Mechanics of Materials (MindTap Course List)
9th Edition
ISBN: 9781337093347
Author: Barry J. Goodno, James M. Gere
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 11, Problem 11.3.17P
Three pinned-end columns of the same material have the same length and the same cross-sectional area (see figure). The columns are free to buckle in any direction. The columns have cross sections as: (a) a circle, (b) a square, and (e) an equilateral triangle.
Determine the ratios Pa: Pb: Pcof the critical loads for these columns.
Expert Solution & Answer
Trending nowThis is a popular solution!
Chapter 11 Solutions
Mechanics of Materials (MindTap Course List)
Ch. 11 - A rigid bar of length L is supported by a linear...Ch. 11 - The figure shows an idealized structure consisting...Ch. 11 - -2-3. Two rigid bars are connected with a...Ch. 11 - Repeat Problem 11.2-3 assuming that R= 10 kN ·...Ch. 11 - The figure shows an idealized structure consisting...Ch. 11 - An idealized column consists of rigid bar ABCD...Ch. 11 - An idealized column is made up of rigid segments...Ch. 11 - The figure shows an idealized structure consisting...Ch. 11 - The figure shows an idealized structure consisting...Ch. 11 - The figure shows an idealized structure consisting...
Ch. 11 - The figure shows an idealized structure consisting...Ch. 11 - Rigid column ABCD has an elastic support at B with...Ch. 11 - An idealized column is made up of rigid bars ABC...Ch. 11 - An idealized column is composed of rigid bars ABC...Ch. 11 - Repeat Problem 11.2-14 using L = 12 ft, ß = 0.25...Ch. 11 - An idealized column is composed of rigid bars ABC...Ch. 11 - Column AB has a pin support at A,a roller support...Ch. 11 - Slender column ABC is supported at A and C and is...Ch. 11 - Calculate the critical load PCTfor a W 8 × 35...Ch. 11 - Solve the preceding problem for a W 250 × 89 steel...Ch. 11 - Solve Problem 11.3-3 for a W 10 × 45 steel column...Ch. 11 - A horizontal beam AB is pin-supported at end A and...Ch. 11 - A column ABC is supported at ends A and C and...Ch. 11 - Find the controlling buckling load (kN) for the...Ch. 11 - A column, pinned at top and bottom, is made up of...Ch. 11 - Repeat Problem 11.3-9. Use two C 150 × 12.2 steel...Ch. 11 - A horizontal beam AB is pin-supported at end A and...Ch. 11 - -12 A horizontal beam AB is supported at end A and...Ch. 11 - A horizontal beam AB has a sliding support at end...Ch. 11 - A slender bar AB with pinned ends and length L is...Ch. 11 - A rectangular column with cross-sectional...Ch. 11 - .16 Three identical, solid circular rods, each of...Ch. 11 - Three pinned-end columns of the same material have...Ch. 11 - A long slender column ABC is pinned at ends A and...Ch. 11 - The roof over a concourse at an airport is...Ch. 11 - The hoisting arrangement for lifting a large pipe...Ch. 11 - A pinned-end strut of aluminum (E = 10,400 ksi)...Ch. 11 - The cross section of a column built up of two...Ch. 11 - The truss ABC shown in the figure supports a...Ch. 11 - A truss ABC supports a load W at joint B, as shown...Ch. 11 - An S6 × 12.5 steel cantilever beam AB is supported...Ch. 11 - The plane truss shown in the figure supports...Ch. 11 - A space truss is restrained at joints O, A,B, and...Ch. 11 - A fixed-end column with circular cross section is...Ch. 11 - A cantilever aluminum column has a square tube...Ch. 11 - An aluminum pipe column (E = 10,400 ksi) with a...Ch. 11 - Solve the preceding problem for a steel pipe...Ch. 11 - A wide-flange steel column (E = 30 × l06 psi) of...Ch. 11 - Prob. 11.4.6PCh. 11 - The upper end of a WE × 21 wide-flange steel...Ch. 11 - A vertical post AB is embedded in a concrete...Ch. 11 - The horizontal beam ABC shown in the figure is...Ch. 11 - The roof beams of a warehouse are supported by...Ch. 11 - Determine the critical load Pcrand the equation of...Ch. 11 - A fixed-pinned column is a W310 × 21 steel shape...Ch. 11 - Find the Controlling buckling load (kips) for the...Ch. 11 - Prob. 11.4.14PCh. 11 - A rigid L-shaped frame is supported by a steel...Ch. 11 - An aluminum tube AB with a circular cross section...Ch. 11 - The frame ABC consists of two members AB and BC...Ch. 11 - An aluminum bar having a rectangular cross section...Ch. 11 - ‘11.5-2 A steel bar having a square cross section...Ch. 11 - A simply supported slender column is subjected to...Ch. 11 - A brass bar of a length L = 0.4 m is loaded at end...Ch. 11 - Determine the bending moment M in the pinned-end...Ch. 11 - Plot the load-deflection diagram for a pinned-end...Ch. 11 - Solve the preceding problem for a column with e =...Ch. 11 - A wide-flange member (W200 × 22.5) is