# D. Design Capacity of Beams

Beams along the bearing capacity of beams through a long span of each cross section, beam cross section of the design include a component of the capacity of checking and regulating the provision of construction or other design requirements such as thickness reinforcement, reinforcement ratio, bar diameter.

## General Provisions

1. Flexural capacity is calculated according to the following fundamental assumptions:

1. section to maintain plane strain;
2. does not take into account the tensile strength of concrete;
2. Compressive stress-strain relationship of concrete in accordance with the provisions of Article 7.1.2-3 standard values.

1. Ultimate compressive strain of concrete is in accordance with section following formula:

 εcu = 0.0033 - (fcu,k - 50) × 10 -5 (7.1.2-5)

where
 εcu = cross section of the concrete ultimate compressive strain, while in the non-uniform compression, press formula (7.1.2-5) calculations, such as the calculation of ε cu is greater than 0.0033, is taken as 0.0033; when in axial When pressure is taken as ε 0; fcu,k = concrete cube compressive strength of standard value β1 = coefficient, when the concrete strength when no more than C50, β1 taken as 0.8, when the concrete strength grade of C80 time, β1 taken as 0.74, during determined by linear interpolation. α1 = rectangular stress diagram of the stress is taken as design value of concrete compressive strength fc multiplied by the coefficient α1. When the concrete strength when no more than C50, α1 taken as 1.0, when the concrete strength grade of C80 time, α1 taken as 0.94, during determined by linear interpolation.
3. Longitudinal tension and compression zone of reinforced concrete damage yield simultaneously, the relative height of compression zone limits ξb By the following formula:

 $ξ b = β 1 1 + f y E s ε c u$ (7.1.4-1)

### Net Concrete Cover Thickness

Input by the user of longitudinal force ordinary reinforced and prestressed steel, the concrete cover thickness (reinforced concrete surface to the outer edge of the distance) should not be less than the nominal diameter of steel, and shall comply with Table 9.2.1 of GB50010-2002 requirements.

## General Provisions on Seismic Design

### Seismic fortification intensity level and

Provide beam seismic rating, fortification intensity, structure type and component type of input. Program based on user input seismic fortification intensity levels and components of the beam design and construction inspection.

### Seismic bearing capacity adjustment factor

Consider the combination of earthquake concrete structure, its cross-section bearing capacity of the internal forces generated by seismic load bearing capacity divided by the seismic design value adjustment factor γRE, Seismic bearing capacity adjustment factor γRE 11.1.6 in accordance with GB50010-2002 form used. For the beam component, γRE value is 0.75.

## Calculation of Concrete Beams

### Bearing Capacity

1. Rectangular Bending Capacity: rectangular cross section or flange in the tension side of the inverted T-shaped cross-section flexural members, the flexural capacity should meet the following requirements:

 M ≤ α1fcbx(h0- x/2) + f'yA's(h0- α's) (7.2.1-1)

Concrete Compression Zone according to the following formula:

 α1fcbx=fyAs-f'yA's+fpyAp (7.2.1-2)

Concrete Compression Zone still should meet the following conditions:

 x≤ξbh0 (7.2.1-3)

 x≥2α' (7.2.1-4)

2. When included in the calculation of longitudinal compression reinforcement general, should meet the GB50010-2002 formula (7.2.1-4) conditions; if not satisfied this condition, the flexural capacity should meet the following requirements:

 M≤fpyAp(h-ap-a's)+fyAs(h-as-a's)+(σ'p0-f'py)A'p(a'p-a's) (7.2.5)

3. Bending Flexural bearing capacity calculations, as required by the structure or by checking Limit State requirements configured sectional area of longitudinal tensile steel bending capacity requirements greater than the area of reinforcement, the calculation of concrete compression Height x, only the conditions included in the required bending capacity vertical cross-section area of tensile steel.

4. T-Section Bending Capacity: flange in the compression zone of the T shape, I shaped cross-section flexural members (Figure 7.2.2), its flexural capacity should meet the following requirements:

1. When the following conditions are met

 fyAs+fpyAp≤α1fcb'fh'f+f'yA's-(σ'p0-f'py)A'p (7.2.2-1)

Should be a width b 'f rectangular cross section;

2. When satisfied equation (7.2.2-1) the conditions

 M≤α1fcbx(h0-x/2)+α1fc(b'f-b)h'f(h0-h’f/2)+f'yA's(h0-α's)-(σ'p0-f'py)A'p(h0-α'P) (7.2.2-2)

Concrete Compression Zone according to the following formula:

 α1fc[bx+(b'f-b)h'f]=fyAs-f'yA's+fpyAp+(σ'p0-f'py)A'p (7.2.2-3)

