Explanation Given information: The load on the column is denoted by P . The Young’s modulus of the wooden column, E = 10 GPa . The yield stress of the wooden column, σ Y = 15 MPa . The width of the cross-sectional area of the column, b = 50 mm . The depth of the cross-sectional area of the column, d = 150 mm . The eccentricity ( e ) of the loading is 150 mm . The ends of the column are pinned. Calculation: Calculate the cross-sectional area ( A ) of the rectangular column using the relation: A = b d (1) Substitute 50 mm for b and 150 mm for d Equation (1): A = 50 × 150 = 7500 mm 2 × 1 m 2 10 6 mm 2 = 0.0075 m 2 Calculate the moment of inertia ( I y ) using the relation: I y = 1 12 d b 3 (2) Substitute 50 mm for b and 150 mm for d Equation (2): I y = 1 12 × 150 × 50 3 = 1 , 562 , 500 mm 4 × 1 m 4 10 12 mm 4 = 1.5625 × 10 − 6 m 4 Calculate the moment of inertia ( I x ) using the relation: I x = 1 12 b d 3 (3) Substitute 50 mm for b and 150 mm for d Equation (3): I x = 1 12 × 50 × 150 3 = 14 , 062 , 500 mm 4 × 1 m 4 10 12 mm 4 = 14.0625 × 10 − 6 m 4 Calculate the value of radius of gyration ( r x ) using a relation: r x = I x A (4) Substitute 14.0625 × 10 − 6 m 4 for I x and 0.0075 m 2 for A in Equation (4). r x = 14.0625 × 10 − 6 m 4 0.0075 m 2 = 1875 × 10 − 6 m 2 = 0.0433 m Consider the buckling of column about y-y axis: The wooden column is pinned, thus the value of effective length factor ( K ) is 1. Check the safety of the column based on the buckling criteria. Show the expression for Euler’s formula as follows: P cr = π 2 E I y ( K L ) y 2 (5) Here, E is the Young’s modulus, I is the moment of inertia, K is the effective length factor, L is the length of the member. Substitute 10 GPa for E , 1.5625 × 10 − 6 m 4 for I y , 10 ft for L , and 1 for K in Equation (5). P cr = π 2 ( 10 GPa ) ( 1.5625 × 10 − 6 m 4 ) ( 1 × 35 ) 2 = π 2 ( 10 GPa × 10 9 N m 2 1 GPa ) ( 1.5625 × 10 − 6 m 4 ) ( 1 × 3.5 m ) 2 = 15.421 × 10 4 12.25 N = 12 , 588.57 N × 1 kN 1 , 000 N P cr = 12.59 kN ≈ 12

10th Edition

ISBN: 9780134319650

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

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.

Videos

Question

Chapter 13.5, Problem 13.56P

To determine

The maximum eccentric load that can be supported by the column without yielding or buckling.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.5, Problem 13.55P

Chapter 13.5, Problem 13.57P

Students have asked these similar questions

The brass rod is ixed at one end and free at the other end. If the length of the rod is L = 2 m, determine the greatest allowable load P that can be applied so that the rod does not buckle or yield. Also, determine the largest sidesway delection of the rod due to the loading. Ebr = 101 GPa, sY = 69 MPa.

The steel pipe is fixed supported at its ends. If it is 4 m long and has an outer diameter of 50 mm, determine its required thickness so that it can support an axial load of P = 100 kN without buckling. Est = 200 GPa, sY = 250 MPa.

The 2014-T6 aluminum rod AC is reinforced with the firmly bonded A992 steel tube BC. When no load is applied to the assembly, the gap between end C and the rigid support is 0.5 mm. Determine the support reactions when the axial force of 400 kN is applied.

Chapter 13 Solutions

Mechanics of Materials (10th Edition)

Ch. 13.3 - A 50-in long steel rod has a diameter of 1 in....Ch. 13.3 - A 12-ft wooden rectangular column has the...Ch. 13.3 - The A992 steel column can be considered pinned at...Ch. 13.3 - A steel pipe is fixed supported at its ends. If it...Ch. 13.3 - Determine the maximum force P that can be...Ch. 13.3 - The A992 steel rod BC has a diameter of 50 mm and...Ch. 13.3 - Determine the critical buckling load for the...Ch. 13.3 - The column consists of a rigid member that is...Ch. 13.3 - The aircraft link is made from an A992 steel rod....Ch. 13.3 - Rigid bars AB and BC are pin connected at B. If...