compressed...Ch. 11 - A wide-f hinge member (W 10 × 30) is compressed by...Ch. 11 - Solve the preceding problem (W 250 × 44.8) if the...Ch. 11 - The column shown in the figure is fixed at the...Ch. 11 - An aluminum box column with a square cross section...Ch. 11 - Solve the preceding problem for an aluminum column...Ch. 11 - A steel post /t if with a hollow circular cross...Ch. 11 - A frame ABCD is constructed of steel wide-flange...Ch. 11 - A steel bar has a square cross section of width b...Ch. 11 - ]11.6-2 A brass bar (E = 100 GPa) with a square...Ch. 11 - A square aluminum bar with pinned ends carries a...Ch. 11 - A pinned-and column of a length L = 2A m is...Ch. 11 - A pinned-end strut of a length L = 5.2 ft is...Ch. 11 - A circular aluminum tube with pinned ends supports...Ch. 11 - A steel W 12 × 35 column is pin-supported at the...Ch. 11 - A steel W 310 x 52 column is pin-supported at the...Ch. 11 - A steel column (E = 30 x 103 ksi) with pinned ends...Ch. 11 - A W410 × S5 steel column is compressed by a force...Ch. 11 - A steel column ( E = 30 X 103 ksi) that is fixed...Ch. 11 - AW310 × 74 wide-flange steel column with length L...Ch. 11 - A pinned-end column with a length L = 18 ft is...Ch. 11 - The wide-flange, pinned-end column shown in the...Ch. 11 - A W14 × 53 wide-flange column of a length L = 15...Ch. 11 - A wide-flange column with a bracket is fixed at...Ch. 11 - Determine the allowable axial load Pallowa W 10 X...Ch. 11 - Determine the allowable axial load Pallowfor a W...Ch. 11 - Determine the allowable axial load Pallowfor a W...Ch. 11 - Select a steel wide-flange column of a nominal...Ch. 11 - Prob. 11.9.5PCh. 11 - Select a steel wide-flange column of a nominal...Ch. 11 - Prob. 11.9.7PCh. 11 - Determine the allowable axial load Pallowfor a...Ch. 11 - Determine the allowable axial load Pallowfor a...Ch. 11 - Determine the allowable axial load Pallowfor a...Ch. 11 - -11 Determine the maximum permissible length...Ch. 11 - Determine the maximum permissible length Lmaxfor a...Ch. 11 - A steel pipe column with pinned ends supports an...Ch. 11 - The steel columns used in a college recreation...Ch. 11 - A W8 × 28 steel wide-flange column with pinned...Ch. 11 - Prob. 11.9.16PCh. 11 - Prob. 11.9.17PCh. 11 - Prob. 11.9.18PCh. 11 - Prob. 11.9.19PCh. 11 - Prob. 11.9.20PCh. 11 - Prob. 11.9.21PCh. 11 - An aluminum pipe column (alloy 2014-T6) with...Ch. 11 - Prob. 11.9.23PCh. 11 - Prob. 11.9.24PCh. 11 - Prob. 11.9.25PCh. 11 - Prob. 11.9.26PCh. 11 - Prob. 11.9.27PCh. 11 - Prob. 11.9.28PCh. 11 - Prob. 11.9.29PCh. 11 - Prob. 11.9.30PCh. 11 - A wood column with, a rectangular cross section...Ch. 11 - Prob. 11.9.32PCh. 11 - Prob. 11.9.33PCh. 11 - A square wood column with side dimensions b (see...Ch. 11 - A square wood column with side dimensions b (see...Ch. 11 - Prob. 11.9.36P
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
- The length of the end segments of the bar (see figure) is 20 in. and the length of the prismatic middle segment is 50 in. Also, the diameters at cross sections A. B, C, and D are 0.5, 1.0, 1.0, and 0.5 in., respectively, and the modulus of elasticity is 18 ,000 ksi. (a) Calculate the elongation of a copper bar of solid circular cross section with tapered ends when it is stretched by axial loads of magnitude 3.0 kips (see figure). (b) If the total elongation of the bar cannot exceed 0.025 in., what are the required diameters at B and C? Assume that diameters at A and D remain at 0.5 in.arrow_forward,10-6 A prismatic bar with a diameter d0= 20 mm is being compared with a stepped bar of the same diameter(d| = 20 mm) that is enlarged in the middle region lo a diameter d2= 25 mm (see figure). The radius of the fillets in the stepped bar is 2.0 mm. (a) Does enlarging the bar in the middle region make it stronger than the prismatic bar? Demonstrate your answer by determining the maximum permissible load for the prismatic bar and the maximum permissible load F, for the enlarged bar, assuming that the allowable stress for the material is 80 MPa. (b) What should be the diameter d0of the prismatic bar if it is to have the same maximum permissible load as does the stepped bar?arrow_forwardA two-story building has steel columns AB in the first floor and BC in the second floor, as shown in the figure. The roof load P:equals 400 KN, and the second-floor load P-, equals 720 kN. Each column has a length L = 3.75 m. The cross-sectional areas of the first- and second-floor columns are 11,000 mm" and 3900 mm", respectively. (a) Assuming that E = 206 GPa. determine the total shortenings aof the two columns due to the combined action of the loads Ptand P,. (b) How much additional load P0can be placed at t he top of t he column (point C) if t he total shortening: SACis not to exceed 4.0 mm?arrow_forward
