Engineering Mechanics: Statics & Dynamics (14th Edition)
14th Edition
ISBN: 9780133915426
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 9.2, Problem 61P
Determine the location ȳ of the centroid C of the beam having the cross-sectional area shown.
Prob. 9-61
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The steel curved bar shown has rectangular cross-section with a radial height h = 6 mm and thickness b = 4mm. The
radius of the centroidal axis is R = 80 mm. A force P = 10 N is applied as shown. Assume the steel modulus of
207,000 MPa and G = 79.3(103) MPa, repectively.
elasticity and shear modulus E =
Find the vertical deflection at point B. Use Castigliano's method for a curved flexural member and since R/h > 10,
neglect the effect of shear and axial load, thereby assuming that deflection is due to merely the bending moment.
Note the inner and outer radii of the curves bar are:
r = 80 + ½ (6) = 83 mm, r₁ = 80 − ½ (6) = 77 mm
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Sπ/2 sin² 0 d = √π/² cos² 0 d0 =
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Chapter 9 Solutions
Engineering Mechanics: Statics & Dynamics (14th Edition)
Ch. 9.1 - In each case, use the element shown and specify...Ch. 9.1 - Determine the centroid (x,y) of the shaded area....Ch. 9.1 - Determine the centroid (x,y) of the shaded area....Ch. 9.1 - Determine the centroid of the shaded area. Prob....Ch. 9.1 - Locate the center of mass x of the straight rod if...Ch. 9.1 - Locate the centroid of the homogeneous solid...Ch. 9.1 - Locate the centroid z of the homogeneous solid...Ch. 9.1 - Locate the center of mass of the homogeneous rod...Ch. 9.1 - Prob. 2PCh. 9.1 - Locate the center of gravity x of the homogeneous...
Ch. 9.1 - Locate the center of gravity of the homogeneous...Ch. 9.1 - Prob. 5PCh. 9.1 - Locate the centroid of the area.Ch. 9.1 - Locate the centroid x of the parabolic area. Prob....Ch. 9.1 - Prob. 8PCh. 9.1 - Locate the centroid x of the shaded area. Probs....Ch. 9.1 - Locate the centroid of the shaded area. Probs....Ch. 9.1 - Locate the centroid x of the area. Probs. 9-11/12Ch. 9.1 - Locate the centroid of the area. Probs. 9-11/12Ch. 9.1 - Locate the centroid x of the area. Probs. 9-13/14Ch. 9.1 - Locate the centroid of the area. Probs. 9-13/14Ch. 9.1 - Prob. 15PCh. 9.1 - Prob. 16PCh. 9.1 - Prob. 17PCh. 9.1 - Prob. 18PCh. 9.1 - Prob. 19PCh. 9.1 - Prob. 20PCh. 9.1 - Locate the centroid x of the shaded area. Probs....Ch. 9.1 - Locate the centroid of the shaded area. Probs....Ch. 9.1 - Prob. 23PCh. 9.1 - Locate the centroid of the shaded area. Probs....Ch. 9.1 - Prob. 25PCh. 9.1 - Locate the centroid x of the shaded area. Probs....Ch. 9.1 - Locate the centroid of the shaded area. Probs....Ch. 9.1 - Prob. 28PCh. 9.1 - Prob. 29PCh. 9.1 - Locate the centroid x of the shaded area. Probs....Ch. 9.1 - Prob. 31PCh. 9.1 - Prob. 32PCh. 9.1 - Prob. 33PCh. 9.1 - The steel plate is 0.3 m thick and has a density...Ch. 9.1 - Prob. 35PCh. 9.1 - Prob. 36PCh. 9.1 - Prob. 37PCh. 9.1 - Determine the location r of the centroid C for the...Ch. 9.1 - Locate the center of gravity of the volume. The...Ch. 9.1 - Prob. 40PCh. 9.1 - Locate the centroid z of the frustum of the...Ch. 9.1 - Prob. 42PCh. 9.1 - Locate the centroid of the quarter-cone. Prob....Ch. 9.1 - Prob. 44PCh. 9.1 - Locate the centroid z of the volume. Prob. 9-45Ch. 9.1 - Prob. 46PCh. 9.1 - Prob. 47PCh. 9.1 - Prob. 48PCh. 9.1 - Prob. 49PCh. 9.1 - Prob. 50PCh. 9.2 - Locate the centroid (x,y,z) of the wire bent in...Ch. 9.2 - Prob. 8FPCh. 9.2 - Prob. 9FPCh. 9.2 - Prob. 10FPCh. 9.2 - Prob. 11FPCh. 9.2 - Prob. 12FPCh. 9.2 - Prob. 51PCh. 9.2 - Prob. 52PCh. 9.2 - Prob. 53PCh. 9.2 - Prob. 54PCh. 9.2 - Locate the centroid (x,y) of the metal cross...Ch. 9.2 - Prob. 56PCh. 9.2 - Prob. 57PCh. 9.2 - Determine the location of the centroidal axis xx...Ch. 9.2 - Locate the centroid (x,y) of the shaded area....Ch. 9.2 - Prob. 60PCh. 9.2 - Determine the location of the centroid C of the...Ch. 9.2 - Locate the centroid (x,y) of the shaded area....Ch. 9.2 - Determine the location of the centroid of the...Ch. 9.2 - Locate the centroid (x,y) of the shaded area....Ch. 9.2 - Determine the location (x,y) of the centroid C of...Ch. 9.2 - Determine the location of the centroid C for a...Ch. 9.2 - Locate the centroid of the cross-sectional area...Ch. 9.2 - A triangular plate made of homogeneous material...Ch. 9.2 - A triangular plate made of homogeneous material...Ch. 9.2 - Prob. 70PCh. 9.2 - Prob. 71PCh. 9.2 - Prob. 72PCh. 9.2 - Prob. 73PCh. 9.2 - Prob. 74PCh. 9.2 - Locate the center of mass (x,y,z) of the...Ch. 9.2 - The sheet metal part has the dimensions shown....Ch. 9.2 - Prob. 77PCh. 9.2 - The wooden table is made from a square board...Ch. 9.2 - Prob. 79PCh. 9.2 - Prob. 80PCh. 9.2 - Prob. 81PCh. 9.2 - Prob. 82PCh. 9.2 - Prob. 83PCh. 9.2 - Prob. 84PCh. 9.2 - Determine the distance z to the centroid of the...Ch. 9.2 - Prob. 86PCh. 9.2 - Prob. 87PCh. 9.2 - Prob. 88PCh. 9.2 - Prob. 89PCh. 9.3 - Prob. 13FPCh. 9.3 - Prob. 14FPCh. 9.3 - Prob. 15FPCh. 9.3 - Prob. 16FPCh. 9.3 - Prob. 90PCh. 9.3 - Prob. 91PCh. 9.3 - Prob. 92PCh. 9.3 - Prob. 93PCh. 9.3 - Prob. 94PCh. 9.3 - Prob. 95PCh. 9.3 - Prob. 96PCh. 9.3 - Determine the volume of concrete needed to...Ch. 9.3 - Determine the surface area of the curb. Do not...Ch. 9.3 - Prob. 99PCh. 9.3 - Prob. 100PCh. 9.3 - Prob. 101PCh. 9.3 - Prob. 102PCh. 9.3 - Prob. 103PCh. 9.3 - Prob. 104PCh. 9.3 - Prob. 105PCh. 9.3 - Prob. 106PCh. 9.3 - Prob. 107PCh. 9.3 - Prob. 108PCh. 9.3 - Prob. 109PCh. 9.3 - Prob. 110PCh. 9.3 - Prob. 111PCh. 9.3 - Prob. 112PCh. 9.3 - Prob. 113PCh. 9.3 - Prob. 114PCh. 9.5 - Determine the magnitude of the hydrostatic force...Ch. 9.5 - Determine the magnitude of the hydrostatic force...Ch. 9.5 - Prob. 19FPCh. 9.5 - Prob. 20FPCh. 9.5 - Prob. 21FPCh. 9.5 - The pressure loading on the plate varies uniformly...Ch. 9.5 - The load over the plate varies linearly along the...Ch. 9.5 - Prob. 117PCh. 9.5 - Prob. 118PCh. 9.5 - Prob. 119PCh. 9.5 - When the tide water A subsides, the tide gate...Ch. 9.5 - The tank is filled with water to a depth of d = 4...Ch. 9.5 - Prob. 122PCh. 9.5 - The factor of safety for tipping of the concrete...Ch. 9.5 - Prob. 124PCh. 9.5 - The tank is used to store a liquid having a...Ch. 9.5 - Prob. 126PCh. 9.5 - Prob. 127PCh. 9.5 - Prob. 128PCh. 9.5 - Determine the magnitude of the resultant force...Ch. 9.5 - The semicircular drainage pipe is filled with...Ch. 9.5 - Prob. 1RPCh. 9.5 - Prob. 2RPCh. 9.5 - Prob. 3RPCh. 9.5 - Prob. 4RPCh. 9.5 - Prob. 5RPCh. 9.5 - Prob. 6RPCh. 9.5 - Prob. 7RPCh. 9.5 - Prob. 8RPCh. 9.5 - The gate AB is 8 m wide. Determine the horizontal...Ch. 9.5 - Prob. 10RP
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