Mechanics of Materials
9th Edition
ISBN: 9780133254426
Author: Russell C. Hibbeler
Publisher: Prentice Hall
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 6.4, Problem 6.65P
A shaft is made of a polymer having an elliptical cross section. If it resists an internal moment of M = 50 N · m, determine the maximum bending stress in the material (a) using the flexure formula, where lz =
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Q3:
(10 MARKS)
A piston with a weight of 29.4 N is supported by a spring
and dashpot. A dashpot of damping coefficient c = 275
N.s/m acts in parallel with the spring of stiffness k = 2400
N/m. A fluctuating pressure p = 960 sin 30t N/m² acts on
the piston, whose top surface area is 0.05 m². Determine
the steady-state displacement as a function of time and the
maximum force transmitted to the base.
P=Po sin cot
W
9. Design a spur gear drive required to transmit 45 kW at a pinion speed of 800 r.p.m. The velocity ratio
is 3.5 : 1. The teeth are 20° full-depth involute with 18 teeth on the pinion. Both the pinion and gear
are made of steel with a maximum safe static stress of 180 MPa. Assume a safe stress of 40 MPa for
the material of the shaft and key.
10. Design a pair of spur gears with stub teeth to transmit 55 kW from a 175 mm pinion running at 2500
r.p.m. to a gear running at 1500 r.p.m. Both the gears are made of steel having B.H.N. 260. Approximate
the pitch by means of Lewis equation and then adjust the dimensions to keep within the limits set by
the dynamic load and wear equation.
7. A motor shaft rotating at 1440 r.p.m. has to transmit 15 kW to a low speed shaft rotating at 500 r.p.m.
The teeth are 20° involute with 25 teeth on the pinion. Both the pinion and gear are made of cast iron
with a maximum safe stress of 56 MPa. A safe stress of 35 MPa may be taken for the shaft on which
the gear is mounted. Design and sketch the spur gear drive to suit the above conditions. The starting
torque may be assumed as 1,25 times the running torque.
Ruins 20 LW at 100 nm to another shaft running approxi
Chapter 6 Solutions
Mechanics of Materials
Ch. 6.2 - In each case, the beam is subjected to the...Ch. 6.2 - and then draw the shear and moment diagrams for...Ch. 6.2 - In each case, express the shear and moment...Ch. 6.2 - In each case, express the shear and moment...Ch. 6.2 - In each case, express the shear and moment...Ch. 6.2 - In each case, draw the shear and moment diagrams...Ch. 6.2 - In each case, draw the shear and moment diagrams...Ch. 6.2 - In each case, draw the shear and moment diagrams...Ch. 6.2 - In each case, draw the shear and moment diagrams...Ch. 6.2 - If the force applied to the handle of the load...
Ch. 6.2 - Draw the shear and moment diagrams for the shaft....Ch. 6.2 - The crane is used to support the engine, which has...Ch. 6.2 - Prob. 6.4PCh. 6.2 - •6–5. Draw the shear and moment diagrams for the...Ch. 6.2 - Express the internal shear and moment in terms of...Ch. 6.2 - Prob. 6.7PCh. 6.2 - Prob. 6.8PCh. 6.2 - Prob. 6.9PCh. 6.2 - Members ABC and BD of the counter chair are...Ch. 6.2 - Prob. 6.11PCh. 6.2 - A reinforced concrete pier is used to support the...Ch. 6.2 - Prob. 6.13PCh. 6.2 - The industrial robot is held in the stationary...Ch. 6.2 - Determine the placement distance a of the roller...Ch. 6.2 - Express the internal shear and moment in the...Ch. 6.2 - Draw the shear and moment diagrams for the beam,...Ch. 6.2 - Draw the shear and moment diagrams for the beam....Ch. 6.2 - Draw the shear and moment diagrams for the...Ch. 6.2 - The 150-lb man sits in the center of the boat,...Ch. 6.2 - Prob. 6.22PCh. 6.2 - The footing supports the