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physics
mechanics
Mechanics of Materials 7th edition James M. Gere, Barry J. Goodno - Solutions
Solve the preceding problem for a sign and poles having the following dimensions: h1 = 6.0m, h2 = 1.5m, b = 3.0m, and t = d/10. The design wind pressure is 3.6 kPa, and the allowable stresses in the aluminum are 50 MPa in bending and 14 MPa in shear.
Dimensions of cross section: b = 6in, t = 0.5in, h = 12 in., h1 = 10.5 in., and V = 30 k.A wide-flange beam (see figure) having the cross section described below is subjected to a shear force V. using the dimensions of the cross section, calculate the moment of inertia and then determine the
A hollow steel box beam has the rectangular cross section shown in the figure. Determine the maximum allowable shear force V that may act on the beam if the allowable shear stress in 36 Mpa.
A hollow aluminum box beam has the square cross section shown in the figure. Calculate the maximum and minimum shear stresses Ï„max and Ï„min in the webs of the beam due to a shear force V = 28 k.
The T-beam shown in the figure has cross-sectional dimensions as follows: b = 220mm, t = 15mm, h = 300mm, and h1 = 275. The beam is subjected to a shear force V = 60kN.Determine the maximum shear stress Ï„max in the web of the beam.
Calculate the maximum shear stress τmax in the web of the T-beam shown in the figure if b = 10 in., t = 0.5 in., h = 7 in., h1 = 6.2 in., and the shear force V = 5300 lb.
Dimensions of cross section: b = 180mm, h = 420 mm, h1 = 380 mm, and V = 125 kN.A wide-flange beam (see figure) having the cross section described below is subjected to a shear force V. using the dimensions of the cross section, calculate the moment of inertia and then determine the following
Wide-flange shape W 8 x 28A wide-flange beam (see figure) having the cross section described below is subjected to a shear force V. using the dimensions of the cross section, calculate the moment of inertia and then determine the following quantities:(a) The maximum shear stress Ï„max in
Dimensions of cross section: b = 220mm, t = 12 mm, h = 600mm, h1 = 570 mm, and V = 200 kN.A wide-flange beam (see figure) having the cross section described below is subjected to a shear force V. using the dimensions of the cross section, calculate the moment of inertia and then determine the
Wide-flange shape W 18 x 71, Appendix E, V = 21kA wide-flange beam (see figure) having the cross section described below is subjected to a shear force V. using the dimensions of the cross section, calculate the moment of inertia and then determine the following quantities:(a) The maximum shear
Dimensions of cross section: b =120mm, t =7 mm, h = 350 mm, h1 = 330 and V = 60 kN.A wide-flange beam (see figure) having the cross section described below is subjected to a shear force V. using the dimensions of the cross section, calculate the moment of inertia and then determine the following
A cantilever beam AB of length L = 6.5 ft supports a trapezoidal distributed load of peak intensity q, and minimum intensity q/2, that includes the weight of the beam (see figure). The beam is a steel W 12 x 14 wide-flange shape (see Table E-1(a), Appendix E).Calculate the maximum permissible load
A bridge girder AB on a simple span of length L = 14 m supports a distributed load of maximum intensity q at mid span and minimum intensity q/2 at supports A and B that includes the weight of the girder (see figure).The girder is constructed of three plates welded to form the cross section
A simple beam with an overhang supports a uniform load of intensity q = 1200 lb/ft and a concentrated load P = 3000lb (see figure). The uniform load includes an allowance for the weight of the beam. The allowable stresses in bending and shear are 18 ksi and 11 ksi, respectively.Select from Table
A prefabricated wood I-beam serving as a floor joist has the cross section shown in the figure. The allowable load in shear for the glued joints between the web and the flanges is 65 lb/in. in the longitudinal direction.Determine the maximum allowable shear force Vmax for the beam.
A steel beam is built up from a W 410 x 85 wide-flange beam and two 180mm x 9mm cover plates (see figure). The allowable load in shear on each bolt is 9.8kN.What is the required bolt spacing in the longitudinal direction if the shear force V = 110kN
The three beams shown have approximately the same cross-sectional area. Beam 1 is a W 14 x 82 with flange plates; Beam 2 consists of a web plate with four angles; and Beam 3 is constructed of 2 C shapes with flange plates.(a) Which design has the largest moment capacity?(b) Which has the largest
Two W 310 x 74 steel wide-flange beams are bolted together to form a built-up beam as shown in the figure. What is the maximum permissible bolt spacing if the shear force V = 80kN and the allowable load in shear on each bolt is F = 13.5kN.
