An aluminum tube of length 0.01R (m) is used as column (fixed at both ends) carrying an axial load of 1.333R (N). If the outer diameter of the tube is 0.06R (mm),compute the inner diameter that would provide a factor of safety of 2 against buckling. Use E = 70 GPa for aluminum. Note R=993

An aluminum tube of length 0.01R (m) is used as column (fixed at both ends) carrying an axial load of 1.333R (N). If the outer diameter of the tube is 0.06R (mm),compute the inner diameter that would provide a factor of safety of 2 against buckling. Use E = 70 GPa for aluminum. Note R=993

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter11: Columns

Section: Chapter Questions

Problem 11.9.15P: A W8 × 28 steel wide-flange column with pinned ends carries an axial load P. What is the maximum...

See similar textbooks

Related questions

Q: The column shown is fabricated from two C250 x 30 standard steel shapes (see Appendix B for its…

Q: A circular hollow column has an external diameter of 1.5 m and a wall thickness of 0.25 m. Both ends…

A: Given: Diameter, d = 1.5 m Length, l = 20.8 m E = 200 GPa Find: The…

Q: Question 4. A hollow steel tube 5 m long with external and internal diameters 100 mm and 80 mm…

A: GIVEN DATA LOAD P=150KN LENGTH L=5m OUTER DIA=100mm INNER DIA=80mm CHANGE IN LENGTH =6.4mm FOS=4

Q: Both ends of the fixed (fixed) rod were mounted at 0 °C. Calculate the minimum diameter of the bar…

A: for solution refer below images.

Q: "Prob. 10.3-5. A square, tubular steel column has the di- mensions shown in Fig. P10.3.5, has a…

A: Given:L=3 mP=50 KNEst=210GPaσy=250MPaa=150mmb=125mm

Q: The AB bond must be made of a steel for which the normal stress limit is 450 MPa. Determine the…

Q: The metallic hollow pipe shown in Figure Q2 is fixed at its lower end and free at its top end, and…

Q: A load P is supported by two springs arranged IN SERIES. The upper spring has 20 turns of…

Q: Q3) A short stepped bar is shown in Figure below. The stiffness of the large section is 12 kN/mm and…

A: Given data: k1=12 kN/mmk2=8 kN/mmF=6 kN Need to determine the displacement of the nodes 2 and 3.

Q: A column has pinned ends and is axially loaded in compression. The length is 6 m and the weight is…

Q: 13. Buckling of Columns EXAMPLE 3 An aluminum column of length L and rectangular cross-section has a…

Q: (a) Explain FIVE (5) factors that may influence the optimum column design under an axial compressive…

A: (a) A beam under axial compressive load can fail by two modes, one is by bending and the other is by…

Q: A circular plate of 80 mm radius and 6 mm thick carries a central load of 2 kN. Calculate the…

A: A circular plate with an 80 mm radius and a thickness of 6 mm supports a central load of 2 kN.When…

Q: A solid circular column (one end is fixed, the other end is free) is made from an alloy with a…

Q: Q: compute the total elongation caused by an axial load of 100KN applied to a circular bar, tapering…

A: Given, d1 = 40 mm d2 = 120 mm P = 100 kN = 100 x 103 N E = 200 GPa = 200 x 103 N/mm2 L = 10 m =…

Q: 4. A beam of rectangular cross section, clamped at both ends is subjected to a vertical load P as…

A: Material failure is caused due to the loss of load carrying capacity in a material unit. Designing…

Q: A slender bar AB with pinned ends andlength L is held between immovable supports (seefigure).What…

A: Given L = length A = cross-sectional area I = moment of inertia E = modulus of elasticity…

Q: The column shown is fabricated from two C250 x 30 standard steel shapes (see Appendix B for its…

Q: An elastic column has one end pinned and the other end fixed in a bushing so that the values given…

Q: Q: compute the total elongation caused by an axial load of 100KN applied to a circular bar, tapering…

A: Given:P=100 KNL=10 mD1=40 mmD2=120 mmE=200 GPa

Q: 2) Determine the critical axial buckling load for an 8 % x 12 in glu-laminated column braced at 10…

A: For 834*12 inA=105.00 in2Iy=1260.00 in4, ry=3.5 inIZ=669.922 in4, rZ=2.5 inThe total height=L=…

