### Educational Website Content**Title:** Calculating the Practical Moment Strength for a Precast Inverted T-Girder**Objective:** Learn how to compute the practical moment strength, denoted as \( \phi M_n \), for a simply supported precast inverted T-girder, using specified concrete strength and steel yield strength.**Problem Statement:**Calculate the practical moment strength \( \phi M_n \) for the simply supported precast inverted T-girder depicted. The following properties are provided:- Concrete compressive strength, \( f'_c = 3000 \) psi- Yield strength of steel, \( f_y = 60,000 \) psi**Diagram Description:**The diagram illustrates the cross-sectional dimensions and the arrangement of reinforcement for a precast inverted T-girder:- **T-Girder Dimensions:** - Total height: 16 inches for the web plus 6 inches for the flange. - Flange width: 16 inches. - Web thickness: 10 inches.- **Reinforcement Details:** - Top reinforcement consists of 2 #7 bars, located at the center of the web. - Bottom reinforcement consists of 4 #9 bars, uniformly distributed in the flange.- **Concrete Cover:** - A concrete cover of \( 2 \frac{1}{2} \) inches is provided from the top and bottom surfaces to the center of the respective reinforcement bars. **Instructions:**- Use the provided material strengths and dimensions to compute \( \phi M_n \) applying relevant structural analysis methods and code specifications.- Consider the position of reinforcement and its role in developing the moment capacity of the girder.This exercise will enhance your understanding of structural design and analysis of precast concrete members.

Shear force is defined as the algebraic sum of the vertical forces at any segment of a beam to the right or left of the section. It is abbreviated as S.F. The term "bending moment" refers to the algebraic total of all the moments generated by forces operating to the right or left of the section. The slope of the moment diagram at a given place corresponds to the shear intensity there. Any two points difference in shear is equal to the region under their respective loading curves. The area under the shear diagram between any two locations is equal to the moment difference between them. Given- d=19.5 inbw=10 inbf=16 ind'=2.5 inf'c=3000 psify=60000 psiThe probable moment strength is the theoretically highest flexural strength that can be estimated for a member's critical section when it is bent in a certain direction, with or without an axial load. By using the equilibrium of forces in the beam's segments, the nominal moment capacity of the beam is determined. On the nominal moment capacity under fire, the benefit of circulating cool water and covering concrete is evaluated. Approximate diameter to outside deformation for bar size #9 is 114and for bar size #7 is 1. As=4-#9=4×1=4 in2A's=2-#7=2×0.6=1.2 in2Neutral axis lies in web portion-C=T0.85×f'c×bw×a+fy×A's=fy×As0.85×3×10×a+60×1.2=60×4a=6.6 4 inPractical moment strength-∅Mn=∅×fy×A's×d-a2∅Mn=0.9×60×4×19.5-6.62∅Mn=3501. 50 k-inHence the practical moment strength is 3501 k-in.

Answered: Compute the practical moment strength…

Engineering

Civil Engineering

Compute the practical moment strength M,, for the simply supported precast inverted T-girder shown. Use f' = 3000 psi and fy = 60,000 psi. 16" 6" ↓ 21/1/2" 2-1/2" IN 10"- ---2-#7 16" 4-#9

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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Concept explainers

Applications of Concrete Framing Systems

A concrete frame is a structure formed by the interconnection of beams and columns to form a structural network. In simple terms, it is the basic skeletal structure of a building or any construction. The concrete framing structure is built on a concrete foundation that forms the base of the entire structure. The concrete frame system is built to support floors, roofs, walls, beams, rafters, joists, etc.

Question

### Educational Website Content

**Title:** Calculating the Practical Moment Strength for a Precast Inverted T-Girder

**Objective:** Learn how to compute the practical moment strength, denoted as \( \phi M_n \), for a simply supported precast inverted T-girder, using specified concrete strength and steel yield strength.

**Problem Statement:**

Calculate the practical moment strength \( \phi M_n \) for the simply supported precast inverted T-girder depicted. The following properties are provided:

- Concrete compressive strength, \( f'_c = 3000 \) psi
- Yield strength of steel, \( f_y = 60,000 \) psi

**Diagram Description:**

The diagram illustrates the cross-sectional dimensions and the arrangement of reinforcement for a precast inverted T-girder:

- **T-Girder Dimensions:**
- Total height: 16 inches for the web plus 6 inches for the flange.
- Flange width: 16 inches.
- Web thickness: 10 inches.

- **Reinforcement Details:**
- Top reinforcement consists of 2 #7 bars, located at the center of the web.
- Bottom reinforcement consists of 4 #9 bars, uniformly distributed in the flange.

- **Concrete Cover:**
- A concrete cover of \( 2 \frac{1}{2} \) inches is provided from the top and bottom surfaces to the center of the respective reinforcement bars.

**Instructions:**

- Use the provided material strengths and dimensions to compute \( \phi M_n \) applying relevant structural analysis methods and code specifications.
- Consider the position of reinforcement and its role in developing the moment capacity of the girder.

This exercise will enhance your understanding of structural design and analysis of precast concrete members.

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