A welded steel girder having the cross section shown in the figure is fabricated of two 300mm x 25mm flange plates and a 800mm x 16mm web plate. The plates are joined by four fillet welds that run continuously for the length of the girder. Each weld has an allowable load in shear of
A welded steel girder having the cross section shown in the figure is fabricated of two 20in x 1 in. flange plates and a 60in x 5/16in. web plate.The plates are joined by four longitudinal fillet welds that run continuously throughout the length of the girder.If the girder is subjected to a shear
A box beam of wood is constructed of two 260mm x 50mm boards and two 260 x 25mm boards (see figure). The boards are nailed at a longitudinal spacing s = 100mm. If each nail has a allowable shear force F = 1200N, what is the maximum allowable shear force Vmax?
A box beam is constructed of four wood boards as shown in the figure part (a). The webs are 8 in. x 1 in. and the flanges are 6 in. x 1 in. boards (actual dimensions), joined by screws for which the allowable load in shear is F = 250 lb per screw.(a) Calculate the maximum permissible longitudinal
Two wood box beams (beams A and B) have the same outside dimensions (200mm x 360mm) and the same thickness (t = 20mm) throughout, as shown |in the figure on the next page. Both beams are formed by nailing, with each nail having an allowable shear load of 250 N. The beams are designed for a shear
A hollow wood beam with plywood webs has the cross-sectional dimensions shown in the figure. The plywood is attached to the flanges by means of small nails. Each nail has an allowable load in shear of 30 lb.Find the maximum allowable spacing of the nails at cross sections where the shear force V is
A beam of T cross section is formed by nailing together two boards having the dimensions shown in the figure.If the total shear force V acting on the cross section is 1500 N and each nail may carry 760 N in shear, what is the maximum allowable nail spacing s?
The T-beam shown in the figure is fabricated by welding together two steel plates. If the allowable load for each weld is 1.8k/in. in the longitudinal direction, what is the maximum allowable shear force V?
While drilling a hole with a brace and bit, you exert a downward force P = 25lb on the handle of the brace (see figure).The diameter of the crank arm is d = 7/16in. and its lateral offset is b = 4-7/8 in.Determine the maximum tensile and compressive stresses σ1 and σc,
A flying buttress transmits a load P = 25kN, acting at an angle of 60o to the horizontal, to the top of a vertical buttress AB (see figure). The vertical buttress has height h = 5.0m and rectangular cross section of thickness t = 1.5m and width b = 1.0m (perpendicular to the plane of the figure).
A plain concrete wall (i.e., a wall with no steel reinforcement) rests on a secure foundation and serves as a small dam on a creek (see figure). The height of the wall is h = 6.0ft and the thickness of the wall is t = 1.0ft.(a) Determine the maximum tensile and compressive stresses σt
A circular post, a rectangular post, and a post of cruciform cross section are each compressed by loads that produce a resultant force P acting at the edge of the cross section (see figure). The diameter of the circular post and the depths of the rectangular and cruciform posts are the same.(a) For
Two cables, each carrying a tensile force P = 1200lb, are bolted to a block of steel (see figure). The block has thickness t = 1 in. and b = 3 width in.(a) If the diameter of the cable is 0.25 in., what are the maximum tensile and compressive stresses σt and σc, respectively,
A bar AB supports a load P acting at the centroid of the end cross section (see figure) in the middle region of the bar the cross-sectional area is reduced by removing one-half of the bar.(a) If the end crosses sections of the bar are square with sides of length b, what are the maximum tensile and
A short column constructed of a W 12 x 35 wide-flange shape is subjected to a resultant compressive load P = 12k having its line of action at the midpoint of one flange (see figure).(a) Determine the maximum tensile and compressive stresses σt and σc, respectively, in the
A short column of wide-flange shape is subjected to a compressive load that produces a resultant force P = 55kN acting at the midpoint of one flange (see figure).(a) Determine the maximum tensile and compressive stresses σt and σc, respectively, in the column.(b) Locate the
A tension member constructed of an L 4 x 4 x 1/2 inch angle section (see Table E-4(a) inAppendix E) is subjected to a tensile load P = 12.5 kips that acts through the point where the midlines of the legs intersect [see figure part (a)].(a) Determine the maximum tensile stress σt in the
A short length of a 200 x 17.1 channel is subjected to an axial compressive P force that has its line of action through the midpoint of the web of the channel [(see figure(a)].(a) Determine the equation of the neutral axis under this loading condition.(b) If the allowable stresses in tension and
Aluminum pole for a street light weights 4600N and supports an arm that weights 660 N (see figure). The center of gravity of the arm is 1.2 m from the axis of the pole. A wind force of 300 N also acts in the (-y) direction at 9 m above the base. The outside diameter of the pole (at its base) is 225
A curved bar ABC having a circular axis (radius.) is loaded by forces P = 400lb (see figure). The cross section of the bar is rectangular with height and thickness t.If the allowable tensile stress in the bar is 12,000 psi and the height h = 1.25 in., what is the minimum required thickness tmin?
