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Mechanics of Materials 7th edition James M. Gere, Barry J. Goodno - Solutions

A symmetric beam ABCD with overhangs at both ends supports a uniform load of intensity q (see figure).
The simple beam shown in the figure supports a concentrated load P acting at distance a from the left-hand support and distance b from the right-hand support.
An overhanging beam ABC supports a concentrated load P at the end of the overhang (see figure). Span AB has length L and the overhang has length a.
The cantilever beam shown in the figure supports a triangularly distributed load of maximum intensity q0.
A simple beam ACB supports a uniform load of intensity q on the left-hand half of the span (see figure).
A cantilever beam ACB supports two concentrated loads P1 and P2, as shown in the figure.
The cantilever beam ACB shown in the figure is subjected to a uniform load of intensity q acting between points A and C.
The frame ABC supports a concentrated load P at point C (see figure). Members AB and BC have lengths h and b, respectively.
A simple beam ABCDE supports a uniform load of intensity q (see figure). The moment of inertia in the central part of the beam (BCD) is twice the moment of inertia in the end parts (AB and DE). Find the deflection δC at the midpoint C of the beam. (Obtain the solution by using the modified form of
A propped cantilever beam AB of length L is loaded by a counterclockwise moment M0 acting at support B (see figure). Beginning with the second-order differential equation of the deflection curve (the bending-moment equation), obtain the reactions, shear forces, bending moments, slopes, and
A counterclockwise moment M0 acts at the midpoint of a fixed-end beam ACB of length L (see figure).Beginning with the second-order differential equation of the deflection curve (the bending-moment equation), determine all reactions of the beam and obtain the equation of the deflection curve for the
A propped cantilever beam of length L is loaded by a concentrated moment M0 at midpoint C. Use the second-order differential equation of the deflection curve to solve for reactions at A and B. Draw shear-force and bending-moment diagrams for the entire beam. Also find the equations of the
A fixed-end beam AB of length L supports a uniform load of intensity q (see figure).Beginning with the second-order differential equation of the deflection curve (the bending-moment equation), obtain the reactions, shear forces, bending moments, slopes, and deflections of the beam. Construct the
A cantilever beam AB of length L has a fixed support at A and a roller support at B (see figure). The support at B is moved downward through a distance Î´B.Using the fourth-order differential equation of the deflection curve (the load equation), determine the reactions of the beam and
A cantilever beam of length L and loaded by uniform load of intensity q has a fixed support at A and spring support at B with rotational stiffness kR. A rotation at B, Î¸B, results in a reaction moment MB = kR x Î¸B.Find rotation and displacement at end B. Use the
A cantilever beam of length L and loaded by a triangularly distributed load of maximum intensity q0 at B.Use the fourth-order differential equation of the deflection curve to solve for reactions at A and B and also the equation of the deflection curve.
A propped cantilever beam of length L is loaded by a parabolically distributed load with maximum intensity q0 at B. (a) Use the fourth-order differential equation of the deflection curve to solve for reactions at A and B and also the equation of the deflection curve. (b) Repeat (a) if the parabolic
A fixed-end beam of length L is loaded by distributed load in the form of a cosine curve with maximum intensity q0 at A.(a) Use the fourth-order differential equation of the deflection curve to solve for reactions at A and B and also the equation of the deflection curve.(b) Repeat (a) using the
A fixed-end beam of length L is loaded by a bdistributed load in the form of a cosine curve with maximum intensity q0 at A.(a) Use the fourth-order differential equation of the deflection curve to solve for reactions at A and B and also the equation of the deflection curve.(b) Repeat (a) if the
A fixed-end beam of length L is loaded by triangularly distributed load of maximum intensity q0 at B.Use the fourth-order differential equation of the deflection curve to solve for reactions at A and B and also the equation of the deflection curve.
A proposed cantilever beam AB of length L carries a concentrated load P acting at the position shown in the figure.Determine the reactions RA, RB, and MA for this beam. Also, draw the shear-force and bending-moment diagrams, labeling all critical ordinates.
A propped cantilever beam has flexural rigidity the beam, EL = 4.5 MN.m2. When the loads shown are applied to it settles at joint B by 5 mm. Find the reaction at joint B.
