Structural Analysis
Structural Analysis
6th Edition
ISBN: 9781337630931
Author: KASSIMALI, Aslam.
Publisher: Cengage,
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A singly reinforced beam will be provided with the reinforcing bars corresponding to 90% of the maximum reinforcement ratio specified in the ACI Code for a tension-controlled (i.e., underreinforced) design.

 

The materials used have the following properties:

??′ = 4000 psi, ?? = 80000 psi, ?? = 0.002

 

  • Estimated the steel area ??
  • Sketch the stress and strain distributions in the beam cross-section. The diagrams should show the location of the neutral axis and the compressive/tensile forces acting on the cross-section
  • Calculate the nominal moment strength ?? and the design moment strength ??? [in kips-ft] Briefly explain how the formula of moment calculation can be derived
  • Assume that the design moment strength is less than the factored moment. Hence, compression rebars will be added. The effective depth is ?′ = 1.5′′. Determine the steel area of compression rebars ??′ so that the compression bars yield at the flexural failure
  • Based on ??′ determined in part d calculate the nominal moment strength ?? and the design moment strength ??? [in kips-ft]. Also briefly explain how the formula of moment calculation can be deriven. 
# Beam Design with Reinforcement Bars ## Overview A singly reinforced beam will be provided with reinforcing bars corresponding to 90% of the maximum reinforcement ratio as specified in the ACI Code for a tension-controlled (underreinforced) design. ### Material Properties - **Concrete compressive strength** \( f'_{c} \): 4000 psi - **Yield strength of steel** \( f_{y} \): 80000 psi - **Strain at yield** \( \varepsilon_{y} \): 0.002 ## Task Breakdown ### a. Estimating the Steel Area (\( A_{s} \)) Calculate the estimated steel area \( A_{s} \) without selecting specific rebars. ### b. Stress and Strain Distribution Create diagrams to show stress and strain distributions in the beam cross-section. Include: - Location of the neutral axis - Compressive and tensile forces acting on the cross-section ### c. Moment Calculation Determine: - Nominal moment strength \( M_{n} \) - Design moment strength \( \phi M_{n} \) (in kips-ft) Provide an explanation of how the formula for moment calculation can be derived. ### d. Additional Compression Rebars Assume the design moment strength is less than the factored moment: - Add compression rebars - Effective depth \( d' = 1.5'' \) - Compute steel area of compression rebars \( A'_{s} \) so compression bars yield during flexural failure ### e. Reevaluating Moment Strength Using \( A'_{s} \) from part d, calculate revised: - Nominal moment strength \( M_{n} \) - Design moment strength \( \phi M_{n} \) (in kips-ft) Include a brief explanation of the formula used in moment calculation. ### Diagram Description - The beam is illustrated with a height \( h = 20'' \) and width \( b = 12'' \). - Effective depth \( d = 17.5'' \) is shown. This breakdown guides the design and analysis of a reinforced concrete beam, focusing on stress and strength considerations.
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Transcribed Image Text:# Beam Design with Reinforcement Bars ## Overview A singly reinforced beam will be provided with reinforcing bars corresponding to 90% of the maximum reinforcement ratio as specified in the ACI Code for a tension-controlled (underreinforced) design. ### Material Properties - **Concrete compressive strength** \( f'_{c} \): 4000 psi - **Yield strength of steel** \( f_{y} \): 80000 psi - **Strain at yield** \( \varepsilon_{y} \): 0.002 ## Task Breakdown ### a. Estimating the Steel Area (\( A_{s} \)) Calculate the estimated steel area \( A_{s} \) without selecting specific rebars. ### b. Stress and Strain Distribution Create diagrams to show stress and strain distributions in the beam cross-section. Include: - Location of the neutral axis - Compressive and tensile forces acting on the cross-section ### c. Moment Calculation Determine: - Nominal moment strength \( M_{n} \) - Design moment strength \( \phi M_{n} \) (in kips-ft) Provide an explanation of how the formula for moment calculation can be derived. ### d. Additional Compression Rebars Assume the design moment strength is less than the factored moment: - Add compression rebars - Effective depth \( d' = 1.5'' \) - Compute steel area of compression rebars \( A'_{s} \) so compression bars yield during flexural failure ### e. Reevaluating Moment Strength Using \( A'_{s} \) from part d, calculate revised: - Nominal moment strength \( M_{n} \) - Design moment strength \( \phi M_{n} \) (in kips-ft) Include a brief explanation of the formula used in moment calculation. ### Diagram Description - The beam is illustrated with a height \( h = 20'' \) and width \( b = 12'' \). - Effective depth \( d = 17.5'' \) is shown. This breakdown guides the design and analysis of a reinforced concrete beam, focusing on stress and strength considerations.
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