Vigas - ACI Example - Continous Beam

FLEXÃO SIMPLES

Neste exemplo, será dimensionada a armadura longitudinal e transversal de uma viga submetida a Flexão Simples seguindo modelo do ACI-SP17-14 - Beam Example 1 - Continous Interior Beam:


eb929f81daf40cefcbf335bf7db4af71.png



Given:

Load

Service additional dead load D = 15 psf

Service live load L = 65 psf


Material properties

fy = 60000 psi

fck = 5000 psi

Ec = 4030000 psi

Es = 29000000 psi

Span length: 36 ft

Beam width: 18 in.

Beam Depth: 30 in

Column dimensions: 24 in. x 24 in

Tributary width: 14 ft

Slab thickness: 7 in.


Self-weight

Beam: wb = 0.56 kip/ft

Slab: ws = 1.1 kip/ft


Shear diagram:


ACI


8c6d9fc977d531e500eb89d7b917b5e4.png


Moment diagram:


ACI

da9b15ecfaf00fce3d271b91ce581ef6.png


Required Reinforcement:


1.

84685fd3cf7db7fb454d725c7e42b097.png

b023249920cb5edd6a542939476718f9.png


2.

5778206cc9fc86baa322f9c75d06a3ea.png

7b236bbace74ec0e3bfaedde05793913.png


3.

5969405b0cdad6b3656be8660c748807.png

aeff2491dde7538cb2eef16770cf9c3f.png


4.

3ecbc0c8be444785de11d80582318ac6.png

ccf7d5e2a94f8879e159626f8efadcb7.png

5.

757f41fe89a1b04bf720f7f7ecfe3bdb.png

0cbaf76ecd7b795b89a49508d9c195f0.png

Tension Controlled! → ø 0,90 OK!

As,min (ACI 318-19 – 9.6.1.2)

521d928e46422a1a38ed9f235a318ac9.png

b717df68a29850e56ed190dd17bd2de9.png

68a0447134fecbadd153ad29da9f382f.png

Shear:


7bb367397cb7c88332f5a35676605d1d.png 8f7f445e0ea052aaa7c2dce63eb7896c.png b5814122497bdf8d134ad80174465a80.png

e704730270fb24cdec958eee0f11fb8d.png

aa092ba20fe90ba03b3d4b4d49c21dfb.png

4f04751db19bc5a1e3a27180433cca8d.png

Vs ≤ Vs,lim OK!

    Ø0,75 → øVn ≥ Vu → 63,50 ≥ 63,50 → OK!!

    Shear Reinforcement:


    d469bfd6460185519229e2e0df97f6a5.png


    f9b1871d2f759f26e5f26e73c15d8b49.png

    7db4708d8881091a1f44b2275c418446.png7db4708d8881091a1f44b2275c418446.png

    1a5b39d95181673f2a90c0c8c79359af.png1a5b39d95181673f2a90c0c8c79359af.png0,009 ≤ 0,016 → 4ab3c11a642ded3c352fedae41c99a35.png!!


    Espaçamento:

    06d1e07ea784adbc04a385a9e9430ab3.png

    137f3665b6abc22807d973713b96543f.png

    8b4c578af9c587a34a740e9beac68d2c.png8b4c578af9c587a34a740e9beac68d2c.png→ #3 c/ 12 in → 0,018 in²/in


    øVn (75,62 kip) ≥ Vu (63,50 kip)



    Final Design using #7 and #3 stirrups in TQS:


    8737482300f7180f23d8b2a99deb3860.png


    60c1db4cf64df1e1fbb56287b7cb0feb.png



    Vigas - Flexão Simples - Viga Continua 6
    Pilar - Flexão Composta Obliqua 1