load transmitted by the...Ch. 6.2 - Express the shear and moment in terms of x for 0 ...Ch. 6.2 - Draw the shear and moment diagrams for the beam...Ch. 6.2 - Draw the shear and moment diagrams for the beam....Ch. 6.2 - Draw the shear and moment diagrams for the beam....Ch. 6.2 - Prob. 6.29PCh. 6.2 - 6–30. The beam is bolted or pinned at A and rests...Ch. 6.2 - The support at A allows the beam to slide freely...Ch. 6.2 - The smooth pin is supported by two leaves A and B...Ch. 6.2 - The shaft is supported by a smooth thrust bearing...Ch. 6.2 - Draw the shear and moment diagrams for the...Ch. 6.2 - Draw the shear and moment diagrams for the beam....Ch. 6.2 - Prob. 6.36PCh. 6.2 - Draw the shear and moment diagrams for the beam...Ch. 6.2 - The beam is used to support a uniform load along...Ch. 6.2 - Draw the shear and moment diagrams for the double...Ch. 6.2 - Draw the shear and moment diagrams for the simply...Ch. 6.2 - The compound beam is fixed at A, pin connected at...Ch. 6.2 - Draw the shear and moment diagrams for the...Ch. 6.2 - The compound beam is fixed at A, pin connected at...Ch. 6.2 - Draw the shear and moment diagrams for the beam....Ch. 6.2 - A short link at B is used to connect beams AB and...Ch. 6.2 - 6–46. Determine the placement b of the hooks to...Ch. 6.4 - Determine the moment of inertia of the cross...Ch. 6.4 - Determine the location of the centroid, y, and the...Ch. 6.4 - In each case, show how the bending stress acts on...Ch. 6.4 - Sketch the bending stress distribution over each...Ch. 6.4 - If the beam is subjected to a bending moment of M...Ch. 6.4 - If the beam is subjected to a bending moment of M...Ch. 6.4 - If the beam is subjected to a bending moment of M...Ch. 6.4 - If the beam is subjected to a bending moment of M...Ch. 6.4 - If the beam is subjected to a bending moment of M...Ch. 6.4 - Prob. 6.47PCh. 6.4 - Determine the moment M that will produce a maximum...Ch. 6.4 - Determine the maximum tensile and compressive...Ch. 6.4 - 6–50. A member has the triangular cross section...Ch. 6.4 - Prob. 6.51PCh. 6.4 - Prob. 6.52PCh. 6.4 - Prob. 6.53PCh. 6.4 - If the built-up beam is subjected to an internal...Ch. 6.4 - If the built-up beam is subjected to an internal...Ch. 6.4 - Prob. 6.56PCh. 6.4 - Prob. 6.57PCh. 6.4 - Prob. 6.58PCh. 6.4 - Prob. 6.59PCh. 6.4 - Prob. 6.60PCh. 6.4 - 6–61. The beam is subjected to a moment of 15 kip...Ch. 6.4 - 6–62. A box beam is constructed from four pieces...Ch. 6.4 - Prob. 6.63PCh. 6.4 - The axle of the freight car is subjected to a...Ch. 6.4 - A shaft is made of a polymer having an elliptical...Ch. 6.4 - Solve Prob. 6-65 if the moment M = 50 N m is...Ch. 6.4 - Prob. 6.67PCh. 6.4 - The shaft is supported by smooth journal bearings...Ch. 6.4 - Prob. 6.69PCh. 6.4 - Prob. 6.70PCh. 6.4 - The boat has a weight of 2300 lb and a center of...Ch. 6.4 - Determine the absolute maximum bending stress in...Ch. 6.4 - Determine the smallest allowable diameter of the...Ch. 6.4 - The pin is used to connect the three links...Ch. 6.4 - The shaft is supported by a thrust bearing at A...Ch. 6.4 - Prob. 6.76PCh. 6.4 - If the beam is subjected to an internal moment of...Ch. 6.4 - If the allowable tensile and compressive stress...Ch. 6.4 - If the beam is subjected to an internal moment of...Ch. 6.4 - If the beam is subjected to a moment of M = 100 kN...Ch. 6.4 - If the beam is made of material having an...Ch. 6.4 - The shaft is supported by a smooth thrust bearing...Ch. 6.4 - The shaft is supported by a thrust bearing at A...Ch. 6.4 - If the intensity of the load w = 15 kN/m,...Ch. 6.4 - If the allowable bending stress is allow = 150...Ch. 6.4 - Prob. 6.86PCh. 6.4 - Prob. 6.87PCh. 6.4 - *6–88. If the beam has a square cross section of 9...Ch. 6.4 - If the compound beam in Prob. 642 has a square...Ch. 6.4 - If the beam in Prob. 628 has a rectangular cross...Ch. 6.4 - Determine the absolute maximum bending stress in...Ch. 6.4 - Determine, to the nearest millimeter, the smallest...Ch. 6.4 - 6–93. The wing spar ABD of a light plane is made...Ch. 6.4 - Prob. 6.94PCh. 6.4 - Prob. 6.95PCh. 6.4 - A log that is 2 ft in diameter is to be cut into a...Ch. 6.4 - A log that is 2 ft in diameter is to be cut into a...Ch. 6.4 - If the beam in Prob.63 has a rectangular cross...Ch. 6.4 - Prob. 6.99PCh. 6.4 - If d = 450 mm, determine the absolute maximum...Ch. 6.4 - If the allowable bending stress is allow = 6 MPa,...Ch. 6.4 - Prob. 6.102PCh. 6.4 - 6–103. If the overhanging beam is made of wood...Ch. 6.5 - Determine the bending stress at corners A and B....Ch. 6.5 - Determine the maximum bending stress in the beams...Ch. 6.5 - The member has a square cross section and is...Ch. 6.5 - The member has a square cross section and is...Ch. 6.5 - Consider the general case of a prismatic beam...Ch. 6.5 - 6–107. If the beam is subjected to the internal...Ch. 6.5 - 6-108. If the wood used for the T-beam has an...Ch. 6.5 - 6-109. The box beam is subjected to the internal...Ch. 6.5 - 6-110. If the wood used for the box beam has an...Ch. 6.5 - 6-111. If the beam is subjected to the internal...Ch. 6.5 - 6-112. If the beam is made from a material having...Ch. 6.5 - Prob. 6.113PCh. 6.5 - 6-114. The T-beam is subjected to a bending moment...Ch. 6.5 - 6-115. The beam has a rectangular cross section....Ch. 6.5 - For the section, Iy' = 31.7(10-6) m4, Iz' =...Ch. 6.5 - For the section, Iy' = 31.7(10-6) m4, Iz' =...Ch. 6.5 - If the applied distributed loading of w = 4 kN/m...Ch. 6.5 - Determine the maximum allowable intensity w of the...Ch. 6.9 - The composite beam is made of steel (A) bonded to...Ch. 6.9 - The composite beam is made of steel (A) bonded to...Ch. 6.9 - Segment A of the composite beam is made from...Ch. 6.9 - Segment A of the composite beam is made from...Ch. 6.9 - Prob. 6.124PCh. 6.9 - The wooden section of the beam is reinforced with...Ch. 6.9 - The wooden section of the beam is reinforced with...Ch. 6.9 - Prob. 6.127PCh. 6.9 - The steel channel is used to reinforce the wood...Ch. 6.9 - Prob. 6.129PCh. 6.9 - 6-130. The beam is made from three types of...Ch. 6.9 - 6-131. The concrete beam is reinforced with three...Ch. 6.9 - *6-132. The wide-flange section is reinforced with...Ch. 6.9 - Prob. 6.133PCh. 6.9 - If the beam is subjected to a moment of M = 45 kN...Ch. 6.9 - Prob. 6.135PCh. 6.9 - For the curved beam in Fig. 640a, show that when...Ch. 6.9 - The curved member is subjected to the moment of M...Ch. 6.9 - The curved member is made from material having an...Ch. 6.9 - The curved beam is subjected to a moment of M = 40...Ch. 6.9 - The curved beam is made from material having an...Ch. 6.9 - If P = 3 kN, determine the bending stress at...Ch. 6.9 - If the maximum bending stress at section a-a is...Ch. 6.9 - The elbow of the pipe has an outer radius of 0.75...Ch. 6.9 - Prob. 6.144PCh. 6.9 - Prob. 6.145PCh. 6.9 - Prob. 6.146PCh. 6.9 - Prob. 6.147PCh. 6.9 - Prob. 6.148PCh. 6.9 - Prob. 6.149PCh. 6.9 - 6-150. The bar is subjected to a moment of M = 153...Ch. 6.9 - Prob. 6.151PCh. 6.9 - Prob. 6.152PCh. 6.9 - Prob. 6.153PCh. 6.9 - 6-154. The simply supported notched bar is...Ch. 6.9 - Prob. 6.155PCh. 6.9 - *6-156. Determine the length L of the center...Ch. 6.9 - Prob. 6.157PCh. 6.10 - Determine the shape factor for the wide-flange...Ch. 6.10 - 6-159. The beam is made of an elastic