Explanation Given information: A rectangular bar made up of aluminum alloy 2014-T6. The width of cross-sectional area of the bar, b = 4 in . The depth of cross-sectional area of the bar, d = 6 in . The bottom end of the bar is fixed and top end is pinned. The length of the bar, L = 10 ft . Consider the maximum allowable load acting on the bar as P. Show the expression of aluminum bar (2014-T6 alloy) of Sec 13.6 as follows: σ allow = [ 54 , 000 ( K L r ) 2 ] ksi, K L r > 55 Here, σ allow is the allowable stress and ( K L r ) is the slenderness ratio. Show the expression for Equation 13-30 as follows: σ max = P A + M c I Here, σ max is the maximum compressive stress, P is the load, A is the cross-section area, M is the moment, c is the distance between the centroid of member and outer fiber, and I is the moment of inertia. Calculation: Calculate the cross-sectional area ( A ) of the rectangular bar using the relation: A = b d (1) Substitute 4 in . for b and 6 in . for d in Equation (1): A = 4 × 6 = 24 in . 2 Calculate the moment of inertia about x- axis using the relation: I x = b d 3 12 (2) Substitute 4 in . for b and 6 in . for d in Equation (2): I x = 4 × 6 3 12 = 72 in . 4 Calculate the moment of inertia about y- axis using the relation: I y = d b 3 12 (3) Substitute 4 in . for b and 6 in . for d in Equation (3): I y = 6 × 4 3 12 = 32 in . 4 Calculate the least radius of gyration ( r y ) using relation: r y = I y A (4) Substitute 32 in . 4 for I y and 24 in . 2 for A in Equation (4): r y = 32 24 = 1.155 in . Calculate the slenderness ratio of bar about y-y axis using the relation: Slenderness ratio = ( K L r ) y (5) The bar is fixed at one end and pinned at another end. Thus, the value of effective length factor, K = 0.7 . Substitute 0.7 for K , 10 ft for L and 1.155 in . for r in Equation (5). Slenderness ratio = 0

10th Edition

ISBN: 9780134319650

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Concept explainers

Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial …

Videos

Question

Chapter 13.7, Problem 13.121P

To determine

To find: the maximum allowable eccentric load P that can be applied to the bar.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.7, Problem 13.120P

Chapter 13.7, Problem 13.122P

Students have asked these similar questions

The distributed load is supported by two pin-connected columns, each having a solid circular cross- section. If AB is made up of aluminum and CD of steel, determine the required diameter of each column so that both will buckle at the same time. (Esteel = 200 GPa, Sy,steel = 250 MPa, Eal = 70 GPa and Sy,al = 100 MPa). 18 kN/m 3 m 0.75 m 0.75 m

A 20-ft-long column is made of aluminum alloy 2014-T6. If it is pinned at its top and bottom, and a compressive load P is applied at point A, determine the maximum allowable magnitude of P using the equations of Sec. 13.6 and the interaction formula with (sb)allow = 20 ksi.

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 allowable eccentric load P that can be applied to the bar.

Solution Summary: The author explains the maximum allowable eccentric load P that can be applied to a rectangular bar made of aluminum alloy 2014-T6.

Concept explainers

Videos

To find: the maximum allowable eccentric load P that can be applied to the bar.

Want to see the full answer?

Chapter 13 Solutions