A rigid frame ABC is formed by welding two steel pipes at B (see figure). Each pipe has cross-sectional area A = 11.31 x 103mm2, moment of inertia I = 46.37 x 106 mm4, and outside diameter d = 200mm.Find the maximum tensile and compressive stresses σ1 and σc, respectively, in
A palm tree weighing 1000 lb is inclined at an angle of 60o (see figure). The weight of the tree may be resolved into two resultant forces, a force P1 = 900lb acting at a point 12 ft from the base and a force P2 = 100lb acting at the top of the tree, which is 30 ft long. The diameter at the base of
A vertical pole of aluminum is fixed at the base and pulled at the top by a cable having a tensile force T (see figure). The cable is attached at the outer edge of a stiffened cover plate on top of the pole and makes an angle α = 20° at the point of attachment. The pole has length
Because of foundation settlement, a circular tower is leaning at an angle α to the vertical (see figure). The structural core of the tower is a circular cylinder of height h, outer diameter d2, and inner diameter d1. For simplicity in the analysis, assume that the weight of the tower
A steel bar of solid circular cross section and length L 2.5m is subjected to an axial tensile force T = 24kN and a bending moment M = 3.5kNm (see figure).(a) Based upon an allowable stress in tension of 110Mpa, determine the required diameter of the bar; disregard the weight of the bar itself.(b)
A cylindrical brick chimney of height H weighs w = 825 lb/ft of height (see figure). The inner and outer diameters are d1 = 3 ft and d2 = 4 ft, respectively. The wind pressure against the side of the chimney is p = 10 lb/ft2 of projected area.Determine the maximum height H if there is to be no
A composite beam consisting of fiberglass faces and a core of particle board has the cross section shown in the figure. The width of the beam is 2.0 in., the thickness of the faces is 0.10 in., and the thickness of the core is 0.50 in. The beam is subjected to a bending moment of 250 lb-in. acting
A simply supported composite beam 3 m long carries a uniformly distributed load of intensity q = 3.0 kN/m (see figure). The beam is constructed of a wood member, 100 mm wide by 150 mm deep, reinforced on its lower side by a steel plate 8 mm thick and 100 mm wide.Find the maximum bending stresses
A simply supported wooden I-beam with a 12 ft span supports a distributed load of intensity q = 90 lb/ft over its length (see figure part a). The beam is constructed with a web of Douglas-fir plywood and flanges of pine glued to the web as shown in the figure part b. The plywood is 3/8 in. thick;
A simply supported composite beam with a 3.6 m span supports a triangularly distributed load of peak intensity q0 at mid span (see figure part a). The beam is constructed of two wood joists, each 50 mm x 280 mm, fastened to two steel plates, one of dimensions 6 mm x 80 mm and the lower plate of
A wood beam with cross-sectional dimensions 200 mm x 300 mm is reinforced on its sides by steel plates 12 mm thick (see figure). The moduli of elasticity for the steel and wood are Es = 190 GPa and Ew = 11 GPa, respectively. Also, the corresponding allowable stresses are σs = 110 MPa and
A hollow box beam is constructed with webs of Douglas-fir plywood and flanges of pine, as shown in the figure in a cross-sectional view. The plywood is 1 in. thick and 12 in. wide; the flanges are 2 in. x 4 in. (nominal size). The modulus of elasticity for the plywood is 1,800,000 psi and for the
A round steel tube of outside diameter d and an brass core of diameter 2d/3 are bonded to form a composite beam, as shown in the figure. Derive a formula for the allowable bending moment M that can be carried by the beam based upon an allowable stress σs in the steel. (Assume that the moduli of
A beam with a guided support and 10 ft span supports a distributed load of intensity q = 660 lb/ft over its first half (see figure part a) and a moment M0 = 300 ft-lb at joint B.The beam consists of a wood member (nominal dimensions 6 in. x 12 in., actual dimensions 5.5 in. x 11.5 in. in cross
A plastic-lined steel pipe has the cross-sectional shape shown in the figure. The steel pipe has outer diameter d3 = 100 mm and inner diameter d2 = 94 mm. The plastic liner has inner diameter d1 = 82 mm. The modulus of elasticity of the steel is 75 times the modulus of the plastic.Determine the
