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sections shown if f = 4000 psi and f, = 7.5àfe, normal-weight %3D concrete, à = 1.0. 24 in. 4 in. 15 in. 22 in. 1 #11 3 in. 6 in.

sections shown if f = 4000 psi and f, = 7.5àfe, normal-weight %3D concrete, à = 1.0. 24 in. 4 in. 15 in. 22 in. 1 #11 3 in. 6 in.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Just Problem 2.3

**Determining Cracking Moments in Concrete Sections** **Problem 2.3** Determine the cracking moments for the sections shown, given: - Concrete compressive strength, \( f'_c = 4000 \, \text{psi} \) - Modulus of rupture, \( f_r = 7.5 \lambda \sqrt{f'_c} \), for normal-weight concrete - \(\lambda = 1.0\) *Provided Answer:* 25.6 ft-k **Section Diagram Explanation:** 1. **Diagram of the T-beam section:** - The diagram is a T-shaped cross-section of a concrete beam. - The horizontal top flange of the T-section: - Width: 24 inches - Thickness: 4 inches - The vertical stem (web) of the T-section: - Total height from top to bottom: 22 inches - Height of the web only: 15 inches - Thickness of the web: 6 inches - Rebar: 1 bar, noted as #11, positioned 3 inches from the bottom of the web. **Dimensional Details:** - The top horizontal flange dimension is specified as 24 inches in width. - The overall height of the T-section is given as 22 inches. - The thickness of the top flange is 4 inches, and the thickness of the vertical stem is 6 inches. - The height of the vertical stem alone (without the flange) is 15 inches. - A rebar (denoted by a black dot and labeled "1 #11") is embedded 3 inches from the bottom of the vertical stem. These dimensions and strength parameters are crucial for calculating the cracking moment, which reflects the moment at which cracking initiates in the concrete section due to tensile stress.
Transcribed Image Text:**Determining Cracking Moments in Concrete Sections** **Problem 2.3** Determine the cracking moments for the sections shown, given: - Concrete compressive strength, \( f'_c = 4000 \, \text{psi} \) - Modulus of rupture, \( f_r = 7.5 \lambda \sqrt{f'_c} \), for normal-weight concrete - \(\lambda = 1.0\) *Provided Answer:* 25.6 ft-k **Section Diagram Explanation:** 1. **Diagram of the T-beam section:** - The diagram is a T-shaped cross-section of a concrete beam. - The horizontal top flange of the T-section: - Width: 24 inches - Thickness: 4 inches - The vertical stem (web) of the T-section: - Total height from top to bottom: 22 inches - Height of the web only: 15 inches - Thickness of the web: 6 inches - Rebar: 1 bar, noted as #11, positioned 3 inches from the bottom of the web. **Dimensional Details:** - The top horizontal flange dimension is specified as 24 inches in width. - The overall height of the T-section is given as 22 inches. - The thickness of the top flange is 4 inches, and the thickness of the vertical stem is 6 inches. - The height of the vertical stem alone (without the flange) is 15 inches. - A rebar (denoted by a black dot and labeled "1 #11") is embedded 3 inches from the bottom of the vertical stem. These dimensions and strength parameters are crucial for calculating the cracking moment, which reflects the moment at which cracking initiates in the concrete section due to tensile stress.
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