A cantilever beam is supported by a tie rod at B as shown. Both the tie rod and the beam are steel E = 30 x 106 with psi. The tie rod is just taut before the distributed load is applied.(a) Find the tension force in the tie rod. (b) Draw shear-force and bending-moment diagrams for the beam,
The figure shows a nonprismatic, propped cantilever beam AB with flexural rigidity 2EI from A to C and EI from C to B. Determine all reactions of the beam due to the uniform load of intensity q.
A beam ABC is fixed at end A and supported by beam DE at point B (see figure). Both beams have the same cross section and are made of the same material.(a) Determine all reactions due to the load P.(b) What is the numerically largest bending moment in either beam?
A three-span continuous beam ABCD with three equal spans supports a uniform load of intensity q (see figure). Determine all reactions of this beam and drawn the shear-force and bending-moment diagrams, labeling all critical ordinates.
A beam rests on supports at A and B and is loaded by a distributed load with intensity q as shown. A small gap Î” exists between the unloaded beam and the support at C. Assume that span length L = 40in and flexural rigidity of the beam EI = 0.4 x 109 lb-in2.Plot a graph of the bending
A fixed-end beam AB of length L is subjected to a moment acting M0 at the position shown in the figure.(a) Determine all reactions for this beam.(b) Draw shear-force and bending-moment diagrams for the special case in which a = b = L/2.
A temporary wood flume serving as a channel for irrigation water is shown in the figure. The vertical boards forming the sides of the flume are sunk in the ground, which provides a fixed support. The top of the flume is held by tie rods that are tightened so that there is no deflection of the
Two identical, simply supported beams AB and CD are placed so that they cross each other at their midpoints (see figure). Before the uniform load is applied, the beams just touch each other at the crossing point.Determine the maximum bending moments (MAB)max and (MCD)max in beams AB and CD,
The cantilever beam AB shown in the figure is an S6 x 12.5 steel I-beam with E = 30 x 106 psi. The simple beam DE is a wood beam 4 in. x 12 in. (normal dimension) in cross section with E = 1.5 x 106 psi. A steel rod AC of diameter 0.25 in., length 10 ft, and E = 30 x 106 psi serves as a hanger
A beam with a guided support at B is loaded by a uniformly distributed load with intensity q. Use the method of superposition to solve for all reactions. Also draw shear-force and bending moment diagrams, labeling all critical ordinates.
The beam AB shown in the figure is simply supported at A and B and supported on a spring of stiffness k at its midpoint C. The beam has flexural rigidity EI and length 2L.What should be the stiffness k of the spring in order that the maximum bending moment in the beam (due to the uniform load) will
The continuous frame ABC has a fixed support at A, a roller support at C, and a rigid corner connection at B (see figure).Members AB and BC each have length L and flexural rigidity EI. A horizontal force P acts at midheight of member AB. (a) Find all reactions of the frame. (b) What is the largest
The continuous frame ABC has a pinned support at A, a guided support at C, and a rigid corner connection at B (see figure). Members AB and BC each have length L and flexural rigidity EI. A horizontal force P acts at mid height of member AB.(a) Find all reactions of the frame.(b) What is the largest
A wide-flange beam ABC rests on three identical spring supports A, B and C (see figure). The flexural rigidity of the beam is EI = 6912 x 106 1b-in.2 and each spring has stiffness k = 62,500 1b/in. The length of the beam is L = 16 ft.If the load P is 6000 1b, what are the reactions RA, RB, and RC?
A fixed-end beam AB of length L is subjected to a uniform load of intensity q acting over the middle region of the beam (see figure).(a) Obtain a formula for the fixed-end moments MA and MB in terms of the load q, the length L, and the length b of the loaded part of the beam.(b) Plot a graph of the
A beam supporting a uniform load of intensity q throughout its length rests on pistons at points A, C and B (see figure). The cylinders are filled with oil and are connected by a tube so that the oil pressure on each piston is the same. The pistons at A and B have diameter d1, and the pistons at
A thin steel beam AB used in conjunction with an electromagnet in a high-energy physics experiment is securely bolted to rigid supports (see figure). A magnetic field produced by coils C results in a force acting on the beam. The force is trapezoid dally distributed with maximum intensity q0 = 18
A propped cantilever beam of length 2L with support at B is loaded by a uniformly distributed load with intensity q. Use the method of superposition to solve for all reactions. Also draw shear-force and bending moment diagrams, labeling all critical ordinates.
