Mechanics of Materials, 7th Edition
7th Edition
ISBN: 9780073398235
Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 4.5, Problem 47P
A concrete slab is reinforced by
Fig. P4.47
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4.37 A W 200 x 31.3 rolled-steel beam is subjected to a couple M of moment 45
kN-m. Knowing that E= Z00GPA, v=0.29, determine (a) the radius of curvature
P. (b) the radius of curvature p' of a transverse cross section.
SOLUTION
250 mm
PROBLEM 4.3
18 mm
The wide-flange beam shown is
made of a high-strength, low
alloy steel for which o, = 450
MPa. Using a factor of safety of
3.0, determine the largest
couple that can be applied to
the beam when it is bent about
C
360 mm
M.
+ 10 mm
the z axis.
[Ans. 243.3 kNm]
18 mm
Fig. P4.3
and P4.4
PROBLEM 4.4
Solve Prob, 4.3. assuming that
5.86 The cast iron inverted T-section supports two concentrated loads of magnitude P. The working stresses are 48 MPa in tension, 140 MPa in compression, and 30 MPa in shear. (a) Show that the neutral axis of the cross section is located at d ¼ 48:75 mm and that the moment of inertia of the cross-sectional area about this axis is I ¼ 11:918 106 mm4. (b) Find the maximum allowable value of P.
Chapter 4 Solutions
Mechanics of Materials, 7th Edition
Ch. 4.3 - 4.1 and 4.2 Knowing that the couple shown acts in...Ch. 4.3 - 4.1 and 4.2 Knowing that the couple shown acts in...Ch. 4.3 - Using an allowable stress of 155 MPa, determine...Ch. 4.3 - Solve Prob. 4.3, assuming that the wide-flange...Ch. 4.3 - Using an allowable stress of 16 ksi, determine the...Ch. 4.3 - Knowing that the couple shown acts in a vertical...Ch. 4.3 - 4.7 and 4.8 Two W4 13 rolled sections are welded...Ch. 4.3 - 4.7 and 4.8 Two W4 13 rolled sections are welded...Ch. 4.3 - 4.9 through 4.11 Two vertical forces are applied...Ch. 4.3 - 4.9 through 4.11 Two vertical forces are applied...
Ch. 4.3 - 4.9 through 4.11 Two vertical forces are applied...Ch. 4.3 - Knowing that a beam of the cross section shown is...Ch. 4.3 - Knowing that a beam of the cross section shown is...Ch. 4.3 - Solve Prob. 4.13, assuming that the beam is bent...Ch. 4.3 - Knowing that for the extruded beam shown the...Ch. 4.3 - The beam shown is made of a nylon for which the...Ch. 4.3 - Solve Prob. 4.16, assuming that d = 40 mm.Ch. 4.3 - Knowing that for the beam shown the allowable...Ch. 4.3 - 4.19 and 4.20 Knowing that for the extruded beam...Ch. 4.3 - 4.19 and 4.20 Knowing that for the extruded beam...Ch. 4.3 - Straight rods of 6-mm diameter and 30-m length are...Ch. 4.3 - A 900-mm strip of steel is bent into a full circle...Ch. 4.3 - Straight rods of 0.30-in. diameter and 200-ft...Ch. 4.3 - A 60-Nm couple is applied to the steel bar shown,...Ch. 4.3 - (a) Using an allowable stress of 120 MPa,...Ch. 4.3 - A thick-walled pipe is bent about a horizontal...Ch. 4.3 - A couple M will be applied to a beam of...Ch. 4.3 - A portion of a square bar is removed by milling,...Ch. 4.3 - In Prob. 4.28, determine (a) the value of h for...Ch. 4.3 - For the bar and loading of Concept Application...Ch. 4.3 - Prob. 31PCh. 4.3 - It was assumed in Sec. 4.1B that the normal...Ch. 4.5 - 4.33 and 4.34 A bar having the cross section shown...Ch. 4.5 - 4.33 and 4.34 A bar