The cross section of a sandwich beam consisting of aluminum alloy faces and a foam core is shown in the figure. The width b of the beam is 8.0 in., the thickness t of the faces is 0.25 in., and the height hc of the core is 5.5 in. (total height h = 6.0 in.). The moduli of elasticity are 10.5 x 106
The cross section of a sandwich beam consisting of fiberglass faces and a lightweight plastic core is shown in the figure. The width b of the beam is 50 mm, the thickness t of the faces is 4 mm, and the height hc of the core is 92 mm (total height h = 100 mm). The moduli of elasticity are 75 GPa
A bimetallic beam used in a temperature-control switch consists of strips of aluminum and copper bonded together as shown in the figure, which is a cross-sectional view. The width of the beam is 1.0 in., and each strip has a thickness of 1/16 in.Under the action of a bending moment M = 12 lb-in.
A wood beam 8 in. wide and 12 in. deep (nominal dimensions) is reinforced on top and bottom by 0.25-in.-thick steel plates (see figure part a).(a) Find the allowable bending moment Mmax about the z axis if the allowable stress in the wood is 1,100 psi and in the steel is 15,000 psi. (Assume that
The cross section of a bimetallic strip is shown in the figure. Assuming that the moduli of elasticity for metals A and B are EA = 168 GPa and EB = 90 GPa, respectively, determine the smaller of the two section moduli for the beam. (Recall that section modulus is equal to bending moment divided by
A W 12 x 50 steel wide-flange beam and a segment of a 4-inch thick concrete slab (see figure) jointly resist a positive bending moment of 95 k-ft. The beam and slab are joined by shear connectors that are welded to the steel beam. (These connectors resist the horizontal shear at the contact
A wood beam reinforced by an aluminum channel section is shown in the figure. The beam has a cross section of dimensions 150 mm by 250 mm, and the channel has a uniform thickness of 6 mm. If the allowable stresses in the wood and aluminum are 8.0 MPa and 38 MPa, respectively, and if their moduli of
A simple beam of span length 3.2 m carries a uniform load of intensity 48 kN/m. The cross section of the beam is a hollow box with wood flanges and steel side plates, as shown in the figure. The wood flanges are 75 mm by 100 mm in cross section, and the steel plates are 300 mm deep.What is the
A simple beam that is 18 ft long supports a uniform load of intensity q. The beam is constructed of two C 8 x 11.5 sections (channel sections or C shapes) on either side of a 4 x 8 (actual dimensions) wood beam (see the cross section shown in the figure part a). The modulus of elasticity of the
The composite beam shown in the figure is simply supported and carries a total uniform load of 50 kN/m on a span length of 4.0 m. The beam is built of a wood member having cross-sectional dimensions 150 mm x 250 mm and two steel plates of cross-sectional dimensions 50 mm x 150 mm.Determine the
The cross section of a beam made of thin strips of aluminum separated by a lightweight plastic is shown in the figure. The beam has width b = 3.0 in., the aluminum strips have thickness t = 0.1 in, and the plastic segments have heights d = 1.2 in. and 3d = 3.6 in. The total height of the beam is h
Consider the preceding problem if the beam has width b = 75 mm, the aluminum strips have thickness t = 3 mm, the plastic segments have heights d =40 mm and 3d = 120 mm, and the total height of the beam is h = 212 mm. Also, the moduli of elasticity are Ea =75 GPa and Ep = 3 GPa,
A simple beam that is 18 ft long supports a uniform load of intensity q. The beam is constructed of two angle sections, each L 6 x 4 x 1/2, on either side of a 2 in. x 8 in. (actual dimensions) wood beam (see the cross section shown in the figure part a). The modulus of elasticity of the steel is
The cross section of a composite beam made of aluminum and steel is shown in the figure. The moduli of elasticity are Ea = 75 GPa and Es = 200 GPa.Under the action of a bending moment that produces a maximum stress of 50 MPa in the aluminum, what is the maximum stress σs in the steel?