Two flat beams AB and CD, lying in horizontal planes, cross at right angles and jointly support a vertical load P at their midpoints (see figure). Before the load P is applied, the beams just touch each other. Both beams are made of the same material and have the same widths. Also, the ends of both
A propped cantilever beam of length 2L is loaded by a uniformly distributed load with intensity q. The beam is supported at B by a linearly elastic spring with stiffness k. Use the method of superposition to solve for all reactions. Also draw shear-force and bending-moment diagrams, labeling all
A propped cantilever beam of length 2L is loaded by a uniformly distributed load with intensity q. The beam is supported at B by a linearly elastic rotational spring with stiffness kR, which provides a resisting moment MB due to rotation Î¸B. Use the method of superposition to solve for
Determine the fixed-end moments (MA and MB) and fixed-end forces (RA and RB) for a beam of length L supporting a triangular load of maximum intensity q0 (see figure). Then draw the shear-force and bending-moment diagrams, labeling all critical ordinates.
A continuous beam ABC with two unequal spans, one of length L and one of length 2L, supports a uniform load of intensity q (see figure).Determine the reactions RA, RB, and RC for this beam. Also, draw the shear-force and bending-moment diagrams, labeling all critical ordinates.
Beam ABC is fixed at support A and rests (at point B) upon the midpoint of beam DE (see the first part of the figure). Thus, beam ABC may be represented as a propped cantilever beam with an overhang BC and a linearly elastic support of stiffness k at point B (see the second part of the figure).The
A cable CD of length H is attached to the third point of a simple beam AB of length L (see figure). The moment of inertia of the beam is I, and the effective cross-sectional area of the cable is A. The cable is initially taut but without any initial tension.
A propped cantilever beam, fixed at the left-hand end A and simply supported at the right-hand end B, is subjected to a temperature differential with temperature T1 on its upper surface and T2 on its lower surface (see figure).
Solve the preceding problem by integrating the differential equation of the deflection curve. In preceding problem
A two-span beam with spans of lengths L and L/3 is subjected to a temperature differential with temperature T1 on its upper surface and T2 on its lower surface (see figure).
Solve the preceding problem by integrating the differential equation of the deflection curve In preceding problem
Assume that the deflected shape of a beam AB with immovable pinned supports (see figure) is given by the equation v = Î´ sin Ï€ x/L, where Î´ is the deflection at the midpoint of the beam and L is the length. Also, assume that the beam has constant axial rigidity
(a) A simple beam AB with length L and height h supports a uniform load of intensity q (see the first part of the figure). Obtain a formula for the curvature shortening Î» of this beam. Also, obtain a formula for the maximum bending stress Ïƒb in the beam due to the load q.(b)
A square aluminum bar with pinned ends carries a load P = 25 k acting at distance e = 2.0 in. from the center (see figure on the previous page). The bar has length L = 54 in. and modulus of elasticity E = 10,600 ksi. If the stress in the bar is not exceed 6 ksi, what is the minimum permissible
A pinned-end column of length L = 2.1 m is constructed of steel pipe (E = 210 GPa) having inside diameter d1 = 60 mm and outside diameter d2 = 68 mm (see figure.) A compressive load P = 10 kN acts with eccentricity e = 30 mm.(a) What is the maximum compressive stress (max in the column?(b) If the
A pinned-end strut of length L = 5.2 ft is is constructed of steel pipe (E = 30 ( 103 ksi) having inside diameter d1 = 2.0 in. and outside diameter d2 = 2.2 in. (see figure). A compressive load P = 2.0 k is applied with eccentricity e = 1.0 in. (a) What is the maximum compressive stress (max in the
