Homework Help is Here – Start Your Trial Now!
Engineering
Civil Engineering
A beam is subjected to equal bending moments of M₂ = 3300 N-m. The cross-sectional dimensions are b= 190 mm, c = 26 mm, d= 75 mm, and t = 5 mm. Determine: (a) the centroid location, the moment of inertia about the z axis, and the controlling section modulus about the z axis. (b) the bending stress at point H. Tensile stress is positive, while compressive stress is negative. (c) the bending stress at point K. Tensile stress is positive, while compressive stress is negative. (d) the maximum bending stress produced in the cross section. Tensile stress is positive, while compressive stress is negative. M₂ N M₂ (typ) H K d

A beam is subjected to equal bending moments of M₂ = 3300 N-m. The cross-sectional dimensions are b= 190 mm, c = 26 mm, d= 75 mm, and t = 5 mm. Determine: (a) the centroid location, the moment of inertia about the z axis, and the controlling section modulus about the z axis. (b) the bending stress at point H. Tensile stress is positive, while compressive stress is negative. (c) the bending stress at point K. Tensile stress is positive, while compressive stress is negative. (d) the maximum bending stress produced in the cross section. Tensile stress is positive, while compressive stress is negative. M₂ N M₂ (typ) H K d

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
### Problem Description A beam is subjected to equal bending moments of \( M_z = 3300 \, \text{N}\cdot\text{m} \). The cross-sectional dimensions are given as follows: - \( b = 190 \, \text{mm} \) - \( c = 26 \, \text{mm} \) - \( d = 75 \, \text{mm} \) - \( t = 5 \, \text{mm} \) **Required:** Determine: (a) The centroid location, the moment of inertia about the z-axis, and the controlling section modulus about the z-axis. (b) The bending stress at point \( H \). Note that tensile stress is considered positive, while compressive stress is negative. (c) The bending stress at point \( K \). Again, tensile stress is positive, and compressive stress is negative. (d) The maximum bending stress produced in the cross section. Tensile stress is positive, while compressive stress is negative. ### Diagram Explanation The illustration provides two views of the beam: - **3D View:** - The diagram shows the beam with the bending moments \( M_z \) applied at both ends, which are indicated by curved arrows around the beam's z-axis. - **Cross-sectional View:** - The L-shaped cross-section is detailed with dimensions labeled: - \( b \), the width of the base, is 190 mm. - \( c \), the height of the upper flange, is 26 mm. - \( d \), the overall height including the web, is 75 mm. - Points \( H \) and \( K \) are marked on the cross-section. - \( t \) is the thickness, noted as type (typical) for various portions of the cross-section. The y and z-axes are drawn to aid in identifying dimensions relevant to the calculation of the centroids, moments of inertia, and stresses. The section moduli are evaluated about the z-axis.
Transcribed Image Text:### Problem Description A beam is subjected to equal bending moments of \( M_z = 3300 \, \text{N}\cdot\text{m} \). The cross-sectional dimensions are given as follows: - \( b = 190 \, \text{mm} \) - \( c = 26 \, \text{mm} \) - \( d = 75 \, \text{mm} \) - \( t = 5 \, \text{mm} \) **Required:** Determine: (a) The centroid location, the moment of inertia about the z-axis, and the controlling section modulus about the z-axis. (b) The bending stress at point \( H \). Note that tensile stress is considered positive, while compressive stress is negative. (c) The bending stress at point \( K \). Again, tensile stress is positive, and compressive stress is negative. (d) The maximum bending stress produced in the cross section. Tensile stress is positive, while compressive stress is negative. ### Diagram Explanation The illustration provides two views of the beam: - **3D View:** - The diagram shows the beam with the bending moments \( M_z \) applied at both ends, which are indicated by curved arrows around the beam's z-axis. - **Cross-sectional View:** - The L-shaped cross-section is detailed with dimensions labeled: - \( b \), the width of the base, is 190 mm. - \( c \), the height of the upper flange, is 26 mm. - \( d \), the overall height including the web, is 75 mm. - Points \( H \) and \( K \) are marked on the cross-section. - \( t \) is the thickness, noted as type (typical) for various portions of the cross-section. The y and z-axes are drawn to aid in identifying dimensions relevant to the calculation of the centroids, moments of inertia, and stresses. The section moduli are evaluated about the z-axis.
Expert Solution
Step 1: Introduction and given data

The moment about the z-axis, Mz = 3300 Nm

b = 190mm, d = 75mm , c = 26mm, and t = 5mm


Tensile stress (+)ive and compressive (-)ive.

To determine

  • The centroid and the neutral axis about the z-axis and the controlling section modulus about the z-axis
  • The bending stress at point H
  • The bending stress at point K
  • The maximum bending stress in the cross-section.
steps

Step by step

Solved in 4 steps with 10 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Work and energy
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
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