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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