plastic...Ch. 6.10 - Prob. 6.160PCh. 6.10 - Prob. 6.161PCh. 6.10 - Prob. 6.162PCh. 6.10 - Determine the plastic moment Mp that can be...Ch. 6.10 - Determine the shape factor for the beam. Prob....Ch. 6.10 - The beam is made of elastic perfectly plastic...Ch. 6.10 - Determine the shape factor for the beam. Prob....Ch. 6.10 - The beam is made of an elastic perfectly plastic...Ch. 6.10 - Prob. 6.168PCh. 6.10 - Prob. 6.169PCh. 6.10 - 6-170. The box beam is made from an...Ch. 6.10 - 6-171. The beam is made from elastic-perfectly...Ch. 6.10 - *6-172. Determine the shape factor for the...Ch. 6.10 - Prob. 6.173PCh. 6.10 - Prob. 6.174PCh. 6.10 - 6-175. The box beam is made from an...Ch. 6.10 - The wide-flange member is made from an elastic...Ch. 6.10 - Prob. 6.177PCh. 6.10 - The plexiglass bar has a stress-strain curve that...Ch. 6.10 - The stress-strain diagram for a titanium alloy can...Ch. 6.10 - A beam is made from polypropylene plastic and has...Ch. 6.10 - Prob. 6.181PCh. 6.10 - The bar is made of an aluminum alloy having a...Ch. 6 - Using appropriate measurements and data, explain...Ch. 6 - Determine the shape factor for the wide-flange...Ch. 6 - Prob. 6.184RPCh. 6 - The compound beam consists of two segments that...Ch. 6 - The composite beam consists of a wood core and two...Ch. 6 - 6-187. Solve Prob. 6-186 if the moment is applied...Ch. 6 - If it resists a moment of M = 125 N m, determine...Ch. 6 - Determine the maximum bending stress in the handle...Ch. 6 - The curved beam is subjected to a bending moment...Ch. 6 - Determine the shear and moment in the beam as...Ch. 6 - A wooden beam has a square cross section as shown...Ch. 6 - Draw the shear and moment diagrams for the shaft...Ch. 6 - The strut has a square cross section a by a and is...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- 6. A two stage reduction drive is to be designed to transmit 2 kW; the input speed being 960 r.p.m. and overall reduction ratio being 9. The drive consists of straight tooth spur gears only, the shafts being spaced 200 mm apart, the input and output shafts being co-axial.arrow_forward2 A metal block of mass m = 10 kg is sliding along a frictionless surface with an initial speed Vo, as indicated below. The block then slides above an electromagnetic brake that applies a force FEB to the block, opposing its motion. The magnitude of the electromagnetic force varies quadratically with the distance moved along the brake (x): 10 FEB = kx², with k = 5 N m² V₁ = 8 m/s m = 10 kg FEB Frictionless surface Electromagnetic brake ⇒x Determine how far the block slides along the electromagnetic brake before stopping, in m.arrow_forwardQ1: Determine the length, angle of contact, and width of a 9.75 mm thick leather belt required to transmit 15 kW from a motor running at 900 r.p.m. The diameter of the driving pulley of the motor is 300 mm. The driven pulley runs at 300 r.p.m. and the distance between the centers of two pulleys is 3 meters. The density of the leather is 1000 kg/m³. The maximum allowable stress in the leather is 2.5 MPa. The coefficient of friction between the leather and pulley is 0.3. Assume open belt drive.arrow_forward