Q: 5. Two C310x45 channels are latticed together so they have equal moments of inertia about the…

Q: An aluminum bar (Alloy 1100-H14) having a cross-sectional area of 325mm carries the axial loads…

Q: If you double the length of a column by what factor is it buckling load

A: Given data Double the length of a column

Q: Problem 2. A steel bar 50 mm in diameter and 2 m long is surrounded by a shell of a cast iron 5 mm…

Q: Column is designed and fabricated using Aluminum alloy having hollow cross- section as shown.…

A: Given data: Modulus of elasticity = 10.4×103 ksi Yield strength = 40 ksi…

Q: A 51 mm diameter steel rod (E = 207 GPA) with pinned end conditions is to be subjected to an axail…

A: Given Diameter, d = 51 mm E = 207 GPa Find Maximum length, L

Q: N for Newton, m for meter, mm for millimeter, N/(mm^2) for Stress, mm^2 or m^2 for Area, mm^4…

Q: The column shown is fabricated from two C250 x 30 standard steel shapes (see Appendix B for its…

A: The section properties for a standard C250×30 shape are given in appendix BA=3790 mm2, d=254 mm,…

Q: 3. Two columns A C and BC have a circular cross section of radius 5 cm, yield strength oY=100 MPa,…

A: Given: Load P=100kN Diameter of the links=0.05×2=0.1m E=100GPa

Q: 3) An aluminium pipe column (E=70 GPa) with length L=3 m has inside and outside diameters di-130 mm…

A: Given Data E=70 GPa D1=130 mm D2=150 mm L=3 m

Q: "Prob. 10.3-5. A square, tubular steel column has the d mensions shown in Fig. P10.3.5, has a length…

A: given:axial compression load P=50KNlength L=3mEst=210GPa σy=250MPa

Q: Calculate the horizontal displacement at Joint H if the steel truss is loaded as shown in Figure…

Q: A column, pinned at top and bottom, is made up of two C 10 x 25 steel shapes (see figure) that act…

A: Given data *The length is L = 26 ft *The young modulus of elasticity is E = 30000 ksi

Q: b) A square cross section is made of wood with 2 m long pin-ended column as shown in Figure 7. Given…

A: Given data: E=13 GPaσall=12 MPaFOS=2.5 Need to determine the required size for the column.

Q: The bottom shell of a steel tanker is longitudinally framed. The spacings of transverse floor and…

A: given; ⇒length of bar (L)=0.8m=800mm⇒bar dimension =150mm*10mmso;⇒width (b)=150mm⇒thickness…

Q: 3) A 0.5 inch diameter aluminum rod is used to support a decorative overhang. If the 7ft rod deforms…

A: NOTE:- As per our company guidelines we are supposed to answer only one question. Kindly repost…

Q: Determine the critical axial buckling load for an 8 ¾ x 12 in. glu-laminated column braced at 10 ft…

A: Given, Young's modulus of elasticity, E=1.8× 106 psi Moment of inertia, I=b h312I=12×…

Q: Find the critical buckling load of the 7 m long, cross-section column made of A-36 steel with hinged…

A: Given: The length of column, L = 7 m The modulus of elasticity, E = 200 GPa The outer diameter of…

Q: The figures below show a formed sheet-steel bracket. The total distributed load “W” on the bracket…

Q: Consider the steel truss and member cross-section presented in figures below. All the members of the…

Q: An aluminium rod is fixed at its base and free at the top as shown in Figure 1. If the imposed…

A: given; load(P)=200KN =200*103Ndiameter(d)=200mmelasticity(E)=72GPa…

Q: 9- Compute the total elongation caused by an axial load of 100 kN applied to a flat bar 20 mm thick…

A: Find the total elongation caused by an axial load 100 KN applied to a flat bar 20 mm thick ,…

Q: Question 3 An aluminum tube AB of circular secton has a fixed support at the base and is pinned at…

A: Apply moment equilibrium condition.

Q: The structure supports force P=75 kN, as shown in Figure 6. The solid circular rod BD is made of…

Concept explainers

Buckling of columns

The column is described as a vertical member of the structure that carries an axial compressive load, and buckling is a lateral deformation of the column under the application of load.