A circular aluminum tube with pinned ends supports a load P = 18 kN acting at distance e = 50 mm from the center (see figure). The length of the tube is 3.5m and its modulus of elasticity is 73 GPa. If the maximum permissible stress in the tube is 20 MPa,what is the required outer diameter d2 if
A steel column (E = 30 ( 103 ksi) with pinned ends is constructed of W 10 ( 60 wide-flange shape (see figure).The column is 24 ft long. The resultant of axial loads acting on the column is a force P acting with eccentricity e = 2.0 in.(a) If P = 120 k, determine the maximum compressive stress (max
A W 410 ( 85 steel column is compressed by a force P = 340 kN acting with an eccentricity e = 38 mm(, as shown in the figure. The column has pinned ends and length L. Also,the steel has modulus of elasticity E = 200 GPa and yield stress (Y = 250 MPa.(a) If the length L = 3 m, what is the maximum
A steel column (E = 30 ( 103 ksi) that is fixed at the base and free at the top is constructed of a W 8 ( 35 wide-flange member (see figure). The column is 9.0 ft long. The force P acting at the top of the column has an eccentricity e = 1.25 in.(a) If P = 40 k, what is the maximum compressive
Determine the allowable axial load Pallow for a W 10 ( 45 steel wide-flange column with pinned ends (see figure) for each of the following lengths: L = 8 ft, 16 ft, 24 ft, and 32 ft. (Assume E = 29,000 ksi and (Y = 36 ksi.)
Determine the allowable axial load Pallow for a steel pipe column that is fixed at the base and free at the top (see figure) for each of the following lengths: L = 2.6 m, 2.8 m, 3.0 m, and 3.2 m. The column has outside diameter d = 140 mm and wall thickness t = 7 mm. (Assume E = 200 GPa and (Y =
Determine the maximum permissible length Lmax for a steel pipe column that is fixed at the base and free at the top and must support an axial load P = 40 k (see figure). The column has outside diameter d = 4.0 in. wall thickness t = 0.226 in., E = 29,000 ksi, and (Y = 42 ksi.
Determine the maximum permissible length Lmax for a steel pipe column that is fixed at the base and free at the top and must support an axial load P = 500 kN (see figure). The column has outside diameter d = 200 mm, wall thickness t = 10 mm, E = 200 GPa, and (Y = 250 MPa.
A steel pipe column with Pinned ends supports an axial load P = 21 k. The pipe has outside and inside diameters of 3.5 in. and 2.9 in., respectively. What is the maximum permissible length Lmax of the column if E = 29,000 ksi and (Y = 36 ksi?
A steel column used in a college recreation center are 16.75 m long and are formed by welding three wide-flange sections (see figure). The columns are pin-supported at the ends and may buckle in any direction.Calculate the allowable load Pallow for one column, assuming E = 200 GPa and (Y = 250 MPa.
A W 8 (28 steel wide-flange column with pinned ends carries an axial load P. What is the maximum permissible length Lmax of the column if (a) P = 50 k, and (b) P = 100 k? (Assume E = 29,000 ksi and (Y = 36 ksi.)
A W 250 ( 67 steel wide-flange column with pinned ends carries an axial load P. What is the maximum permissible length Lmax of the column if (a) P = 560 kN, and (b) P = 890 kN? (Assume E = 200 GPa and (Y = 290 MPa.)
Find the required outside diameter d for a steel pipe column (see figure) of length L = 20 ft that is pinned at both ends and must support an axial load P = 25 k. Assume that the wall thickness t is equal to d/20. (Use E = 29,000 ksi and (Y = 36 ksi.)
Find the required outside diameter d for a steel pipe column (see figure) of length L = 3.5 m that is pinned at both ends and must support an axial load P = 130 kN. Assume that the wall thickness t is equal to d/20. (Use E = 200 GPa and (Y = 275 MPa.)
Find the required outside diameter d for a steel pipe column (see figure) of length L = 11.5 ft that is pinned at both ends and must support an axial load P = 80 k. Assume that the wall thickness t is 0.30 in. (Use E = 29,000 ksi and (Y = 42 ksi.)
