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G-02 (Shear Design of Concrete Beams)

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Objective

To verify the shear design the rectangular and circular concrete beams (columns)

 

Problem Description

The following concrete beams (columns) are to be designed according to ACI 318-02 code.  The concrete cover to stirrup is 1.5 inches.

Beam

Dimension (in)

fc (ksi)

fys (ksi)

Longitudinal Bar Size

Stirrup Size

Pu (kips)

Vu (kips)

1

Rectangular

12 x 16

4

40

#6

#3

160

(compression)

20

2

Circular

Diameter 14

4

40

#6

#3

10

(compression)

30

 

 

Finite Element Model

2 beam elements with appropriate material and design criteria assigned

Model type: 2D Frame

 

Results

The design result of the first beam element is compared with the [Ref 1].  The second beam element is a round column subjected to compression and is designed as follows:

G-02 (Shear Design of Concrete Beams)1 lbs

G-02 (Shear Design of Concrete Beams)2 kips

G-02 (Shear Design of Concrete Beams)3 in.

Note: For circular section, bw = 2R, d = 0.8(2R) are used to compute Vc and Vs, according to ACI 318-02 11.3.3 and 11.5.7.3

The following table showsG-02 (Shear Design of Concrete Beams)4and required stirrup spacing for the two beam elements.  The program does not round the required stirrup spacing to the practical dimension.

 

Beam

ENERCALC 3D

Reference / Theoretical

G-02 (Shear Design of Concrete Beams)5(kips)

s (in)

G-02 (Shear Design of Concrete Beams)6(kips)

s (in)

1

22.175

6.88

22.2

6.9

2

15.359

5.05

15.358

5.05

 

Comments

The results given by ENERCALC 3D are very close to the reference and theoretical values.  The model consists of multiple simply supported beams.  Nodal moments of same signs are applied to nodes to achieve uniform shears in each member.

 

Reference

[1]. “Notes on ACI 318-02 Building Code Requirements for Structural Concrete”, 8th Edition, pp. 12-19, Portland Cement Association, 2002