A square foundation of width B = 5ft is subjected to an applied load of 100 kips, find the change in stress 8ft below the bottom of the footing: e) 2:1 method f) M and N method g) Stress isobars h) Newmark Method

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
### Calculating Stress Changes Below a Foundation

**Problem Statement:**

A square foundation with a width \( B = 5 \) feet is subjected to an applied load of 100 kips. Find the change in stress 8 feet below the bottom of the footing using the following methods:

e) 2:1 method  
f) M and N method  
g) Stress isobars  
h) Newmark Method  

#### Explanation:

1. **2:1 Method:**
   - The 2:1 method is a simplistic approach to estimate the vertical stress distribution below a footing. The method assumes a uniform load distribution spreading out at a 2:1 slope from the base of the footing. The change in stress (\( \Delta \sigma \)) at a depth \( z \) below the footing can be calculated with the formula:
     \[
     \Delta \sigma = \frac{Q}{(B + z)^2}
     \]
     where \( Q \) is the applied load and \( B \) is the width of the footing.

2. **M and N Method:**
   - The M and N method is a more refined approach based on elasticity theory, which accounts for the footing shape and depth more accurately than the 2:1 method. The method involves using tables or charts that provide influence values (M and N) based on the geometry and depth.

3. **Stress Isobars:**
   - Stress isobars are contour lines representing constant stress values within a soil mass under a given load. They can be used to visualize how stress dissipates in the soil. These isobars are usually determined using theoretical formulas or numerical methods such as the Boussinesq equation.

4. **Newmark Method:**
   - The Newmark method uses a graphical technique with influence charts to determine the stress distribution under a loaded area. Influence charts represent the change in stress at various depths caused by a uniformly loaded area.

Each of these methods provides a different level of accuracy and application complexity. For educational purposes, understanding the assumptions and limitations of each method is crucial before applying them to real-world scenarios.
Transcribed Image Text:### Calculating Stress Changes Below a Foundation **Problem Statement:** A square foundation with a width \( B = 5 \) feet is subjected to an applied load of 100 kips. Find the change in stress 8 feet below the bottom of the footing using the following methods: e) 2:1 method f) M and N method g) Stress isobars h) Newmark Method #### Explanation: 1. **2:1 Method:** - The 2:1 method is a simplistic approach to estimate the vertical stress distribution below a footing. The method assumes a uniform load distribution spreading out at a 2:1 slope from the base of the footing. The change in stress (\( \Delta \sigma \)) at a depth \( z \) below the footing can be calculated with the formula: \[ \Delta \sigma = \frac{Q}{(B + z)^2} \] where \( Q \) is the applied load and \( B \) is the width of the footing. 2. **M and N Method:** - The M and N method is a more refined approach based on elasticity theory, which accounts for the footing shape and depth more accurately than the 2:1 method. The method involves using tables or charts that provide influence values (M and N) based on the geometry and depth. 3. **Stress Isobars:** - Stress isobars are contour lines representing constant stress values within a soil mass under a given load. They can be used to visualize how stress dissipates in the soil. These isobars are usually determined using theoretical formulas or numerical methods such as the Boussinesq equation. 4. **Newmark Method:** - The Newmark method uses a graphical technique with influence charts to determine the stress distribution under a loaded area. Influence charts represent the change in stress at various depths caused by a uniformly loaded area. Each of these methods provides a different level of accuracy and application complexity. For educational purposes, understanding the assumptions and limitations of each method is crucial before applying them to real-world scenarios.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 4 images

Blurred answer
Knowledge Booster
Foundation plan layout
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
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