having the cross section shown...Ch. 4.5 - 4.35 and 4.36 For the composite bar indicated,...Ch. 4.5 - Prob. 36PCh. 4.5 - 4.37 and 4.38 Wooden beams and steel plates are...Ch. 4.5 - 4.37 and 4.38 Wooden beams and steel plates are...Ch. 4.5 - 4.39 and 4.40 A copper strip (Ec = 105 GPa) and an...Ch. 4.5 - 4.39 and 4.40 A copper strip (Ec = 105 GPa) and an...Ch. 4.5 - 4.41 and 4.42 The 6 12-in. timber beam has been...Ch. 4.5 - 4.41 and 4.42 The 6 12-in. timber beam has been...Ch. 4.5 - 4.43 and 4.44 For the composite beam indicated,...Ch. 4.5 - Prob. 44PCh. 4.5 - Prob. 45PCh. 4.5 - Prob. 46PCh. 4.5 - A concrete slab is reinforced by 58-in.-diameter...Ch. 4.5 - Solve Prob. 4.47, assuming that the spacing of the...Ch. 4.5 - The reinforced concrete beam shown is subjected to...Ch. 4.5 - Prob. 50PCh. 4.5 - Knowing that the bending moment in the reinforced...Ch. 4.5 - A concrete beam is reinforced by three steel rods...Ch. 4.5 - The design of a reinforced concrete beam is said...Ch. 4.5 - For the concrete beam shown, the modulus of...Ch. 4.5 - 4.55 and 4.56 Five metal strips, each 0.5 1.5-in....Ch. 4.5 - 4.55 and 4.56 Five metal strips, each 0.5 1.5-in....Ch. 4.5 - The composite beam shown is formed by bonding...Ch. 4.5 - A steel pipe and an aluminum pipe are securely...Ch. 4.5 - The rectangular beam shown is made of a plastic...Ch. 4.5 - Prob. 60PCh. 4.5 - Knowing that M = 250 Nm, determine the maximum...Ch. 4.5 - Knowing that the allowable stress for the beam...Ch. 4.5 - Semicircular grooves of radius r must be milled as...Ch. 4.5 - Prob. 64PCh. 4.5 - A couple of moment M = 2 kNm is to be applied to...Ch. 4.5 - The allowable stress used in the design of a steel...Ch. 4.6 - The prismatic bar shown is made of a steel that is...Ch. 4.6 - Prob. 68PCh. 4.6 - Prob. 69PCh. 4.6 - Prob. 70PCh. 4.6 - The prismatic rod shown is made of a steel that is...Ch. 4.6 - Solve Prob. 4.71, assuming that the couples M and...Ch. 4.6 - 4.73 and 4.74 A beam of the cross section shown is...Ch. 4.6 - 4.73 and 4.74 A beam of the cross section shown is...Ch. 4.6 - 4.75 and 4.76 A beam of the cross section shown is...Ch. 4.6 - Prob. 76PCh. 4.6 - 4.77 through 4.80 For the beam indicated,...Ch. 4.6 - Prob. 78PCh. 4.6 - Prob. 79PCh. 4.6 - 4.77 through 4.80 For the beam indicated,...Ch. 4.6 - 4.81 through 4.83 Determine the plastic moment Mp...Ch. 4.6 - Prob. 82PCh. 4.6 - Prob. 83PCh. 4.6 - Determine the plastic moment Mp of a steel beam of...Ch. 4.6 - Determine the plastic moment Mp of the cross...Ch. 4.6 - Determine the plastic moment Mp of a steel beam of...Ch. 4.6 - Prob. 87PCh. 4.6 - Prob. 88PCh. 4.6 - Prob. 89PCh. 4.6 - Prob. 90PCh. 4.6 - Prob. 91PCh. 4.6 - Prob. 92PCh. 4.6 - Prob. 93PCh. 4.6 - Prob. 94PCh. 4.6 - Prob. 95PCh. 4.6 - Prob. 96PCh. 4.6 - Prob. 97PCh. 4.6 - Prob. 98PCh. 4.7 - Knowing that the magnitude of the horizontal force...Ch. 4.7 - A short wooden post supports a 6-kip axial load as...Ch. 4.7 - Two forces P can be applied separately or at the...Ch. 4.7 - A short 120 180-mm column supports the three...Ch. 4.7 - As many as three axial loads, each of magnitude P...Ch. 4.7 - Two 10-kN forces are applied to a 20 60-mm...Ch. 4.7 - Portions of a 1212-in. square bar have been bent...Ch. 4.7 - Knowing