A beam is constructed of two angle sections, each L 5 x 3 x 1/2, which reinforce a 2 x 8 (actual dimensions) wood plank (see the cross section shown in the figure). The modulus of elasticity for the wood is Ew = 1.2 x 106 psi and for the steel is Es = 30 x 106 psi.Find the allowable bending moment
A beam of rectangular cross section supports an inclined load P having its line of action along a diagonal of the cross section (see figure). Show that the neutral axis lies along the other diagonal.
Solve the preceding problem using the following data: W 310 x 129 section, L = 1.8 m, P = 9.5 kN, and α = 60°.
A cantilever beam of W 12 x 14 section and length L x 9 ft supports a slightly inclined load P x 500 lb at the free end (see figure).(a) Plot a graph of the stress σA at point A as a function of the angle of inclination a.(b) Plot a graph of the angle b, which locates the neutral axis
A cantilever beam built up from two channel shapes, each C 200 x 17.1, and of length L supports an inclined load P at its free end (see figure).Determine the orientation of the neutral axis and calculate the maximum tensile stress σmax due to the load P. Data for the beam are as
A built-up steel beam of I-section with channels attached to the flanges (see figure part a) is simply supported at the ends. Two equal and oppositely directed bending moments M0 act at the ends of the beam, so that the beam is in pure bending. The moments act in plane mm, which is oriented at an
A wood beam of rectangular cross section (see figure) is simply supported on a span of length L. The longitudinal axis of the beam is horizontal, and the cross section is tilted at an angle a. The load on the beam is a vertical uniform load of intensity q acting through the centroid C.Determine the
Solve the preceding problem for the following data: b = 6 in. h = 10 in. L = 12.0 ft, tan a = 1/3, q = 325 lb/ft.
A simply supported wide-flange beam of span length L carries a vertical concentrated load P acting through the centroid C at the midpoint of the span (see figure). The beam is attached to supports inclined at an angle α to the horizontal.Determine the orientation of the neutral axis
Solve the preceding problem using the following data: W 8 x 21 section, L = 84 in., P = 4.5 k, and α = 22.5°
A wood cantilever beam of rectangular cross section and length L supports an inclined load P at its free end (see figure).Determine the orientation of the neutral axis and calculate the maximum tensile stress σmax due to the load Pt Data for the beam are as follows: b = 80 mm, h = 140
Solve the preceding problem for a cantilever beam with data as follows: b = 4 in., h = 9 in., L = 10.0 ft, P = 325 lb, and α = 45°.