Ch. 13.3 - A 2014-T6 aluminium alloy column has a length of 6...Ch. 13.3 - Solve Prob. 13-5 if the column is pinned at its...Ch. 13.3 - The W12 50 is made of A992 steel and is used as a...Ch. 13.3 - The W12 50 is made of A992 steel and is used as a...Ch. 13.3 - A steel column has a length of 9 m and is fixed at...Ch. 13.3 - A steel column has a length of 9 m and is pinned...Ch. 13.3 - The A992 steel angle has a cross-sectional area of...Ch. 13.3 - The 50-mm-diameter C86100 bronze rod is fixed...Ch. 13.3 - Determine the maximum load P the frame can support...Ch. 13.3 - The W8 67 wide-flange A-36 steel column can be...Ch. 13.3 - Prob. 13.15P Ch. 13.3 - Prob. 13.16P Ch. 13.3 - The 10-ft wooden rectangular column has the...Ch. 13.3 - The 10-fl wooden column has the dimensions shown....Ch. 13.3 - Determine the maximum force P that can be applied...Ch. 13.3 - The A-36 steel pipe has an outer diameter of 2 in....Ch. 13.3 - The A-36 steel pipe has an outer diameter of 2 in....Ch. 13.3 - The deck is supported by the two 40-mm-square...Ch. 13.3 - The deck is supported by the two 40-mm-square...Ch. 13.3 - The beam is supported by the three pin-connected...Ch. 13.3 - The W14 30 A992 steel column is assumed pinned at...Ch. 13.3 - The A992 steel bar AB has a square cross section....Ch. 13.3 - The linkage is made using two A992 steel rods,...Ch. 13.3 - The linkage is made using two A992 steel rods,...Ch. 13.3 - The linkage is made using two A-36 steel rods,...Ch. 13.3 - The linkage is made using two A-36 steel rods,...Ch. 13.3 - The steel bar AB has a rectangular cross section....Ch. 13.3 - Determine if the frame can support a load of P =...Ch. 13.3 - Determine the maximum allowable load P that can be...Ch. 13.3 - Prob. 13.34P Ch. 13.3 - Prob. 13.35P Ch. 13.3 - The members of the truss are assumed to be pin...Ch. 13.3 - Solve Prob. 1336 for member AB, which has a radius...Ch. 13.3 - The truss is made from A992 steel bars, each of...Ch. 13.3 - The truss is made from A992 steel bars, each of...Ch. 13.3 - Prob. 13.40P Ch. 13.3 - The ideal column has a weight w (force/length) and...Ch. 13.3 - The ideal column is subjected to the force F at...Ch. 13.3 - The column with constant El has the end...Ch. 13.3 - Consider an ideal column as in Fig.13-10 c, having...Ch. 13.3 - Consider an ideal column as in Fig. 13-10d, having...Ch. 13.5 - The wood column is fixed at its base and free at...Ch. 13.5 - The W10 12 structural A-36 steel column is used...Ch. 13.5 - The W10 12 structural A-36 steel column is used...Ch. 13.5 - The aluminium column is fixed at the bottom and...Ch. 13.5 - Prob. 13.50P Ch. 13.5 - Prob. 13.51P Ch. 13.5 - The aluminum rod is fixed at its base and free and...Ch. 13.5 - Assume that the wood column is pin connected at...Ch. 13.5 - Prob. 13.54P Ch. 13.5 - The wood column is pinned at its base and top. If...Ch. 13.5 - Prob. 13.56P Ch. 13.5 - Prob. 13.57P Ch. 13.5 - Prob. 13.58P Ch. 13.5 - Prob. 13.59P Ch. 13.5 - The wood column is pinned at its base and top. If...Ch. 13.5 - The brass rod is fixed at one end and free at the...Ch. 13.5 - The brass rod is fixed at one end and free at the...Ch. 13.5 - Prob. 13.63P Ch. 13.5 - A W14 30 structural A-36 steel column is pin...Ch. 13.5 - Prob. 13.65P Ch. 13.5 - The 6061-T6 aluminum alloy solid shaft is fixed at...Ch. 13.5 - The 6061-T6 aluminum alloy solid shaft is fixed at...Ch. 13.5 - The W14 53 structural A992 steel column is fixed...Ch. 13.5 - The W14 53 column is fixed at its base and free...Ch. 13.5 - Prob. 