Homework Help is Here – Start Your Trial Now!
Engineering
Civil Engineering
Stability Classify each of the following systems as stable or unstable. If unstable, indicate which "degrees of freedom" are unrestrained. B 50 mm- 1m k 3 m B 3 m 600 N -50 mm 2m 500 N m A -3 m [assume the cables are effective in tension or compression] D 2m 10 mm 3 m [A, B, and C are smooth journal supports]

Stability Classify each of the following systems as stable or unstable. If unstable, indicate which "degrees of freedom" are unrestrained. B 50 mm- 1m k 3 m B 3 m 600 N -50 mm 2m 500 N m A -3 m [assume the cables are effective in tension or compression] D 2m 10 mm 3 m [A, B, and C are smooth journal supports]

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
**Stability** Classify each of the following systems as stable or unstable. If unstable, indicate which "degrees of freedom" are unrestrained. --- ### Diagram 1: **Description:** - This system shows a horizontal beam with point supports at both ends marked as A and C. - The beam length is divided into two segments: 50 mm to point B and another 50 mm to point C. - There are springs (denoted by k) under points A and B. - A vertical force F is applied at point C. - There’s also an additional 10 mm gap beneath point C. **Stability Analysis:** - The beam is supported at both ends with point B acting as an intermediary with spring support, suggesting potential stability depending on the stiffness of the springs (k). - Consideration of the force F and the 10 mm gap at point C is crucial for determining stability. --- ### Diagram 2: **Description:** - A three-dimensional cable structure is shown with points A, B, C, D, and E. - Points C and D are connected by cables to a central point A on the z-axis, each 2 m away. - The base is formed of points B and E on the x-y plane, each 3 m apart, with a 600 N force at point E. **Cables:** - Assume the cables are effective in tension or compression. **Stability Analysis:** - Determine stability based on the tension or compression forces in the cables and their ability to counterbalance the applied force and maintain equilibrium. --- ### Diagram 3: **Description:** - This diagram features a bent beam supported at three points (A, B, C). - Point A is at a height of 1 m along the z-axis. - Point B is positioned at a tangent with 3 m on the x-axis and 1 m along the y-axis. - Point C is further 2 m along the y-axis. - A 500 N vertical force is applied downward at point B. **Supports:** - Points A, B, and C are smooth journal supports. **Stability Analysis:** - Evaluate the system's balance considering the applied force and the smoothness of the journal supports, which allow rotation but prevent translation. --- For each diagram, analyze mechanical conditions, such as force application and structural constraints, to determine whether the system is in a state of stable equilibrium
Transcribed Image Text:**Stability** Classify each of the following systems as stable or unstable. If unstable, indicate which "degrees of freedom" are unrestrained. --- ### Diagram 1: **Description:** - This system shows a horizontal beam with point supports at both ends marked as A and C. - The beam length is divided into two segments: 50 mm to point B and another 50 mm to point C. - There are springs (denoted by k) under points A and B. - A vertical force F is applied at point C. - There’s also an additional 10 mm gap beneath point C. **Stability Analysis:** - The beam is supported at both ends with point B acting as an intermediary with spring support, suggesting potential stability depending on the stiffness of the springs (k). - Consideration of the force F and the 10 mm gap at point C is crucial for determining stability. --- ### Diagram 2: **Description:** - A three-dimensional cable structure is shown with points A, B, C, D, and E. - Points C and D are connected by cables to a central point A on the z-axis, each 2 m away. - The base is formed of points B and E on the x-y plane, each 3 m apart, with a 600 N force at point E. **Cables:** - Assume the cables are effective in tension or compression. **Stability Analysis:** - Determine stability based on the tension or compression forces in the cables and their ability to counterbalance the applied force and maintain equilibrium. --- ### Diagram 3: **Description:** - This diagram features a bent beam supported at three points (A, B, C). - Point A is at a height of 1 m along the z-axis. - Point B is positioned at a tangent with 3 m on the x-axis and 1 m along the y-axis. - Point C is further 2 m along the y-axis. - A 500 N vertical force is applied downward at point B. **Supports:** - Points A, B, and C are smooth journal supports. **Stability Analysis:** - Evaluate the system's balance considering the applied force and the smoothness of the journal supports, which allow rotation but prevent translation. --- For each diagram, analyze mechanical conditions, such as force application and structural constraints, to determine whether the system is in a state of stable equilibrium
Expert Solution
Step 1 Introduction

A structure can be stable if the reactions at the supports are not concurrent or not passing from a single point. Degree of freedom is defined as the number of allowable translational or rotational motion of a structure. 

 

steps

Step by step

Solved in 2 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Compression members
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.
Recommended textbooks for you
Structural Analysis
Structural Analysis
Civil Engineering
ISBN:
9781337630931
Author:
KASSIMALI, Aslam.
Publisher:
Cengage,
Structural Analysis (10th Edition)
Structural Analysis (10th Edition)
Civil Engineering
ISBN:
9780134610672
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Principles of Foundation Engineering (MindTap Cou…
Principles of Foundation Engineering (MindTap Cou…
Civil Engineering
ISBN:
9781337705028
Author:
Braja M. Das, Nagaratnam Sivakugan
Publisher:
Cengage Learning
Fundamentals of Structural Analysis
Fundamentals of Structural Analysis
Civil Engineering
ISBN:
9780073398006
Author:
Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning
Publisher:
McGraw-Hill Education
Sustainable Energy
Sustainable Energy
Civil Engineering
ISBN:
9781337551663
Author:
DUNLAP, Richard A.
Publisher:
Cengage,
Traffic and Highway Engineering
Traffic and Highway Engineering
Civil Engineering
ISBN:
9781305156241
Author:
Garber, Nicholas J.
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS