Explanation Given information: A column is made up of aluminum alloy 2014-T6. The ends of the column are fixed. The length of the column, L = 16 ft . Consider the maximum allowable load acting on the column as P acting at point A. The eccentricity ( e ) of the load from the neutral axis is 4.25 in . Show the expression of aluminum column (2014-T6 alloy) of Sec 13.6 as follows: σ allow = [ 30.7 − 0.23 ( K L r ) ] , 12 < K L r < 55 Here, σ allow is the allowable stress, and ( K L r ) is the slenderness ratio. Show the expression for maximum stress as follows: σ max = P A + M c I Here, σ max is the maximum stress, P is the load, A is the cross-sectional 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: Show the cross-section of the column as shown in Figure 1. Refer to Figure 1. The cross-section of the column consists of rectangle PQRS and rectangle 1. The width and depth of the rectangle PQRS are b 2 = 8 in . and d 2 = 9 in . The width and depth of the rectangle 1 are b 1 = 3.75 in . and d 1 = 8 in . Calculate the cross-sectional area ( A ) of the column using the relation: A = b 2 d 2 − 2 b 1 d 1 (1) Substitute 8 in . for b 1 , 8 in . for d 1 , 8 in . for b 2 and 9 in . for d 2 in Equation (1): A = 8 × 9 − ( 2 × 3.75 × 8 ) = 12 in . 2 Calculate the moment of inertia about x- axis using the relation: I x = b 2 d 2 3 12 − 2 × b 1 d 1 3 12 (2) Substitute 3.75 in . for b 1 , 8 in . for d 1 , 8 in . for b 2 and 9 in . for d 2 in Equation (2): I x = 8 × 9 3 12 − 2 × 3.75 × 8 3 12 = 486 − 320 = 166 in . 4 The width and depth of the flanges are b f = 8 in . and d f = 0.5 in . The width and depth of the web are b w = 0.5 in . and d w = 8 in . Calculate the moment of inertia about y- axis using the relation: I y = { ( Moment of inertia of flanges ) + ( Moment of inertia of web ) } = 2 × d f b f 3 12 + d w b w 3 12 (3) Substitute 8 in . for b f , 0.5 in . for d f , 0.5 in . for b w , and 8 in

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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 13.7, Problem 13.117P

To determine

To find: the value of maximum allowable load P that can be applied to the column.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.7, Problem 13.116P

Chapter 13.7, Problem 13.118P

Students have asked these similar questions

Finite Element Analysis

A small auditorium that can accommodate 30 people allows smoking. The design engineers of the auditorium assume that the smokers each are responsible for an average of 50 micrograms per minute of tobacco smoke being added to the auditorium space. The volumetric flow rate of recirculated room air is 200 cfm. Outdoor air is also supplied, and is mixed with the recirculated room air. The system has a ventilation effectiveness of 80%. In an effort to maintain the level of particulate matter from the tobacco smoke in the auditorium to no more than 5.5 micrograms per cubic foot, filters with an effective efficiency of 90% are added to the ventilation system downstream of the point in the system where outdoor air and recirculated room air are mixed. a) What is the necessary volumetric flow rate (in cfm) for the supply outdoor air? Assume the outdoor air is clean. b) The outdoor air taken into the system becomes contaminated with tobacco smoke due to a leak in an adjacent building’s…

Chapter 13 Solutions

Mechanics of Materials

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 - 13-1. 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...

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.