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A beam is to be designed for loads causing a maximum factored shear of 60.0 kips, using concrete with [tex]f'_{c} = 5000 \text{ psi}[/tex]. Proceed on the basis that the concrete dimensions will be determined by diagonal tension.

Select the appropriate width and effective depth:

(a) For a beam in which no web reinforcement is to be used.

(b) For a beam in which only the minimum web reinforcement is provided, as given by Eq. (5.13).

(c) For a beam in which web reinforcement provides shear strength [tex]V_s = 2 V_c[/tex].

Follow the ACI Code requirements and let [tex]d = 2b[/tex] in each case. Assume that [tex]p_w = 0.012[/tex].

Given:
[tex]V_u = 60 \text{ kip}[/tex]
[tex]f'_{c} = 5000 \text{ psi}[/tex]
[tex]f_y = 60000 \text{ psi}[/tex]
[tex]p_w = 0.012[/tex]

Answer :

Final answer:

When designing a beam for different scenarios of web reinforcement, the appropriate width and effective depth can be determined by following the ACI Code requirements. In the case of no web reinforcement, the width and effective depth can be calculated based on the ACI Code guidelines for diagonal tension. For the minimum web reinforcement scenario, the ACI Code provides an equation (5.13) to determine the required area of web reinforcement. Finally, for web reinforcement providing shear strength Vs = 2 Vc, the ACI Code provides guidelines to calculate the required area of web reinforcement. By considering the given parameters and following the ACI Code requirements, the appropriate width and effective depth can be determined.

Explanation:

When designing a beam, it is important to consider the maximum factored shear and the type of reinforcement used. In this case, we are given the maximum factored shear of 60.0 kips and the concrete strength of fe = 5000 psi. The ACI Code provides guidelines for designing beams with different scenarios of web reinforcement.

To determine the appropriate width and effective depth for each scenario, we need to follow the ACI Code requirements. Let's consider each scenario:

  1. No web reinforcement: In this scenario, the width and effective depth can be determined based on the ACI Code requirements for diagonal tension. Since no web reinforcement is used, the shear strength of the beam will be provided solely by the concrete. The ACI Code provides equations and tables to calculate the required width and effective depth based on the maximum factored shear and the concrete strength.
  2. Minimum web reinforcement: In this scenario, the ACI Code specifies the minimum web reinforcement required. The equation (5.13) in the ACI Code provides the minimum area of web reinforcement based on the maximum factored shear, the concrete strength, and other parameters. By using this equation and the given values, we can calculate the required width and effective depth.
  3. Web reinforcement providing shear strength Vs = 2 Vc: In this scenario, the web reinforcement is designed to provide shear strength equal to twice the shear strength of the concrete. The ACI Code provides guidelines for determining the required area of web reinforcement to achieve this shear strength. By following these guidelines and considering the given values, we can calculate the required width and effective depth.

By following the ACI Code requirements and considering the given parameters, we can determine the appropriate width and effective depth for each scenario.

Learn more about designing a beam for different scenarios of web reinforcement here:

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