Explanation Calculation: Concept Used: Write the expression for direction cosine in x-direction. λ x = x F − x N L ...... (I) Here, coordinate of x at near end of the member is x F and coordinate of x at far end of the member is x N . Write the expression for direction cosine in x-direction. λ y = y F − y N L ...... (II) Here, coordinate of y at near end of the member is y F and coordinate of y at far end of the member is y N . Calculation: The following figure shows the structure. Figure (1) Write the transformation of the local coordinates to global coordinates. Write the expression to calculate the value ofxcoordinate of member 1. Substitute 0 ft for x F , 0 ft for x N and 10 ft for L in Equation (I). λ x = 0 ft − 0 ft 10 ft = 0 Write the expression to calculate the value ofy-coordinate of member 1. Substitute 10 ft for y F , 0 ft for y N and 10 ft for L in Equation (II). λ y = 10 ft − 0 ft 10 ft = 1 Write the stiffness matrix of member 1. k 1 = ( 12 E I L 3 0 6 E I L 2 − 12 E I L 3 0 6 E I L 2 0 A E L 0 0 − A E L 0 6 E I L 2 0 4 E I L − 6 E I L 2 0 2 E I L − 12 E I L 3 0 − 6 E I L 2 12 E I L 3 0 − 6 E I L 2 0 − A E L 0 0 A E L 0 6 E I L 2 0 2 E I L − 6 E I L 2 0 4 E I L ) For member 1, A = 10 in 2 , E = ( 29 × 10 3 ) ksi , I = 300 in 4 , L = 10 ft . Calculate the terms in the stiffness matrix. A E L = ( 10 in 2 ) ( 29 × 10 3 ksi ) ( 10 × 12 ) in = 2416.67 kips / in 6 E I L 2 = 6 × ( 29 × 10 3 ksi ) ( 300 in 4 ) ( 10 × 12 ) 2 in = 3625 kips 12 E I L 3 = 12 ( 29 × 10 3 ksi ) ( 300 in 4 ) ( 10 × 12 ) 3 in 3 = 60.42 kips / in 4 E I L = 4 ( 29 × 10 3 ksi ) ( 300 in 4 ) ( 10 × 12 ) in = 290000 kip-in 2 E I L = 2 ( 29 × 10 3 ksi ) ( 300 in 4 ) ( 10 × 12 ) in = 145000 kip-in Substitute 2416.67 kips / in for A E L , 3625 kips for 6 E I L 2 , 60.42 kips / in for 12 E I L 3 , 290000 kip-in for 4 E I L , 145000 kip-in for 2 E I L in the stiffness matrix. Thus the stiffness matrix of member 1 is as follows. k 1 = ( 60.42 0 3625 − 60.42 0 3625 0 2416.67 0 0 − 2416.67 0 3625 0 290000 − 3625 0 145000 − 60.42 0 − 3625 60.42 0 − 3625 0 − 2416.67 0 0 2416.67 0 3625 0 145000 − 3625 0 290000 ) Write the expression to calculate the value ofxcoordinate of member 2. Substitute 20 ft for x F , 0 ft for x N and 20 ft for L in Equation (I). λ x = 20 ft − 0 ft 20 ft = 1 Write the expression to calculate the value ofycoordinate of member 2. Substitute 10 ft for y F , 10 ft for y N and 20 ft for L in Equation (II). λ y = 10 ft − 10 ft 20 ft = 0 Write the stiffness matrix of member 2. k 2 = ( A E L 0 0 − A E L 0 0 0 12 E I L 3 6 E I L 2 0 − 12 E I L 3 6 E I L 2 0 6 E I L 2 4 E I L 0 − 6 E I L 2 2 E I L − A E L 0 0 A E L 0 0 0 − 12 E I L 3 − 6 E I L 2 0 12 E I L 3 − 6 E I L 2 0 6 E I L 2 2 E I L 0 − 6 E I L 2 4 E I L ) For member 2, A = 10 in 2 , E = ( 29 × 10 3 ) ksi , I = 300 in 4 , L = 20 ft . Calculate the terms in the stiffness matrix. A E L = ( 10 in 2 ) ( 29 × 10 3 ksi ) ( 20 × 12 ) in = 1208.33 kips / in 6 E I L 2 = 6 × ( 29 × 10 3 ksi ) ( 300 in 4 ) ( 20 × 12 ) 2 in = 906.25 kips 12 E I L 3 = 12 ( 29 × 10 3 ksi ) ( 300 in 4 ) ( 20 × 12 ) 3 in 3 = 7

Structural Analysis, Student Value Edition Plus Mastering Engineering With Pearson Etext -- Access Card Package (10th Edition)

10th Edition

ISBN: 9780134702216

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Concept explainers

Load on Structures

Civil engineers primarily deal with beams in their day-to-day applications. A beam is a structural member that resists shear loadings. There are various types of beams such as cantilever beam, simply supported beam, and over the hanging beam. All these b…

Question

Chapter 16, Problem 16.15P

To determine

The support reactions of the structure.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 16, Problem 16.14P

Chapter 16, Problem 16.16P

Students have asked these similar questions

I need detailed help solving this exercise from homework of Engineering Mathematics II.I do not really understand how to do, please do it step by step, not that long but clear. Thank you!P.S.: Please do not use AI, thanks!

Chapter 16 Solutions

Structural Analysis, Student Value Edition Plus Mastering Engineering With Pearson Etext -- Access Card Package (10th Edition)

Ch. 16 - Prob. 16.1P Ch. 16 - Prob. 16.2P Ch. 16 - Prob. 16.3P Ch. 16 - Prob. 16.4P Ch. 16 - Prob. 16.5P Ch. 16 - Prob. 16.6P Ch. 16 - Prob. 16.7P Ch. 16 - Prob. 16.8P Ch. 16 - Prob. 16.9P Ch. 16 - Prob. 16.10P

Ch. 16 - Prob. 16.11P Ch. 16 - Prob. 16.12P Ch. 16 - Prob. 16.13P Ch. 16 - Prob. 16.14P Ch. 16 - Prob. 16.15P Ch. 16 - Prob. 16.16P Ch. 16 - Prob. 16.17P Ch. 16 - Prob. 16.18P

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.

Similar questions

SEE MORE QUESTIONS

Recommended textbooks for you

Structural Analysis
Civil Engineering
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:Cengage,
Structural Analysis (10th Edition)
Civil Engineering
ISBN:9780134610672
Author:Russell C. Hibbeler
Publisher:PEARSON
Principles of Foundation Engineering (MindTap Cou...
Civil Engineering
ISBN:9781337705028
Author:Braja M. Das, Nagaratnam Sivakugan
Publisher:Cengage Learning
Fundamentals of Structural Analysis
Civil Engineering
ISBN:9780073398006
Author:Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning
Publisher:McGraw-Hill Education
Sustainable Energy
Civil Engineering
ISBN:9781337551663
Author:DUNLAP, Richard A.
Publisher:Cengage,
Traffic and Highway Engineering
Civil Engineering
ISBN:9781305156241
Author:Garber, Nicholas J.
Publisher:Cengage Learning