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Calculate the instantaneous dead load deflection and the instantaneous dead-live load deflection for a simply supported beam with a span of 28 ft. The beam supports a service dead load of 1.5 kips/ft (including self-weight) and a service live load of 1.5 kips/ft.

Assume the moment of inertia of the uncracked transformed section is the same as the moment of inertia of the gross section, [tex]I_g = 18432 \, \text{in}^4[/tex]. Given values are:

- [tex]M_{er} = 60.72 \, \text{kip-ft}[/tex]
- [tex]I_{cr} = 8646 \, \text{in}^4[/tex]
- Effective depth [tex]d = 20.5''[/tex]
- Concrete compressive strength [tex]f'_c = 4000 \, \text{psi}[/tex]
- Steel yield strength [tex]f_y = 60000 \, \text{psi}[/tex]

Proceed with the calculations.

Answer :

To calculate the instantaneous dead load deflection and the instantaneous dead-live load deflection for a simply supported beam, we need to follow these steps:

Multiply the service dead load of 1.5 kips/ft by the span of 28 ft to get the total dead load.
Total Dead Load = 1.5 kips/ft * 28 ft = 42 kips
Multiply the service live load of 1.5 kips/ft by the span of 28 ft to get the total live load.
Total Live Load = 1.5 kips/ft * 28 ft = 42 kips
Add the total dead load and total live load to get the total load.
Total Load = Total Dead Load + Total Live Load = 42 kips + 42 kips = 84 kips
Use the equation for deflection of a simply supported beam:
δ_dead = (5 * Total Dead Load * span^4) / (384 * E * ig * ler^3)

Where:
δ_dead = instantaneous dead load deflection
Total Dead Load = total dead load on the beam
span = span of the beam
E = modulus of elasticity (fe' in this case)
ig = moment of inertia of the gross section
ler = effective length (8646 in)
^3 = raised to the power of 3
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