### Concrete compression zone height limit of seismic

For the seismic component: in the calculation, included in the longitudinal compression reinforcement in concrete compression zone of beam end shall meet the following requirements:

A seismic level

 ξb ≤ 0.25 (11.3.1-1)

Second, three seismic rating

 ξb ≤ 0.35 (11.3.1-2)

### Reinforcement ratio test

1. Configuration bar when the protective layer thickness in accordance with user input calculated as; to complete the inspection section bearing capacity of reinforced configuration, when the actual use of force reinforced the role of location as a point of steel.
2. Flexural members, offset tension, axial tension component side of the minimum tensile steel reinforcement ratio of 0.2 and 45ft/fy the larger value;
3. The seismic structure:

Table 1. Longitudinal tensile steel frame beam minimum reinforcement percentage (%); Table 11.3.6-1
Seismic Level Beam Position
Bearing Span

1

0.4 and 80ft/fy in the large value

0.3 and65ft/fy in the large value

2

0.3 and 65ft/fy in the large value

0.25 and 55ft/fy in the large value

3,4

0.25 and 55ft/fy in the large value

0.2 and 45ft/fy in the large value

Beam, the lower the minimum longitudinal steel reinforcement ratio, non-seismic design should not be less than 0.30%, respectively; seismic design, special one, one and two respectively, not less than 0.60%, 0.50% and 0.40%; ( JGJ 10.2.8-1)

4. The largest component seismic reinforcement rate: end of the beam longitudinal reinforcement ratio of tension reinforcement should not exceed 2.5%.

### Reinforcing the principles and methods of allocation

1. As selected through a long beam under the critical section, thus setting the upper and lower steel reinforcement combinations.
1. Through long tendons meet the upper
1. At least two, the corner bar.
2. Of the secondary seismic level, the bar diameter of not less than 14mm, and should not be less than the beam, respectively top and bottom ends of the longitudinal section of the reinforced area of the larger 1 / 4; on 3, 4 seismic rating , bar diameter not less than 12mm.
3. The first row of steel from the non-pass a long column (beam) side has been extended to ln / 3 position; second row extend ln / 4 position; ln value is defined as: for end bearing, net-based cross-span; For the intermediate bearing, ln on both sides for the bearing of a large net across the span.
4. Reinforced concrete longitudinal beam support section of negative moment reinforcement in tension should not be cut off in the tension zone. When to cut, in accordance with the provisions of reinforcement anchorage length (GB50010-2002 9.3.1), retained after anchoring length cut off under stress conditions.
2. Through the lower part of a long bar to meet:
1. At least two, the corner bar.
2. When the earthquake, the full reach into bearing.
3. Non-seismic, do not reach into the lower bearing of the beam longitudinal reinforcement cut off dot pitch bearing edge distance 0.1ln.

## Test Oblique Section

Program based on user input information to carry out shear reinforcement component of shear resistance test, specified as follows:

### Non-Seismic Shear Resistance Test

1. Rectangular, T-shaped and I-shaped cross-section flexural members, the shear section shall meet the following conditions:

When the hw / b ≤ 4:

V ≤ 0.25βcfcbh0 (7.5.1-1)

When the hw / b ≥ 6

V ≤ 0.2βcfcbh0 (7.5.1-2)

Combination of box beam cross section the maximum shear design values shall meet the following requirements:

V ≤ 0.2βcfcbh0 (JGJ 10.2.9-1)

2. Not configured stirrups and bent sheet metal reinforcement general bending members, the diagonal section of the shear capacity shall meet the following requirements:

V ≤ 0.7β h ft bh0 (7.5.3-1)

βh = (800 / h0) 1 / 4 (7.5.3-2)

3. Rectangular, T-shaped and I-shaped cross-section flexural members in general, when the only configuration stirrups, its diagonal section of the shear capacity shall meet the following requirements:

V ≤ 0.7ftbh0 +1.25 fyv (Asv / s) h0 (7.5.4-1)

### Seismic shear resistance test

1. Consider the combination of the framework of the seismic design of beam end shear value Vb according to the actual value;

2. Consider the combination of the frame beam earthquake, when the inter-high ratio of l0 / h> 2.5, its shear cross-section should conform to the following conditions:

 Vb ≤ 1 (0.20βcfcbh0) / γRE (11.3.3)

where
 βc = concrete strength factor: When the concrete strength less than C50, the take βc = 1.0; when the concrete strength grade of C80, the take βc = 0.8; during determined by linear interpolation.
3. 3. Consider the combination of earthquake rectangular, T-shaped and I-shaped cross-section of the frame beam, the Shear capacity should meet the following requirements:

