment of inertia about the y' axis is Iy. Determine the area A.Given:IC = 28 in4Ix = 17 in4Iy' = 56 in4a = 3 in
The polar moment of inertia for the area is Jcc about the z' axis passing through the centroid C. If the moment of inertia about the y' axis is Iy' and the moment of inertia about the x axis is Ix.Determine the area A.Given:Jcc = 548 Ã— 106 mm4Iy' = 383 Ã— 106 mm4Ix = 856 Ã— 106 mm4h = 250
Determine the radius of gyration kx of the column’s cross-sectional area.Given:a = 100 mmb = 75 mmc = 90 mmd = 65 mm
Determine the radius of gyration ky of the column’s cross-sectional area.Given:a = 100 mmb = 75 mmc = 90 mmd = 65 mm
Determine the moment of inertia for the beam's cross-sectional area with respect to the x' centroidal axis. Neglect the size of all the rivet heads, R, for the calculation. Handbook values for the area, moment of inertia, and location of the centroid C of one of the angles are listed in the figure.
Locate the centroid yc of the cross-sectional area for the angle. Then find the moment of inertia Ix' about the x' centroidal axis.Given:a = 2 inb = 6 inc = 6 ind = 2 in
Locate the centroid xc of the cross-sectional area for the angle. Then find the moment of inertia Iy' about the centroidal y' axis.Given:a = 2 inb = 6 inc = 6 ind = 2 in
Determine the distance xc to the centroid of the beam's cross-sectional area: then find the moment of inertia about the y' axis.Given:a = 40 mmb = 120 mmc = 40 mmd = 40 mm
Determine the moment of inertia of the beam's cross-sectional area about the x' axis.Given:a = 40 mmb = 120 mmc = 40 mmd = 40 mm
Determine the moments of inertia for the shaded area about the x and y axes.Given:a = 3 inb = 3 inc = 6 ind = 4 inr = 2 in
Determine the location of the centroid y' of the beam constructed from the two channels and the cover plate. If each channel has a cross-sectional area Ac and a moment of inertia about a horizontal axis passing through its own centroid Cc, of Ix'c , determine the moment of inertia of the beam’s
Compute the moments of inertia Ix and Iy for the beams cross-sectional area about the x and y axes.Given:a = 30 mmb = 170 mmc = 30 mmd = 140 mme = 30 mmf = 30 mmg = 70 mm
Determine the distance yc to the centroid C of the beam's cross-sectional area and then compute the moment of inertia Icx' about the x' axis.Given:a = 30 mm e = 30 mmb = 170 mm f = 30 mmc = 30 mm g = 70 mmd = 140 mm
Determine the distance xc to the centroid C of the beam's cross-sectional area and then compute the moment of inertia Iy' about the y' axis.Given:a = 30 mmb = 170 mmc = 30 mmd = 140 mme = 30 mmf = 30 mmg = 70 mm
Determine the location yc of the centroid C of the beam’s cross-sectional area. Then compute the moment of inertia of the area about the x' axisGiven:a = 20 mmb = 125 mmc = 20 mmf = 120 mmg = 20 mmd = f−c/2e = f−c/2
Determine yc, which locates the centroidal axis x' for the cross-sectional area of the T-beam, and then find the moments of inertia Ix' and Iy'.Given:a = 25 mmb = 250 mmc = 50 mmd = 150 mm
Determine the centroid y' for the beam’s cross-sectional area; then find Ix'.Given:a = 25 mmb = 100 mmc = 25 mmd = 50 mme = 75 mm
Determine the moment of inertia for the beam's cross-sectional area about the y axis.Given:a = 25 mmb = 100 mmc = 25 mmd = 50 mme = 75 mm
Determine the moment for inertia Ix of the shaded area about the x axis.Given:a = 6 inb = 6 inc = 3 ind = 6 in
Determine the moment for inertia Iy of the shaded area about the y axis.Given:a = 6 inb = 6 inc = 3 ind = 6 in
Locate the centroid yc of the channel's cross-sectional area, and then determine the moment of inertia with respect to the x' axis passing through the centroid.Given:a = 2 inb = 12 inc = 2 ind = 4 in
Determine the moments for inertia Ix and Iy of the shaded area.Given:r1 = 2 inr2 = 6 in
Determine the moment of inertia for the parallelogram about the x' axis, which passes through the centroid C of the area.
Determine the moment of inertia for the parallelogram about the y' axis, which passes through the centroid C of the area.
Determine the moments of inertia for the triangular area about the x' and y' axes, which pass through the centroid C of the area.