Determine the allowable axial load Pallow for a W 310 ( 129 steel wide-flange column with pinned ends (see figure) for each of the following lengths: L = 3 m, 6 m, 9 m, and 12 m. (Assume E = 200 GPa and (Y = 340 MPa.)
Find the required outside diameter d for a steel pipe column (see figure) of length L = 3.0 m that is pinned at both ends and must support an axial load P = 800 kN. Assume that the wall thickness t is 9 mm. (Use E = 200 GPa and (Y = 300 MPa.)
An aluminum pipe column (alloy 2014-T6) with pinned ends has outside diameter d2 = 5.60 in. and inside diameter d1 = 4.80 in. (see figure).Determine the allowable axial load Pallow for each of the following lengths: L = 6 ft, 8 ft, 10 ft, and 12 ft.
An aluminum pipe column (alloy 2014-T6) with pinned ends has outside diameter D2 = 120 mm and inside diameter d1 = 110 mm (see figure). Determine the allowable axial load Pallow for each of the following lengths: L = 1.0m, 2.0 m, 3.0 m, and 2.0 m. (Convert the given data to USCS units, determine
An aluminum pipe column (alloy 6061-T6) that is fixed at the base and free at the top has outside diameter d2 = 3.25 in. and inside diameter d1 = 3.00 in. (see figure). Determine the allowable axial load Pallow for each of the following lengths: L = 2 ft, 3 ft, 4 ft, and 5 ft.
An aluminum pipe column (alloy 6061-T6) that is fixed at the base and free at the top has outside diameter d2 = 80 mm and inside diameter d1 = 72 mm (see figure).Determine the allowable axial load Pallow for each of the following lengths: L = 0.6 m, 0.8 m, 1.0 m, and 1.2 m.(Convert the given data
A solid round bar of aluminum having diameter d (see figure) is compressed by an axial force P = 60 k. The bar has pinned supports and is made of alloy 2014-T6.(a) If the diameter d = 2.0 in., what is the maximum allowable length Lmax of the bar?(b) If the length L = 30 in., what is the minimum
A solid round bar of aluminum having diameter d (see figure) is compressed by an axial force P = 175 kN. The bar has pinned supports and is made of alloy 2014-T6. (a) If the diameter d = 40 mm, what is the maximum allowable length Lmax of the bar? (b) If the length L = 0.6 m, what is the minimum
A solid round bar of aluminum having diameter d (see figure) is compressed by an axial force P = 10 k. The bar has pinned supports and is made of alloy 6061-T6. (a) If the diameter d = 1.0 in., what is the maximum allowable length Lmax of the bar? (b) If the length L = 20 in., what is the minimum
A solid round bar of aluminum having diameter d (see figure) is compressed by an axial force P = 60 kN. The bar has pinned supports and is made of alloy 6061-T6. (a) If the diameter d = 30 mm, what is maximum allowable length of the bar? (b) If the length L = 0.6 m, what is the minimum required
A wood post of rectangular cross section (see figure) is constructed of 4 in. ( 6 in. structural grade, Douglas fir lumber (Fc = 2,000 psi, E = 1,800,00 psi). The net cross-sectional dimensions of the post are b = 3.5 in. (see Appendix F).Determine the allowable axial load Pallow for each of the
Determine the allowable axial load Pallow for a W 10 ( 60 steel wide-flange column with pinned ends (see figure) for each of the following lengths: L = 10 ft, 20 ft, 30 ft, and 40 ft. (Assume E = 29,000 ksi and (Y = 36 ksi.