A steel beam of I-section (see figure) is simply supported at the ends. Two equal and oppositely directed bending moments M0 act at the ends of the beam, so that the beam is in pure bending. The moments act in plane mm, which is oriented at an angle a to the xy plane.Determine the orientation of
A cantilever beam of wide-flange cross section and length L supports an inclined load P at its free end (see figure).Determine the orientation of the neutral axis and calculate the maximum tensile stress σmax due to the load P.Data for the beam are as follows: W 10 x 45 sections, L = 8.0
A beam of channel section is subjected to a bending moment M having its vector at an angle θ to the z axis (see figure).Determine the orientation of the neutral axis and calculate the maximum tensile stress σt and maximum compressive stress σc in the beam. Use the
A built-up beam supporting a condominium balcony is made up of a structural T (one half of a W 200 x 31.3) for the top flange and web and two angles (2L 102 x 76 x 6.4, long legs back-to-back) for the bottom flange and web, as shown. The beam is subjected to a bending moment M having its vector at
A steel post (E = 30 x 106 psi) having thickness t = 1/8 in. and height L = 72 in. supports a stop sign (see figure). The stop sign post is subjected to a bending moment M having its vector at an angle θ to the z axis.Determine the orientation of the neutral axis and calculate the
A C 200 x 17.1 channel sections has an angle with equal legs attached as shown; the angle serves as a lintel beam. The combined steel section is subjected to a bending moment M having its vector directed along the z axis, as shown in the figure. The centroid C of the combined section is located at
A beam of channel section is subjected to a bending moment M having its vector at an angle u to the z axis (see figure). Determine the orientation of the neutral axis and calculate the maximum tensile stress σt and maximum compressive stress sc in the beam. Use a C 200 x 20.5 channel section with
An angle section with equal legs is subjected to a bending moment M having its vector directed along the 1-1 axis, as shown in the figure.Determine the orientation of the neutral axis and calculate the maximum tensile stress σt and maximum compressive stress σc if the angle is
An angle section with equal legs is subjected to a bending moment M having its vector directed along the 1-1 axis, as shown in the figure. Determine the orientation of the neutral axis and calculate the maximum tensile stress σt and maximum compressive stress σc if the section is an L 152 x 152 x
A beam made up of two unequal leg angles is subjected to a bending moment M having its vector at an angle u to the z axis (see figure part a).(a) For the position shown in the figure, determine the orientation of the neutral axis and calculate the maximum tensile stress σt and maximum
The Z-section of Example 12-7 is subjected to M = 5 kN m, as shown.Determine the orientation of the neutral axis and calculate the maximum tensile stress σt and maximum compressive stress σc in the beam. Use the following numerical data: height h = 200 mm, width b = 90 mm,
The cross section of a steel beam is constructed of a W 18 x 71 wide-flange section with a 6 in x 1/2 in. cover plate welded to the top flange and a C 10 x 30 channel section welded to the bottom flange. This beam is subjected to a bending moment M having its vector at an angle θ to
The cross section of a steel beam is shown in the figure. This beam is subjected to a bending moment M having its vector at an angle θ to the z axis.Determine the orientation of the neutral axis and calculate the maximum tensile stress σt and maximum compressive stress
A beam of semicircular cross section of radius r is subjected to a bending moment M having its vector at an angle θ to the z axis (see figure). Derive formulas for the maximum tensile s, and the maximum compressive stress sc in the beam for θ = 0, 45°, and 90°.
A simple beam of W 10 x 30 wide-flange cross section supports a uniform load of intensity q = 3.0 k/ft on a span of length L = 12 ft (see figure). The dimensions of the cross section are h = 10.5 in., b = 5.81 in., tf = 0.510 in., and tw = 0.300 in.(a) Calculate the maximum shear stress
Solve the preceding problem for a W 250 x 44.8 wide-flange shape with the following data: L = 3.5 m, q = 45 kN / m, h = 267 mm, b = 148 mm, tf = 13 mm, tw = 7.62 mm, d = 0.5 m, and a = 50 mm.
A beam of wide-flange shape, W 8 x 28, has the cross section shown in the figure. The dimensions are b = 6.54 in., h = 8.06 in., tw = 0.285 in., and tf = 0.465 in. The loads on the beam produce a shear force V = 7.5 k at the cross section under consideration.(a) Using centerline dimensions,
Solve the preceding problem for a W 200 x 41.7 shape with the following data: b = 166 mm, h = 205 mm, tw = 7.24 mm, tf = 11.8 mm, and V = 38 kN.
Calculate the distance e from the centerline of the web of a C 15 x 40 channel section to the shear center S (see figure). (For purposes of analysis, consider the flanges to be rectangles with thickness tf equal to the average flange thickness given in Table E-3a in Appendix E.)
Derive the following formula for the distance e from the centerline of the wall to the shear center S for the C-section of constant thickness shown in the figure:Also, check the formula for the special cases of a channel section (a = 0) and a slit rectangular tube (a = h/2).
Derive the following formula for the distance e from the centerline of the wall to the shear center S for the hat section of constant thickness shown in the figure:Also, check the formula for the special case of a channel section (a = 0).
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