Mechanics of Materials
11th Edition
ISBN: 9780137605460
Author: Russell C. Hibbeler
Publisher: Pearson Education (US)
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 13.3, Problem 41P
The ideal column has a weight w (force/length) and is subjected to the axial load P. Determine the maximum moment in the column at midspan. El is constant, Hint: Establish the differential equation for deflection, Eq.13−1, with the origin at the midspan. The general solution is v = C1 sin kx + C2COS kx + (w/(2P))x2 − (wL/(2P))x− (wEI/P2) where k2 = P/EI.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Determine as expressions of the elastic line, the deflection and the large at point B. E = 200 Gpa and Ix = 39 X 10−6 mm4
I've tried it a few times and I can't get to the template: v(B)= 0.85mm v'(B) = 0
An
aluminum alloy tube with an outside diameter of 3.1 in. and a wall thickness of 0.36 in. is used as a 16-ft-long column. Assume that E
= 9300 ksi and that pinned connections are used at each end of the column. Determine the slenderness ratio L/r and the Euler buckling
load Per for the column.
Answers:
L/r=
Por=
kips
A cantilever, 2.6m long, carrying a uniformly distributed load w along the
entire length, is propped at its free end to the level of the fixed end. If the
load on the prop is then 30 kN, calculate the value of w. Determine also
the slope of the beam at the support. If any formula for deflection is used
it must first be proved. Take E = 210 GN/m² and 1 = 4*10 m².
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 - Determine the critical buckling load for the...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 - Prob. 34PCh. 13.3 - Prob. 35PCh. 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 - Prob. 40PCh. 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 aluminium column is fixed at the bottom and...Ch. 13.5 - Prob. 50PCh. 13.5 - Prob. 51PCh. 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. 54PCh. 13.5 - Prob. 59PCh. 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. 65PCh. 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 - 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. 13.6 - Using the AISC equations, select from AppendixB...Ch. 13.6 - Take Y = 50 ksi.Ch. 13.6 - Using the AISC equations, select from AppendixB...Ch. 13.6 - Prob. 83PCh. 13.6 - Using the AISC equations, select from AppendixB...Ch. 13.6 - Prob. 97PCh. 13.6 - Prob. 98PCh. 13.6 - The tube is 0.25 in. thick, is made of 2014-T6...Ch. 13.6 - Prob. 100PCh. 13.6 - A rectangular wooden column has the cross section...Ch. 13.6 - Prob. 102PCh. 13.7 - The W8 15 wide-flange A-36 steel column is...Ch. 13.7 - Prob. 110PCh. 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 - 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...
Additional Engineering Textbook Solutions
Find more solutions based on key concepts
CONCEPT QUESTIONS
15.CQ3 The ball rolls without slipping on the fixed surface as shown. What is the direction ...
Vector Mechanics for Engineers: Statics and Dynamics
A windowmounted air conditioner removes 3.5kJ from the inside of a home using 1.75 kJ work input. How much ener...
EBK FUNDAMENTALS OF THERMODYNAMICS, ENH
3.3 It is known that a vertical force of 200 lb is required to remove the nail at C from the board. As the nail...
Vector Mechanics for Engineers: Statics, 11th Edition
Convert the following quantities from English to SI units: a. 98 Btu/(hr-ft-F) b. 0.24 Btu/(lbm-F) C. 0.04 Ibm/...
Heating Ventilating and Air Conditioning: Analysis and Design
What types of polymers are most commonly blow molded?
DeGarmo's Materials and Processes in Manufacturing
List several uses of the arbor press.
Machine Tool Practices (10th Edition)
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 number of significant digits is set to 3. The tolerance is +-1 in the 3rd significant digit.arrow_forwardThe rigid arm AB is attached to the end of the solid circular steel rod BC. The rod is supported by bearings at B and a fixed support at C. The bearings at B prevent rod BC from translating up, down, left, or right, but the bearings do allow rod BC to rotate freely about the x axis at B. It is required that the vertical deflection of point A not exceed 0.25 in. when a load of P = 700 lb is applied at A. Determine the minimum diameter needed for rod BC. Use a = 18 in. and b = 45 in. The modulus of rigidity of the rod is G = 11×106 psi. A P Answer: dmin = i a B b in. Carrow_forwardGiven the 200mm x 400mm beam with the loading shown, determine: a. the amount of load P applied on the beam if the deflection on the midspan is 5 mm downward. b. by this same load P, what is the deflection and slope on the beam at point D? Set the parameters as a = 3m, L = 9m , E = 200 GPa. EI is constant.arrow_forward
- Determine the magnitude (positive value) of the deflection at C. Use E-200GPa and I= 6(10) mm². Answer in mm rounded-off to 2 decimal places. A 3m C 3m 20 kN ↓ D Barrow_forwardUsing Castigliano’s theorem, determine horizontal and vertical components of deflection at point C. Given: P=1000 N EA= 2*10^6 Narrow_forward1. Determine the maximum value of P if the stress in the rod is not to exceed 120 MPa. 2. If the rod elongates by 5mm, determine the stress in the rod. 3. Determine the deflection at the midspan end if thebrod is removed. Take P=20 kNarrow_forward
- 4. A cantilever of length 2m carries a point load of 20 kN at the free end and another load of 20 kN at its centre. If E = 10°N/mm?and I = 10®mm for the cantilever then determine by moment area method, the slope and deflection of the cantilever at the free end. 20KN 20 KNarrow_forwardA steel column is of length 8m and diameter 600 mm with both ends hinged.Determine the crippling load by Euler’s formula. Take 5 E = 2.1x10 N/mm2arrow_forwardFor the structure and loading shown below, determine the vertical and horizontal deflections and the rotation at point B. Neglect axial force in the column. L, w B E, I L2 Aarrow_forward
- Determine the equivalent spring stiffness constant of a rigid bar with two spring support on both end and an applied load at the mid-span of the beam. Given that k1 = 10 N/m and k2 = 20 N/marrow_forwardDetermine the maximum load P that the frame can withstand without bending the A992 BC steel part. Due to the split ends of the element, consider that the B and C supports act as joints for buckling on the x - x axis and as fixed supports for buckling on the y-y axis. Note : A similar problem is already solved on bartl*by.i have attached its screen shot here. You can refer it.arrow_forwardWhat is the vertical displacement at joint F. Assume all members are pin connected at their end points. Take A=0.5 in^2 and E=29(10^3) ksi for each member. Use the method of unit load.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
Column buckling; Author: Amber Book;https://www.youtube.com/watch?v=AvvaCi_Nn94;License: Standard Youtube License