- 5. A 15 kW and 1200 r.p.m. motor drives a compressor at 300 r.p.m. through a pair of spur gears having 20° stub teeth. The centre to centre distance between the shafts is 400 mm. The motor pinion is made of forged steel having an allowable static stress as 210 MPa, while the gear is made of cast steel having allowable static stress as 140 MPa. Assuming that the drive operates 8 to 10 hours per day under light shock conditions, find from the standpoint of strength, 1. Module; 2. Face width and 3. Number of teeth and pitch circle diameter of each gear. Check the gears thus designed from the consideration of wear. The surface endurance limit may be taken as 700 MPa. [Ans. m = 6 mm; b= 60 mm; Tp=24; T=96; Dp = 144mm; DG = 576 mm]arrow_forward4. G A micarta pinion rotating at 1200 r.p.m. is to transmit 1 kW to a cast iron gear at a speed of 192 r.p.m. Assuming a starting overload of 20% and using 20° full depth involute teeth, determine the module, number of teeth on the pinion and gear and face width. Take allowable static strength for micarta as 40 MPa and for cast iron as 53 MPa. Check the pair in wear.arrow_forwardI want to solve these choicesarrow_forward
- 2. A spur gear made of bronze drives a mid steel pinion with angular velocity ratio of 32: 1. The pressure angle is 14½. It transmits 5 kW at 1800 r.p.m. of pinion. Considering only strength, design the smallest diameter gears and find also necessary face width. The number of teeth should not be less than 15 teeth on either gear. The elastic strength of bronze may be taken as 84 MPa and of steel as 105 MPa. Lewis factor for 14½½ pressure angle may be taken 0.684 0.124 y = No. of teeth as [Ans. m 3 mm; b= 35 mm; Dp = 48 mm; D= 168 mm]arrow_forwardQ2. Determine the safety factors for the bracket rod shown in Figure 2 based on both the distortion-energy theory and the maximum shear theory and compare them. Given: The material is 2024-T4 aluminum with a yield strength of 47 000 psi. The rod length /= 6 in. and arm a = 8 in. The rod outside diameter od 1.5 in., id = 1 in, h=2 in., t=0.5 in., Load F= 1000 lb. Assumptions: The load is static and the assembly is at room temperature. Consider shear due to transverse loading as well as other stresses. (Note: solve in SI units) wall tube Figure 2 armarrow_forwardThe question has been set up with all the cuts needed to accurately derive expressions for V(x) and M(x). Using the cuts free body diagrams set up below, derive expressions for V(x) and M(x). If you use the method of cuts then validate your answers using calculus or vice versa.arrow_forward
- It is required to treat 130 kmol/hr of chloroform-air feed gas mixture that contains 12% chloroform. It is required to remove 93% of chloroform using 150 kmol/hr of solvent that contains 99.6% water and 0.4% chloroform. The cross sectional area of the column is 0.8 m². Calculate the column height using the following data; kx'.a = 1.35 (kmol/m³.s (Ax)), and ky'.a = 0.06 (kmol/m³.s (Ay)), kx/ky = 1.35, and the equilibrium data are: X 0 0.0133 0.033 y 0 0.01 0.0266 0.049 0.064 0.0747 0.0933 0.1053 0.0433 0.06 0.0733 0.111 0.1 0.12 0.14arrow_forward४ B: Find the numerical solution for the 2D equation below and calculate the temperature values for each grid point shown in Fig. 2 (show all steps). (Do only one trail using following initial values and show the final matrix) [T1] T₂ T3 [T] 1 = [0] 0 0 d dx dx) (ka)+4(ka) = dy -20xy, k = 1 + 0.3 T ge L=3cm, 4x= Ay B.Cs.: at x=0=LT=0°C at y=0-L T=10°C Fig. (2)arrow_forward: +0 العنوان use only Two rods fins) having same dimensions, one made orass (k = 85 Wm K) and the mer of copper (k = 375 W/m K), having of their ends inserted into a furna. At a section 10.5 cm a way from furnace, the temperature of brass rod 120 Find the distance at which the ame temperature would be reached in the per rod ? both ends are ex osed to the same environment. ns 2.05 ۲/۱ ostrararrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Everything About COMBINED LOADING in 10 Minutes! Mechanics of Materials; Author: Less Boring Lectures;https://www.youtube.com/watch?v=N-PlI900hSg;License: Standard youtube license