13.70P Ch. 13.5 - The stress-strain diagram for a material can be...Ch. 13.5 - The stress-strain diagram for a material can be...Ch. 13.5 - The stress-strain diagram for the material of a...Ch. 13.5 - Construct the buckling curve, P/A versus L/ r, for...Ch. 13.5 - The stress-strain diagram of the material can be...Ch. 13.5 - The stress-strain diagram of the material can be...Ch. 13.5 - Prob. 13.77P Ch. 13.6 - Determine the largest length of a W10 12...Ch. 13.6 - Using the AISC equations, select from AppendixB...Ch. 13.6 - Take Y = 50 ksi.Ch. 13.6 - Determine the longest length of a W8 31...Ch. 13.6 - Using the AISC equations, select from AppendixB...Ch. 13.6 - Prob. 13.83P Ch. 13.6 - Using the AISC equations, select from AppendixB...Ch. 13.6 - Prob. 13.85P Ch. 13.6 - Prob. 13.86P Ch. 13.6 - Prob. 13.87P Ch. 13.6 - Prob. 13.88P Ch. 13.6 - Using the AISC equations, check if a column having...Ch. 13.6 - The beam and column arrangement is used in a...Ch. 13.6 - Prob. 13.91P Ch. 13.6 - Prob. 13.92P Ch. 13.6 - The 1-in.-diameter rod is used to support an axial...Ch. 13.6 - The 1-in.-diameter rod is used to support an axial...Ch. 13.6 - Prob. 13.95P Ch. 13.6 - Prob. 13.96P Ch. 13.6 - Prob. 13.97P Ch. 13.6 - Prob. 13.98P Ch. 13.6 - The tube is 0.25 in. thick, is made of 2014-T6...Ch. 13.6 - Prob. 13.100P Ch. 13.6 - A rectangular wooden column has the cross section...Ch. 13.6 - Prob. 13.102P Ch. 13.6 - Prob. 13.103P Ch. 13.6 - The bar is made of aluminum alloy 2014-T6....Ch. 13.6 - Prob. 13.105P Ch. 13.6 - Prob. 13.106P Ch. 13.7 - The W8 15 wide-flange A-36 steel column is...Ch. 13.7 - Solve Prob.13-107 if the column is fixed at its...Ch. 13.7 - Prob. 13.109P Ch. 13.7 - Prob. 13.110P Ch. 13.7 - The W8 15 wide-flange A992 steel column is fixed...Ch. 13.7 - The W8 15 wide-flange A992 steel column is fixed...Ch. 13.7 - The W12 22 wide-flange A-36 steel column is fixed...Ch. 13.7 - Prob. 13.114P Ch. 13.7 - Prob. 13.115P Ch. 13.7 - Prob. 13.116P Ch. 13.7 - A 20-ft-long column is made of aluminum alloy...Ch. 13.7 - A 20-ft-long column is made of aluminum alloy...Ch. 13.7 - The 2014-T6 aluminum hollow column is fixed at its...Ch. 13.7 - The 2014-T6 aluminum hollow column is fixed at its...Ch. 13.7 - Prob. 13.121P Ch. 13.7 - Prob. 13.122P Ch. 13.7 - Prob. 13.123P Ch. 13.7 - Prob. 13.124P Ch. 13.7 - The 10-in.-diameter utility pole supports the...Ch. 13.7 - Using the NFPA equations of Sec 13.6. and Eq....Ch. 13.7 - Prob. 13.127P Ch. 13 - The wood column has a thickness of 4 in. and a...Ch. 13 - The wood column has a thickness of 4 in. and a...Ch. 13 - A steel column has a length of 5 m and is free at...Ch. 13 - The square structural A992 steel tubing has outer...Ch. 13 - If the A-36 steel solid circular rod BD has a...Ch. 13 - If P = 15 kip, determine the required minimum...Ch. 13 - The steel pipe is fixed supported at its ends. If...Ch. 13 - The W200 46 wide-flange A992-steel column can be...Ch. 13 - The wide-flange A992 steel column has the cross...Ch. 13 - The wide-flange A992 steel column has the cross...

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.

The maximum eccentric load that can be supported by the column without yielding or buckling.

Solution Summary: The author calculates the maximum eccentric load that can be supported by the column without yielding or buckling.

Concept explainers

Videos

The maximum eccentric load that can be supported by the column without yielding or buckling.

Want to see the full answer?

Chapter 13 Solutions