Determine the moment of inertia for the beam’s cross-sectional area about the x' axis passing through the centroid C of the cross section.Given:a = 100 mmb = 25 mmc = 200 mmθ = 45 deg
Determine the moment of inertia of the composite area about the x axis.Given:a = 2 inb = 4 inc = 1 ind = 4 in
Determine the moment of inertia of the composite area about the y axis.Given:a = 2 inb = 4 inc = 1 ind = 4 in
Determine the radius of gyration kx for the column's cross-sectional area.Given:a = 200 mmb = 100 mm
Determine the product of inertia for the shaded portion of the parabola with respect to the x and y axes.Given:a = 2 inb = 1 in
Determine the product of inertia for the shaded area with respect to the x and y axes.
Determine the product of inertia of the shaded area of the ellipse with respect to the x and y axes.Given:a = 4 inb = 2 in
Determine the product of inertia of the parabolic area with respect to the x and y axes.
Determine the product of inertia for the shaded area with respect to the x and y axes.Given:a = 8 inb = 2 in
Determine the product of inertia for the shaded parabolic area with respect to the x and y axes.Given:a = 4 inb = 2 in
Determine the product of inertia for the shaded area with respect to the x and y axes.Given:a = 2 mb = 1 m
Determine the product of inertia for the shaded area with respect to the x and y axes.
Determine the product of inertia for the shaded area with respect to the x and y axes.
Determine the product of inertia of the shaded area with respect to the x and y axes.Given:a = 4 inb = 2 in
Determine the product of inertia for the shaded area with respect to the x and y axes.Given:a = 4 ft
Determine the product of inertia for the shaded area with respect to the x and y axes. Use Simpson's rule to evaluate the integral.Given:a = 1 mb = 0.8 m
Determine the product of inertia for the parabolic area with respect to the x and y axes.Given:a = 1 inb = 2 in
Determine the product of inertia for the cross-sectional area with respect to the x and y axes that have their origin located at the centroid C.Given:a = 20 mmb = 80 mmc = 100 mm
Determine the product of inertia for the beam's cross-sectional area with respect to the x and y axes.Given:a = 12 inb = 8 inc = 1 ind = 3 in
Determine the location (xc, yc) of the centroid C of the angle’s cross-sectional area, and then compute the product of inertia with respect to the x' and y' axes.Given:a = 18 mmb = 150 mm
Determine the product of inertia of the beam’s cross-sectional area with respect to the x and y axes that have their origin located at the centroid C.Given:a = 5 mmb = 30 mmc = 50 mm
Determine the product of inertia for the shaded area with respect to the x and y axes.Given:a = 2 inb = 1 inc = 2 ind = 4 in
Determine the product of inertia for the beam's cross-sectional area with respect to the x and y axes that have their origin located at the centroid C.Given:a = 1 in b = 5 in c = 5 in
Determine the product of inertia for the cross-sectional area with respect to the x and y axes.Given:a = 4 inb = 1 inc = 6 in
Determine the product of inertia for the beam's cross-sectional area with respect to the u and v axes.Given:a = 150 mmb = 200 mmt = 20 mmθ = 20 deg
Determine the moments of inertia Iu and Iv and the product of inertia Iuv for the rectangular area. The u and v axes pass through the centroid C.Given:a = 40 mmb = 160 mmθ = 30 deg
Determine the distance yc to the centroid of the area and then calculate the moments of inertia Iu and Iv for the channels cross-sectional area. The u and v axes have their origin at the centroid C. For the calculation, assume all corners to be square.Given:a = 150 mmb = 10 mmc = 50 mmθ = 20 deg
Determine the moments of inertia for the shaded area with respect to the u and v axes.Given:a = 0.5 inb = 4 inc = 5 inθ = 30 deg
Determine the directions of the principal axes with origin located at point O, and the principal moments of inertia for the rectangular area about these axes.Given:a = 6 inb = 3 in
Determine the moments of inertia Iu , Iv and the product of inertia Iuv for the beam's cross-sectional area.Given:θ = 45 dega = 8 inb = 2 inc = 2 ind = 16 in
Determine the directions of the principal axes with origin located at point O, and the principal moments of inertia for the area about these axes.Given:a = 4 inb = 2 inc = 2 ind = 2 inr = 1 in
Determine the principal moments of inertia for the beam's cross-sectional area about the principal axes that have their origin located at the centroid C. Use the equations developed in Section 10.7. For the calculation, assume all corners to be square.Given: a = 4 in b = 4 in t = 3/8 in

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