Mechanics of Materials (10th Edition)
10th Edition
ISBN: 9780134319650
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 1.2, Problem 1.30P
A differential element taken from a curved bar is shown in the figure. Show that dN/dθ = V, dV/dθ = −N, dM/dθ = −T, and dT/dθ = M.
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Chapter 1 Solutions
Mechanics of Materials (10th Edition)
Ch. 1.2 - In each case, explain how to find the resultant...Ch. 1.2 - Determine the resultant internal normal force,...Ch. 1.2 - Determine the resultant internal normal force,...Ch. 1.2 - Determine the resultant internal normal force,...Ch. 1.2 - Determine the resultant internal normal force,...Ch. 1.2 - Determine the resultant internal normal force,...Ch. 1.2 - Determine the resultant internal normal force,...Ch. 1.2 - The shaft is supported by a smooth thrust bearing...Ch. 1.2 - Determine the resultant internal normal and shear...Ch. 1.2 - Determine the resultant internal loadings acting...
Ch. 1.2 - The shaft is supported by a smooth thrust bearing...Ch. 1.2 - Determine the resultant internal loadings acting...Ch. 1.2 - Determine the resultant internal loadings on the...Ch. 1.2 - Determine the resultant internal loadings at cross...Ch. 1.2 - The beam supports the distributed load shown....Ch. 1.2 - The beam supports the distributed load shown....Ch. 1.2 - The boom DF of the jib crane and the column DE...Ch. 1.2 - Determine the resultant internal loadings acting...Ch. 1.2 - Determine the resultant internal loadings acting...Ch. 1.2 - The blade of the hacksaw is subjected to a...Ch. 1.2 - The blade of the hacksaw is subjected to a...Ch. 1.2 - The beam supports the triangular distributed load...Ch. 1.2 - The beam supports the distributed load shown....Ch. 1.2 - The shaft is supported at its ends by two bearings...Ch. 1.2 - The shaft is supported at its ends by two bearings...Ch. 1.2 - The hand crank that is used in a press has the...Ch. 1.2 - Determine the resultant internal loadings acting...Ch. 1.2 - Determine the resultant internal loadings acting...Ch. 1.2 - The metal stud punch is subjected to a force of...Ch. 1.2 - Determine the resultant internal loadings acting...Ch. 1.2 - Determine the resultant internal loadings acting...Ch. 1.2 - Determine the resultant internal loadings acting...Ch. 1.2 - Determine the resultant internal loadings acting...Ch. 1.2 - The pipe has a mass of 12 kg/m. If it is fixed to...Ch. 1.2 - If the drill bit jams when the brace is subjected...Ch. 1.2 - The curved rod AD of radius r has a weight per...Ch. 1.2 - A differential element taken from a curved bar is...Ch. 1.5 - In each case, determine the largest internal shear...Ch. 1.5 - Determine the largest internal normal force in the...Ch. 1.5 - Determine the internal normal force at section A...Ch. 1.5 - The lever is held to the fixed shaft using the pin...Ch. 1.5 - The single-V butt joint transmits the force of 5...Ch. 1.5 - The uniform beam is supported by two rods AB and...Ch. 1.5 - Determine the average normal stress on the cross...Ch. 1.5 - Determine the average normal stress on the cross...Ch. 1.5 - If the 600-kN force acts through the centroid of...Ch. 1.5 - Determine the average normal stress at points A,...Ch. 1.5 - Determine the average normal stress in rod AB if...Ch. 1.5 - The supporting wheel on a scaffold is held in...Ch. 1.5 - Determine the largest intensity w of the uniform...Ch. 1.5 - The bar has a cross-sectional area A and is...Ch. 1.5 - The small block has a thickness of 0.5 in. If the...Ch. 1.5 - If the material fails when the average normal...Ch. 1.5 - If the block is subjected to a centrally applied...Ch. 1.5 - The plate has a width of 0.5 m. If the stress...Ch. 1.5 - The board is subjected to a tensile force of 200...Ch. 1.5 - The boom has a uniform weight of 600 lb and is...Ch. 1.5 - Determine the average normal stress in each of the...Ch. 1.5 - If the average normal