A wood post of rectangular cross section (see figure) is constructed of structural grade, southern pine lumber (Fc = 14 MPa, E = 12 GPa). The cross-sectional dimensions of the post (actural dimensions) are b = 100 mm and h = 150 mm. Determine the allowable axial load Pallow for each of the
A wood post column of rectangular cross section (see figure) is constructed of 4 in. ( 8 in. construction grade, western hemlock lumber (Fc = 1,000 psi, E = 1,300,000 psi). The net cross-sectional dimensions of the column are b = 3.5 in. and h = 7.25 in. (see Appendix F). Determine the allowable
A wood column of rectangular cross section (see figure) is constructed of structural grade, Douglas fir lumber (Fc = 12 MPa, E = 10 GPa). The cross-sectional dimensions of the column (actual dimensions) are b = 140 mm and h = 210 mm. Determine the allowable axial load Pallow for each of the
A square wood column with side dimensions b (see figure) is constructed of a structural grade of Douglas fir for which Fc = 1,700 psi and E = 1,400,000 psi. An axial force P = 40 k acts on the column.(a) If the dimension b = 55 in., what is the maximum allowable length Lmax of the column?(b) If the
A square wood column with side dimensions b (see figure) is constructed of a structural grade of southern pine for which Fc = 10.5 MPa and E = 12 GPa. An axial force P = 200 kN acts on the column. (a) If the dimension b =150 mm, what is the maximum allowable length Lmax of the column? (b) If the
A square wood column with side dimensions b (see figure) is constructed of a structural grade of spruce for which Fc = 900 psi and E = 1,500,000 psi. An axial force P = 8.0 k acts on the column. (a) If the dimension b = 3.5 in., what is the maximum allowable length Lmax of the column? (b) If the
A square wood column with side dimensions b (see figure) is constructed of a structural grade of eastern white pine for which Fc = 8.0 MPa and E = 8.5 GPa. An axial force P = 100 kN acts on the column. (a) If the dimension b = 120 mm, what is the maximum allowable length Lmax of the column? (b) If
Select a steel wide-flange column of nominal depth 250 mm. (W 250 shape) to support an axial load P = 800 kN (see figure). The column has pinned ends and length L = 4.25 m. Assume E = 200 GPa and (Y = 250 MPa. (The selection of columns is limited to those listed in Table E-1(b), Appendix E.)
Select a steel wide-flange column of nominal depth 12 in. (W 12 shape) to support an axial load P = 175 k (see figure). The column has pinned ends and length L = 35 ft. Assume E = 29,000 ksi and (Y = 36 ksi. (The selection of columns is limited to those listed in Table E-1a, Appendix E.)
Select a steel wide-flange column of nominal depth 360 mm (W 360 shape) to support an axial load P = 1100 kN (see figure). The column has pinned ends and length L = 6 m. Assume E = 200 GPa and (Y = 340 MPa. (The selection of columns is limited to those listed in Table E-1 (b), Appendix E.)
Determine the allowable axial load Pallow for a steel pipe column with pinned ends having an outside diameter of 4.5 in. and wall thickness of 0.237 in. for each of the following lengths: L = 6 ft, 12 ft, 18 ft, and 24 ft. (Assume E = 29,000 ksi and (Y = 36 ksi.)
Determine the allowable axial load Pallow for a steel pipe column with pinned ends having an outside diameter of 220 mm and wall thickness of 12 mm for each of the following lengths: L = 2.5 m, 5 m, 7.5 m, and 10 m. (Assume E = 200 GPa and (Y = 250 MPa.)
Determine the allowable axial load Pallow for a steel pipe column that is fixed at the base and free at the top (see figure) for each of the following lengths: L = 6 ft, 9 ft, 12 ft, and 15 ft. The column has outside diameter d = 6.625 in. and wall thickness t = 0.280 in.(Assume E = 29,000 ksi and
The figure shows an idealized structure consisting of one or more rigid bars with pinned connections and linearly elastic springs. Rotational stiffness is denoted (R, and translational stiffness is denoted (.Determine the critical load Pcr for the structure.
The figure shows an idealized structure consisting of one or more rigid bars with pinned connections and linearly elastic springs. Rotational stiffness is denoted (R, and translational stiffness is denoted (.(a) Determine the critical load Pcr for the structure from figure part (a).(b) Find Pcr if
The figure shows an idealized structure consisting of one or more rigid bars with pinned connections and linearly elastic springs. Rotational stiffness is denoted (R and translational stiffiness is denoted (.Determine the critical load Pcr for the structure.
The figure shows an idealized structure consisting of bars AB and BC which are connected using a hinge at B and linearly elastic springs at A and B. Rotational stiffness is denoted (R and translational stiffness is denoted (.(a) Determine the critical load Pcr for the structure from figure part

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