that the allowable stress in section ABD...Ch. 4.7 - A milling operation was used to remove a portion...Ch. 4.7 - A milling operation was used to remove a portion...Ch. 4.7 - The two forces shown are applied to a rigid plate...Ch. 4.7 - Prob. 110PCh. 4.7 - Prob. 111PCh. 4.7 - A short column is made by nailing four 1 4-in....Ch. 4.7 - A vertical rod is attached at point A to the cast...Ch. 4.7 - A vertical rod is attached at point A to the cast...Ch. 4.7 - Knowing that the clamp shown has been tightened...Ch. 4.7 - Prob. 116PCh. 4.7 - Three steel plates, each of 25 150-mm cross...Ch. 4.7 - A vertical force P of magnitude 20 kips is applied...Ch. 4.7 - The four bars shown have the same cross-sectional...Ch. 4.7 - Prob. 120PCh. 4.7 - An eccentric force P is applied as shown to a...Ch. 4.7 - Prob. 122PCh. 4.7 - Prob. 123PCh. 4.7 - Prob. 124PCh. 4.7 - A single vertical force P is applied to a short...Ch. 4.7 - The eccentric axial force P acts at point D, which...Ch. 4.9 - 4.127 through 4.134 The couple M is applied to a...Ch. 4.9 - 4.127 through 4.134 The couple M is applied to a...Ch. 4.9 - 4.127 through 4.134 The couple M is applied to a...Ch. 4.9 - 4.127 through 4.134 The couple M is applied to a...Ch. 4.9 - 4.127 through 4.134 The couple M is applied to a...Ch. 4.9 - 4.127 through 4.134 The couple M is applied to a...Ch. 4.9 - Prob. 133PCh. 4.9 - Prob. 134PCh. 4.9 - 4.135 through 4.140 The couple M acts in a...Ch. 4.9 - 4.135 through 4.140 The couple M acts in a...Ch. 4.9 - Prob. 137PCh. 4.9 - 4.135 through 4.140 The couple M acts in a...Ch. 4.9 - 4.135 through 44.140 The couple M acts in a...Ch. 4.9 - 4.135 through 4.140 The couple M acts in a...Ch. 4.9 - Prob. 141PCh. 4.9 - 4.141 through 4.143 The couple M acts in a...Ch. 4.9 - 4.141 through 4.143 The couple M acts in a...Ch. 4.9 - The tube shown has a uniform wall thickness of 12...Ch. 4.9 - Prob. 145PCh. 4.9 - Knowing that P = 90 kips, determine the largest...Ch. 4.9 - Knowing that a = 1.25 in., determine the largest...Ch. 4.9 - A rigid circular plate of 125-mm radius is...Ch. 4.9 - Prob. 149PCh. 4.9 - A beam having the cross section shown is subjected...Ch. 4.9 - Prob. 151PCh. 4.9 - Prob. 152PCh. 4.9 - Prob. 153PCh. 4.9 - Prob. 154PCh. 4.9 - Prob. 155PCh. 4.9 - Prob. 156PCh. 4.9 - Prob. 157PCh. 4.9 - Prob. 158PCh. 4.9 - A beam of unsymmetric cross section is subjected...Ch. 4.9 - Prob. 160PCh. 4.10 - For the curved bar shown, determine the stress at...Ch. 4.10 - For the curved bar shown, determine the stress at...Ch. 4.10 - Prob. 163PCh. 4.10 - Prob. 164PCh. 4.10 - The curved bar shown has a cross section of 40 60...Ch. 4.10 - Prob. 166PCh. 4.10 - Prob. 167PCh. 4.10 - Prob. 168PCh. 4.10 - The curved bar shown has a cross section of 30 30...Ch. 4.10 - Prob. 170PCh. 4.10 - Prob. 171PCh. 4.10 - Three plates are welded together to form the...Ch. 4.10 - 4.173 and 4.174 Knowing that the maximum allowable...Ch. 4.10 - Prob. 174PCh. 4.10 - Prob. 175PCh. 4.10 - Prob. 176PCh. 4.10 - Prob. 177PCh. 4.10 - Prob. 178PCh. 4.10 - Prob. 179PCh. 4.10 - Knowing that P = 10 kN, determine the stress at...Ch. 4.10 - Prob. 181PCh. 4.10 - Prob. 182PCh. 4.10 - Prob. 183PCh. 4.10 - Prob. 184PCh. 4.10 - Prob. 185PCh. 4.10 - Prob. 186PCh. 4.10 - Prob. 187PCh. 4.10 - Prob. 188PCh. 4.10 - Prob. 189PCh. 4.10 - Prob. 190PCh. 4.10 - For a curved bar of rectagular cross section...Ch. 4 - Two vertical forces are applied to a beam of the...Ch. 4 - Prob. 193RPCh. 4 - Prob. 194RPCh. 4 - Determine the plastic moment Mp of a steel beam of...Ch. 4 - In order to increase corrosion resistance, a...Ch. 4 - The vertical portion of the press shown consists...Ch. 4 - The four forces shown are applied to a rigid plate...Ch. 4 - Prob. 199RPCh. 4 - Prob. 200RPCh. 4 - Three 120 10-mm steel plates have been welded...Ch. 4 - A short length of a W8 31 rolled-steel shape...Ch. 4 - Two thin strips of the same material and same...
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- 5.86 The cast iron inverted T-section supports two concentrated loads of magni- tude P. The working stresses are 48 MPa in tension, 140 MPa in compression, and 30 MPa in shear. (a) Show that the neutral axis of the cross section is located at d = 48.75 mm and that the moment of inertia of the cross-sectional area about this axis is I = 11.918 x 106 mm“. (b) Find the maximum allowable value of P. 1.0 m 1.0 m 15 mm 3 m 150 mm NA- d 15 mm 150 mm FIG. P5.86arrow_forwardA copper strip (E = 105 GPa) and an aluminum strip (E = 75 GPa) are bonded together to form the composite beam shown. Knowing that the beam is bent about a horizontal axis by a couple of moment M = 35 N.m, determine the maximum stress in (a) the aluminum strip, (b) the copper strip. Fig. P4.39 Aluminum Copper 24 mm 6 mm 6 mmarrow_forward4.33 plzarrow_forward
- 7. Straight rods of 0.4ft diameter and 100ft length are stored by coiling the rods inside a drum of 1.25ft in- side diameter. Assuming that the yield strength is not exceeded, determine the maximum stress in the coiled rod, the corresponding bending moment in the rod. Use E = 29 * 10°psi.arrow_forwardParvinbhaiarrow_forwardPlease solve correctlarrow_forward
- A steel bar of 0.8 x 2.5-in. rectangular cross section is subjected to two equal and opposite couples acting in the vertical plane of symmetry of the bar (Fig. . Determine the value of the bending moment M that causes the bar to yield. Assume σY= 36 ksiarrow_forwardTwo equal steel beams are built-in at one end and connected by a steel rod as shown. Show that the pull in the tie rod is: (in the photo) where d is the diameter of the rod, and 1 is the second moment of area of the section of each beam about its neutral axis. (Cambridge)arrow_forward4.23arrow_forward
- A steel bar and an aluminum bar are bonded together to form the composite beam shown. The modulus of elasticity for aluminum is 70 GPa and for steel is 200 GPa. Knowing that the beam is bent about a horizontal axis by a couple of moment M= 1500 N·m, determine the maximum stress in (a) the aluminum, (b) the steel.arrow_forwardA 6 * 10-in. timber beam has been strengthened by bolting to it the steel straps shown. The modulus of elasticity is E= 1.5 *106 psi for the wood and E= 30 * 106 psi for the steel. Knowing that the beam is bent about a horizontal axis by a couple of moment 200 kip·in., determine the maximum stress in (a) the wood, (b) the steel.arrow_forward4.9 plzarrow_forward
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