stress in each of the...Ch. 1.5 - Determine the maximum average shear stress in pin...Ch. 1.5 - If P=5 kN, determine the average shear stress in...Ch. 1.5 - Determine the maximum magnitude P of the loads the...Ch. 1.5 - The column is made of concrete having a density of...Ch. 1.5 - The beam is supported by two rods AB and CD that...Ch. 1.5 - The beam is supported by two rods AB and CD that...Ch. 1.5 - If P = 15 kN, determine the average shear stress...Ch. 1.5 - The railcar docklight is supported by the...Ch. 1.5 - The plastic block is subjected to an axial...Ch. 1.5 - The two steel members are joined together using a...Ch. 1.5 - The bar has a cross-sectional area of 400(106) m2....Ch. 1.5 - The bar has a cross-sectional area of 400(106) m2....Ch. 1.5 - The two members used in the construction of an...Ch. 1.5 - The 2-Mg concrete pipe has a center of mass at...Ch. 1.5 - The 2-Mg concrete pipe has a center of mass at...Ch. 1.5 - The pier is made of material having a specific...Ch. 1.5 - Rods AB and BC have diameters of 4 mm and 6 mm,...Ch. 1.5 - The uniform bar, having a cross-sectional area of...Ch. 1.5 - The bar has a cross-sectional area of 400(106) m2....Ch. 1.5 - The bar has a cross-sectional area of 400(106) m2....Ch. 1.5 - The prismatic bar has a cross-sectional area A. If...Ch. 1.5 - The prismatic bar has a cross-sectional area A. If...Ch. 1.5 - The bars of the truss each have a cross-sectional...Ch. 1.5 - The bars of the truss each have a cross-sectional...Ch. 1.5 - Determine the largest load P that can be applied...Ch. 1.5 - Determine the greatest constant angular velocity ...Ch. 1.5 - The radius of the pedestal is defined by r =...Ch. 1.7 - Rods AC and BC are used to suspend the 200-kg...Ch. 1.7 - If it is subjected to double shear, determine the...Ch. 1.7 - Determine the maximum average shear stress...Ch. 1.7 - If each of the three nails has a diameter of 4 mm...Ch. 1.7 - The strut is glued to the horizontal member at...Ch. 1.7 - Determine the maximum average shear stress...Ch. 1.7 - If the eyebolt is made of a material having a...Ch. 1.7 - If the bar assembly is made of a material having a...Ch. 1.7 - Determine the maximum force P that can be applied...Ch. 1.7 - The pin is made of a material having a failure...Ch. 1.7 - If the bolt head and the supporting bracket are...Ch. 1.7 - Six nails are used to hold the hanger at A against...Ch. 1.7 - If A and B are both made of wood and are 38 in....Ch. 1.7 - Prob. 1.70PCh. 1.7 - The connection is made using a bolt and nut and...Ch. 1.7 - The tension member is fastened together using two...Ch. 1.7 - The steel swivel bushing in the elevator control...Ch. 1.7 - The spring mechanism is used as a shock absorber...Ch. 1.7 - Determine the size of square bearing plates A and...Ch. 1.7 - Determine the maximum load P that can be applied...Ch. 1.7 - Determine the required diameter of the pins at A...Ch. 1.7 - If the allowable tensile stress for wires AB and...Ch. 1.7 - If the allowable tensile stress for wires AB and...Ch. 1.7 - The cotter is used to hold the two rods together....Ch. 1.7 - Determine the required diameter of the pins at A...Ch. 1.7 - The steel pipe is supported on the circular base...Ch. 1.7 - The boom is supported by the winch cable that has...Ch. 1.7 - The boom is supported by the winch cable that has...Ch. 1.7 - The assembly consists of three disks A, B, and C...Ch. 1.7 - The two aluminum rods support the vertical force...Ch. 1.7 - The two aluminum rods AB and AC have diameters of...Ch. 1.7 - Determine the required minimum thickness t of...Ch. 1.7 - Determine the maximum allowable load P that can be...Ch. 1.7 - The compound wooden beam is connected together by...Ch. 1.7 - The hanger is supported using the rectangular pin....Ch. 1.7 - The hanger is supported using the rectangular pin....Ch. 1.7 - The rods AB and CD are made of steel. 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