Question

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1 Calculation of moment of Inertia and effective length for fixed beam.

VIEW

Step 2 Calculation of inner diameter by using critical load formula.

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

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

An aluminum tube AB with a circular cross section has a sliding support at the base and is pinned at the top to a horizontal beam supporting a load Q = 200 kN (sec figure). Determine the required thickness t of the tube if its outside diameter d is 200 mm and the desired factor of safety with respect to Eu 1er buckling is n = 3.0. (Assume E = 72 GPa.)
An aluminum pipe column (E = 10,400 ksi) with a length L = 10.0 ft has inside and outside diameters d1= 5.0 in. and d2= 6.0 in., respectively (sec figure). The column is supported only at the ends and may buckle in any direction. Calculate the critical load Pcrfor the following end conditions: (a) pinned-pinned, (b) fixed-free, (c) fixed-pinned, and (d) fixed-fixed.
A pinned-end strut of aluminum (E = 10,400 ksi) with a length L = 6 ft is constructed of circular tubing with an outside diameter d = 1 in. (sec figure). The strut must resist an axial load F = 4 kips with a factor of safety n = 2.0 with respect to the critical load. Determine the required thickness t of the tube.
A cantilever aluminum column has a square tube cross section with an outer dimension of 150 mm. The column has a length L = 4 m and is designed to support an axial load of 45 kN. Find the minimum required thickness of the section if the factor of safety n = 2.5 with respect to buckling. Assume that the modulus of elasticity is 72 GPa and the proportional limit is 480 MPa.
An idealized column is made up of rigid bars ABC and CD that are joined by a rotational elastic connection at C with stiffness ßR. The column has a roller support at B and a pin support at D. Find an expression for the critical load Pcr of the column.
A rigid L-shaped frame is supported by a steel pipe column AB (sec figure) and is subjected to a horizontal load F = 140 kips. If the pipe has an outside diameter d = 4 in. and a factor of safety of 2.5 is required with respect to Euler buckling, what is the minimum acceptable thickness f of the pipe? Assume that E = 30,000 ksi for AB.
The hoisting arrangement for lifting a large pipe is shown in the figure. The spreader is a steel tubular section with outer diameter 70 mm and inner diameter 57 mm. Its length is 2.6 m, and its modulus of elasticity is 200 GPa. Based upon a factor of safety of 2.25 with respect to Euler buckling of the spreader, what is the maximum weight of pipe that can be lifted? (Assume pinned conditions at the ends of the spreader.)
A wide-flange steel column (E = 30 × l06 psi) of W12 × 87 shape (see figure) h as a length L = 28 ft. It is supported only at the ends and may buckle in any direction. Calculate the allowable load Pallowbased upon the critical load with a factor of safety n = 2.5. Consider the following end conditions: (a) pinned-pinned, (b) fixed-free, (c) fixed-pinned, and (d) fixed-fixed.
The upper end of a WE × 21 wide-flange steel column (E = 30 × 103ksi) is supported laterally between two pipes (see figure). The pipes arc not attached to the column, and friction between the pipes and the column is unreliable. The base of the column provides a fixed support, and the column is 13 ft long. Determine the critical load for the column, considering Euler buckling in the plane of the web and also perpendicular to the plane of the web.
-2-3. Two rigid bars are connected with a rotational spring, as shown in the figure. Assume that the elastic rotational spring constant is R= 75 kip-in./rad. Calculate the critical load Pcrof the system. Assume that L = 6 ft.
A sign for an automobile service station is supported by two aluminum poles of hollow circular cross section, as shown in the figure. The poles are being designed to resist a wind pressure of 75 lb/ft" against the full area of the sign. The dimensions of the poles and sign are hx= 20 ft, /r =5 ft, and h = 10 ft. To prevent buckling of the walls of the poles, the thickness e is specified as one-tenth the outside diameter d. (a) Determine the minimum required diameter of the poles based upon an allowable bending stress of 7500 psi in the aluminum. (b) Determine the minimum required diameter based upon an allowable shear stress of 300 psi.
An idealized column is made up of rigid segments ABC and CD that are joined by an elastic connection at C with rotational stiffness ßR= 100 kip-in./rad. The column has a roller support at B and a sliding support at D. Calculate the critical load Pcrof the column.