Vb ≤ 1 [0.42ftbh0 +1.25 fyvAsvh0 / s] / γRE (11.3.4-1)

### Tie Ratio Test

1. Confining rate: When V > 0.7ft bh0 , the hoop reinforcement ratio ρ svsv = A sv / (b s)] not be less than 0.24f t / f yv

2. 2. Seismic conditions:

Along the beam length of stirrup reinforcement ratio ρsv should meet the following requirements:

Seismic level 1:

ρ sv ≥ 0.30f t / f yv (11.3.9-1)

Seismic level 2:

ρ sv ≥ 0.28f t / f yv (11.3.9-2)

Seismic level 3,4:

ρsv≥0.26ft/fyv (11.3.9-3)

3. High-rise building structures, seismic rating for the particular level of reinforced concrete structures shall meet the basic requirements of a seismic level, the beam end encryption District hoop structure confining rate increases of 10%.

4. Box beam supports of encrypted area with hoop hoop smallest, non-seismic design should not be less than 0.9ft/fyv; seismic design, the special one and one and two respectively, not less than 1.3ft/fyv, 1.2ft/fyv and 1.1ft/fyv. (JGJ 10.2.8 - 2)

### Spacing

1. The maximum stirrup spacing:

1. Non-seismic:

Table 2. The maximum beam stirrup spacing (mm), Table 10.2.10
Beam h V>0.7ftbh0 V≤0.7ftbh0

150 < h ≤ 300

150

200

300<h≤500

200

300

500<h≤800

250

350

h>800

300

400

When the beam with longitudinal compression by computing needs reinforcement, the stirrups should be made of closed, then (d is the minimum diameter of longitudinal compression reinforcement):

Condition Maximum Distance

Beam with longitudinal compression computing needs according to the time bar

Min(15d,400)

Pressure within the longitudinal layer of steel more than 5 and greater than 18mm in diameter

10d

Beam width is greater than 400mm and a layer of pressure within the longitudinal reinforcement than three, or when the beam width of not more than 400mm but a layer of reinforcement within the vertical pressure when more than 4

Composite hoop bar should be set

The spacing of non-encrypted area of the spacing should not be greater than the encryption area 2 times.

2. Seismic encryption District: meet the requirements of Table 6.3.2-2, and a seismic rating, not more than 20 times 200mm and stirrups diameter is greater; 2, 3 seismic level, not more than 20 times 250mm and hoop tendon diameter is greater; 4 seismic rating, not more than 300mm.
2. Encryption area: seismic design, the beam end encryption area stirrup length should conform to the requirements of Table 6.3.2-2; beam end set the framework of the first node from the edge of stirrups should be no larger than 50mm.

Table 3. Frame beam stirrups beam end zone construction requirements encryption, Table 11.3.6-2
Seismic Level Encryption Zone Length (mm) maximum stirrup spacing (mm) Stirrup minimum diameter (mm)

1

2h and 500 of the larger value

6 times the longitudinal bar diameter, high beam, 1 / 4 and 100 in the minimum

10

2

1.5h and 500 of the larger value

8 times the longitudinal bar diameter, high beam, 1 / 4 and 100 in the minimum

8

3

8 times the longitudinal bar diameter, high beam, 1 / 4 and 150 in the minimum

8

4

8 times the longitudinal bar diameter, high beam, 1 / 4 and 150 in the minimum

6

Note: H as the height of the table section.
3. Box beam supports of (left side column height within the beam section 1.5) stirrups should be encrypted, encrypted area stirrup diameter of not less than 10mm, spacing should not exceed 100mm. (JGJ-10.2.8-3)

### Minimum diameter stirrups

1. # Non-seismic design: A cross-section height h> 800mm of the beam, the stirrup diameter not less than 8mm; on the beam height h ≤ 800mm beam, the stirrup diameter not less than 6mm. Beam with vertical compression reinforcement computing needs, the stirrup diameter of not less than the vertical compression reinforcement should be 0.25 times the diameter.
2. Seismic design: minimum diameter shall meet the requirements of Table 6.3.2-2, when the end of the beam longitudinal reinforcement ratio greater than 2%, the minimum diameter of the table in the stirrups should be increased 2mm.

### Side bar (waist bars) layout

When the beam web height h w ≥ 450mm, the two sides of the beam height profile along the vertical structure should be reinforced, each side of the vertical structural steel (not including the beam, the lower part of the reinforced and erect steel) cross-section area of not web-sectional area should be less than 0.1% bh w, and the pitch should be less than 200mm. Here, the web height h w according to GB50010-2002 7.5.1 Article access.