MECHANICS OF MATERIALS-TEXT
9th Edition
ISBN: 2810014920922
Author: HIBBELER
Publisher: PEARSON
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Textbook Question
Chapter 6.4, Problem 6.101P
If the allowable bending stress is σallow = 6 MPa, determine the minimum dimension d of the beam’s cross-sectional area to the nearest mm.
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CORRECT ANSWER ONLY WITH COMPLETE FBD. PREFERABLY HANDWRITTEN. I WILL UPVOTE
1. The beam shown carries the following loads:Total dead load, wDL = 36 kN/mConcentrated live load, PLL = 240 kNThe beam section is HSS16X12X3/8 with properties:Span, L = 6 mArea, A = 12,100 mm2Moment of inertia about x-axis, Ix = 292 x 106 mm4Fy = 345 MPa
1. Calculate the location of the live load, from the left support, for maximum moment to occur at the fixed support.Answer: 2.536 m2. Calculate the maximum moment. Answer: 439.128 kN-m
CORRECT ANSWER AND COMPLETE FBD ONLY. I PREFER HANDWRITTEN BUT ITS OKAY IF NOT. I WILL UPVOTE
2. The space truss shown is supported by ball-and-socket joints at A, B and C. Factored loads P1 and P2 areacting on joints D and E, respectively, towards the negative y-direction.
1. Calculate the stress of member CE, indicate tension or compression. Answer: 23.61 MPa Tension2. Calculate the stress of member AD, indicate tension or compression. Answer: 21.01 MPa Compression3. Calculate the stress of member CD, indicate tension or compression. Answer: 11.03 MPa Tension
CORRECT ANSWER AND COMPLETE FBD ONLY. I PREFER HANDWRITTEN BUT ITS OKAY IF NOT. I WILL UPVOTE
3. The frame has pin supports at A and E, subject to a wind load. Treat joint C to be an internal hinge.
Given:Dimensions, H1 = 3.0 m; H2 = 4.5 m; L = 10.0 mWind loads, wWL (AB) = 4.8 kN/m; wWL (BC) = 3.9 kN/m; wWL (CD) = 1.5 kN/m; wWL (DE) = 1.2 kN/mMembers are made of A36 steel Wide Flange Section with the following properties:Area, A = 64000 mm2Depth, d = 762 mmFlange width, bf = 371 mmThickness of web, tw = 32 mmThickness of flange, tf = 57.9 mmMoment of inertia about x-axis, Ix = 6080 x 106 mm4The wide flange is oriented so that the bending is about the x-axis1. Calculate the stress in member AB, due to the axial load it carries, indicate if tension or compression.Answer: 0.0476 MPa Tension2. Calculate the stress in member DE, due to the axial load it carries, indicate if tension or compression.Answer: 0.2351 MPa Compression3. Calculate the maximum bending stress at B. Answer: 4.282 MPa
Chapter 6 Solutions
MECHANICS OF MATERIALS-TEXT
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...
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- 32 mm 32 mm b' c' C 32 mm 32 mm b PROBLEM 6.41 a The extruded beam shown has a uniform wall thickness of 3 mm. Knowing that the vertical shear in the beam is 9 kN, determine the shearing stress at each of the five points indicated.arrow_forwardIn a structural reliability problem, the resistance (capacity) R and load effect (demand) S random variables associated with a failure mode of the structure of interest are normally distributed and statistically independent with the following probability distribution parameters (or statistics) in consistent units: MR = 12, σR = 3 μs = 5, σs = 2 (a) Determine the exact probability of failure pF ·arrow_forwardThe resistance R and load effect S for a given failure mode are statistically independent random variables with marginal PDF's 1 fR (r) = 0≤r≤100 100' fs(s)=0.05e-0.05s (a) Determine the probability of failure by computing the probability content of the failure domain defined as {rarrow_forwardPlease solve this problem as soon as possible My ID# 016948724arrow_forwardThe gears shown in the figure have a diametral pitch of 2 teeth per inch and a 20° pressure angle. 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