A series of cantilever beams are extending off reinforced concrete columns in a building. Thecantilevers are spaced at 12 feet intervals and each has a span of 10 feet (see figure). Thisbalcony system supports a public area with glass partitions and walls. And as such, thedeflections and vibrations must be controlled to avoid glass damage. Each beam has a 14x20inch cross section. The reinforcement is made up of 2#9 at the top and 2#5 at the bottom. Thestirrups are #3 barsLoads: Live load- 100 psf and superimposed dead load-9 psf.Criteria: fc 4,000 psi and fy - 60,000 psi(a) Compute the instantaneous and long-term deflections and decide whether the deflectionis acceptable. The instantaneous (live load) deflection is limited to L/400 and the totalinstantaneous plus long-term deflection is limited to L/360(b) Determine whether the ACI crack control requirements are met. Note: You will need tocompute the service load stress fs at the tension steel (which is located at the top). Forthis purpose, use the moment of inertial of the cracked section from Part (a)(c) Estimate an approximate value for the fundamental period of vibration of a typicalcantilever beam. The applied force frequency is estimated to be about 3.5 Hz. Determineif the beam sections are acceptable to avoid critical vibrations.L = 10 feet

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Asked Apr 8, 2019
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A series of cantilever beams are extending off reinforced concrete columns in a building. The
cantilevers are spaced at 12 feet intervals and each has a span of 10 feet (see figure). This
balcony system supports a public area with glass partitions and walls. And as such, the
deflections and vibrations must be controlled to avoid glass damage. Each beam has a 14x20
inch cross section. The reinforcement is made up of 2#9 at the top and 2#5 at the bottom. The
stirrups are #3 bars
Loads: Live load- 100 psf and superimposed dead load-9 psf.
Criteria: fc 4,000 psi and fy - 60,000 psi
(a) Compute the instantaneous and long-term deflections and decide whether the deflection
is acceptable. The instantaneous (live load) deflection is limited to L/400 and the total
instantaneous plus long-term deflection is limited to L/360
(b) Determine whether the ACI crack control requirements are met. Note: You will need to
compute the service load stress fs at the tension steel (which is located at the top). For
this purpose, use the moment of inertial of the cracked section from Part (a)
(c) Estimate an approximate value for the fundamental period of vibration of a typical
cantilever beam. The applied force frequency is estimated to be about 3.5 Hz. Determine
if the beam sections are acceptable to avoid critical vibrations.
L = 10 feet
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A series of cantilever beams are extending off reinforced concrete columns in a building. The cantilevers are spaced at 12 feet intervals and each has a span of 10 feet (see figure). This balcony system supports a public area with glass partitions and walls. And as such, the deflections and vibrations must be controlled to avoid glass damage. Each beam has a 14x20 inch cross section. The reinforcement is made up of 2#9 at the top and 2#5 at the bottom. The stirrups are #3 bars Loads: Live load- 100 psf and superimposed dead load-9 psf. Criteria: fc 4,000 psi and fy - 60,000 psi (a) Compute the instantaneous and long-term deflections and decide whether the deflection is acceptable. The instantaneous (live load) deflection is limited to L/400 and the total instantaneous plus long-term deflection is limited to L/360 (b) Determine whether the ACI crack control requirements are met. Note: You will need to compute the service load stress fs at the tension steel (which is located at the top). For this purpose, use the moment of inertial of the cracked section from Part (a) (c) Estimate an approximate value for the fundamental period of vibration of a typical cantilever beam. The applied force frequency is estimated to be about 3.5 Hz. Determine if the beam sections are acceptable to avoid critical vibrations. L = 10 feet

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Step 1

Determine the modular ratio.

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Step 2

Determine the constant using the relation.

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Step 3

Determine the kd using t...

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