- A steel cable with a nominal diameter of 25 mm (see Table 2-1) is used in a construction yard to lift a bridge section weighing 38 kN. as shown in the figure. The cable has an effective modulus of elasticity E = 140 GPa. (a) If the cable is 14 m long, how much will it stretch when the load is picked up? (b) If the cable is rated for a maximum load of 70 kN, that is the factor of safety with respect to failure of the cable?arrow_forwardAround brass bar of a diameter d1= 20mm has upset ends each with a diameter d2= 26 mm (see figure). The lengths of the segments of the bar are L1= 0.3 m and L2= 0.1 m. Quarter-circular fillets are used at the shoulders of the bar, and the modulus of elasticity of the brass is E = 100 GPa. If the bar lengthens by 0.12 mm under a tensile load P, what is the maximum stress ??maxin the bar?arrow_forwardA stepped bar ACB with circular cross sections is held between rigid supports and loaded by an axial force P at midlength (see figure). The diameters for the two parts of the bar are d1= 20 ram and d2= 25 mm, and the material is elastoplastic with yield stress s = 250 MPs. Determine the plastic load Pp.arrow_forward
- Two pipe columns (AB, FC) are pin-connected to a rigid beam (BCD), as shown in the figure. Each pipe column has a modulus of E, but heights (L1or L2) and outer diameters (d1or different for each column. Assume the inner diameter of each column is 3/4 of outer diameter. Uniformly distributed downward load q = 2PIL is applied over a distance of 3L/4 along BC, and concentrated load PIA is applied downward at D. (a) Derive a formula for the displacementarrow_forwardAn aluminum bar AD (see figure) has a cross-sectional area of 0.40 in- and is loaded by Forces Pi= 1700 lb, Pz- 1200 lb, and P3 = 1300 lb. The lengths of the segments of the bar are ti = 60 in., b = 24 in.T and c = 36 in. (a) Assuming that the modulus of elasticity is E = 10.4 × 10o psi. calculate the change in length of the bar. Does the bar elongate or shorten? (b) By what amount ^should the load Pibe increased so that the bar does not change in length when the three loads are applied? (c) IF Pzremains at 1300 lb, what revised cross-sectional area For segment AB will result in no change of length when all three loads are applied?arrow_forwardThe truss ABC shown in the figure supports a vertical load W at joint B. Each member is a slender circular steel pipe (E = 30,000 ksi) with an outside diameter of 4 in. and wall thickness 0.25 in. The distance between supports is 23 ft. Joint B is restrained against displacement perpendicular to the plane of the truss. Determine the critical value Wcr of the load.arrow_forward
- A trimetallic bar is uniformly compressed by an axial force P = 9 kips applied through a rigid end plate (see figure}. The bar consists of a circular steel core surrounded by brass and copper tubes. The steel core has a diameter of L.25 i n., the brass tube has an outer diameter of 1.75 in., and the copper tube has an outer diameter of 2.25 in. The corresponding modulus of elasticity are f, = 30, 000 ksi, Eb= 16,000 ksi, and E = 18,000 ksi Calculate the compressive stresses ers, ab, and cin the steel, brass, and copper, respectively, due to the force P.arrow_forwardThe roof over a concourse at an airport is supported by the use of pretensioned cables. At a typical joint in the roof structure, a strut AB is compressed by the action of tensile forces Fin a cable that makes an angle = 75° with the strut (see figure and photo). The strut is a circular tube of steel (E = 30,000 ksi) with outer diameter d2= 2.5 in. and inner diameter d1= 2.0 in. The strut is 5.75 ft long and is assumed to be pin-connected at both ends. Using a factor of safety n = 2.5 with respect to the critical load, determine the allowable force F in the cable.arrow_forwardA vertical post AB is embedded in a concrete foundation and held at the top by two cables (see figure). The post is a hollow steel tube with modulus of elasticity 200 GPa, outer diameter of 40 mm, and thickness of 5 mm. The cables are tightened equally by turnbuckles. If a factor of safety of 3,0 against Euler buckling in the plane of the figure is desired, what is the maximum allowable tensile force Tallowin the cables?arrow_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 on Axial Loading Normal Stress in 10 MINUTES - Mechanics of Materials; Author: Less Boring Lectures;https://www.youtube.com/watch?v=jQ-fNqZWrNg;License: Standard YouTube License, CC-BY