Mechanics of Materials (10th Edition)
10th Edition
ISBN: 9780134319650
Author: Russell C. Hibbeler
Publisher: PEARSON
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Textbook Question
Chapter 1.7, Problem 1.77P
Determine the required diameter of the pins at A and B to the nearest
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Can you show the free body diagram and the solution?
For the frame shown, a 4226-N load is acting on member ABD at D. If the allowable material shear stress for is 42 MPa, determine the required diameter (rounded off to the nearest 2.5 mm) of the pins at C and D. Pin C and pin D are subjected to double shear and single shear, respectively. If the thickness of member BC is 12 mm and that of member DE is 16 mm, determine the maximum bearing stress at C.
The steel end-cap is fitted into grooves cut in the timber post. The working stresses for the post
are 1.7 MPa in shear parallel to the grain and 5.6 MPa in bearing perpendicular to the grain.
Determine the smallest safe dimensions a and b. Show the free body diagram.
12 kN
+100 mm
12 kN
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. Determine...Ch. 1.7 - The aluminum bracket A is used to support the...Ch. 1.7 - If the allowable tensile stress for the bar is...Ch. 1.7 - The bar is connected to the support using a pin...Ch. 1 - The beam AB is pin supported at A and supported by...Ch. 1 - The long bolt passes through the 30-mm-thick...Ch. 1 - Determine the required thickness of member BC to...Ch. 1 - The circular punch B exerts a force of 2 kN on the...Ch. 1 - Determine the average punching shear stress the...Ch. 1 - The 150 mm by 150 mm block of aluminum supports a...Ch. 1 - The yoke-and-rod connection is subjected to a...Ch. 1 - The cable has a specific weight (weight/volume)...
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- The uniform 3-Mg bar is supported by a smooth wall at A and pin connected a B (double shear). Determine the diameter of the smallest pin that can be used without exceeding the allowable shearing stress in the rivet is 70 MPa. Express your answer in "mm" to the nearest whole number. Note: Use the rule in rounding-off numbers (normal rounding-off). DO NOT PUTA UNIT IN YOUR ANSWER, only the numerical value is required* 10marrow_forward#2 The joint is fastened together using two bolts. Determine the required diameter of the bolts if the shear stress failure for the bolts is Tau = 350MPA. Use a Factor of Safety for Shear of F.S. = 2.5. Set up your FBD and forces on bolts correctly i Tip: F.S. = 80 kN 30 mm- 30 mm 40 kN 40 kNarrow_forwardIf the pin at C has a diameter of 5 mm and is subjected to double shear, the maximum average shear stress, in MPa, is P Barrow_forward
- 4. The frame is subjected to the load of 15 kN which acts on member ABD at D. Determine the required diameter of the pins at D and c if the allowable shear stress for the material is tallow = 115 MPа. Pin c is subjected to single shear, whereas pin D is subjected to double shear. 15 kN Fim-15 m- E 30° 1.5 m 1.5 marrow_forwardThe aluminum tube is subjected to a torque of M = 2 kN m. Determine the average shear stress in the tube if the dimension a = 200 mm. Each side has a thickness oft = 6 mm. Give the answer in the box in MPa with one decimal place. (ANSWER NEATLY AND ASAP ONLY IF CORRECT)arrow_forwardDetermine the required diameter of the pins at A and B if theallowable shear stress for the material is tallow = 100 MPa.Both pins are subjected to double shear.arrow_forward
- Determine the required diameter of the pins at A and B if the allowable shear stress for the material is tallow = 100 MPa. Both pins are subjected to double shear.arrow_forwardF The shaft is loaded with two forces as shown and is fixed at A. The strength is defined as the maximum allowable force F that does not produce shear stress above the material's maximum al- lowable value of 4 ksi. Determine the strength. By what factor would the strength increase if the shaft diameter were doubled? (L₁ = 12 in., L₂ = 6 in., and d = 0.5 in.)arrow_forwardTwo forces, each of magnitude P, are applied to the wrench. The diameter of the steel shaft AB is 30mm. Determine the largest allowable value of P if the shear stress in the shaft is not to exceed 120MPa and it's angle of twist is limited to 7deg. Use G=83GPa for steel. -Draw and label the diagram correctly, No diagram in the solution will be marked wrong. -Shortcut solution will be marked wrong.arrow_forward
- The bell crank is in equilibrium for the forces acting in rods (1) and (2). The bell crank is supported by a pin with a diameter of 14 mm at B that acts in single shear. The thickness of the bell crank is 7 mm. Assume a = 60 mm, b = 100 mm, F₁ = 1000 N, and 9 = 75°. Determine the average shear stress in pin B. Answer in MPa rounded-off to 2 decimal places. Bell crank (2) marrow_forward3 3 3 if its subjected to double shear, determine the average shear stress in the pin. Take P= 610 16 Answer in units of US Customary. 3ft aft E D 2ft- = 610 16 ✓p= The frame Supports the loading shown. The pin at A has a diameter of 0.25 inarrow_forward1. The pictured link acts as a part of the elevator control for a small airplane. If the attached aluminum tube has an inner diameter of 25 mm and a wall thickness of 5 mm, determine the shear stress in the outer and inner surfaces of the tube when a cable force of 600 N is applied to the cables. Also, sketch the shear-stress distribution over the cross-section.arrow_forward
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