Page 228 - Handbook of Civil Engineering Calculations, Second Edition

REINFORCED CONCRETE 2.13

3. Select the stirrup size
Equate the spacing near the support to the minimum practical value, which is generally
considered to be 4 in. (101.6 mm). The equation for stirrup spacing is

A v f y
s (17)
v c
b
2
Then A v sv u
b/( f y ) 4(122)(15)/[0.85(40,000)] 0.215 sq.in. (1.3871 cm ). Since
each stirrup is bent into the form of a U, the total cross-sectional area is twice that of a
2
straight bar. Use no. 3 stirrups for which A v 2(0.11) 0.22 sq.in. (1.419 cm ).
4. Establish the maximum allowable stirrup spacing
0.5
Apply the criteria of the Code, or s max d/4 if v > 6 ( f c
) . The right-hand member of
this inequality has the value 279 lb/sq.in. (1923.70 kPa), and this limit therefore does not
apply. Then s max d/2 11.25 in. (285.75 mm), or s max A v /(0.0015b)
0.22/[0.0015(15)] 9.8 in. (248.92 mm). The latter limit applies, and the stirrup spacing
will therefore be restricted to 9 in. (228.6 mm).
5. Locate the beam sections at which the required stirrup spacing
is 6 in. (152.4 mm) and 9 in. (228.6 mm)
Use Eq. 17. Then A v f y /b 0.85(0.22)(40,000)/15 499 lb/in. (87.38 kN/m). At C: v u
499/6 83 lb/sq.in. (572.3 kPa); v u 83 93 176 lb/sq.in. (1213.52 kPa); AC
(272 176)/2.52 38 in. (965.2 mm). At D: v u
499/9 55 lb/sq.in. (379.2 kPa); v u
55 93 148 lb/sq.in. (1020.46 kPa); AD (272 148)/2.52 49 in. (1244.6 mm).
6. Devise a stirrup spacing conforming to the computed results
The following spacing, which requires 17 stirrups for each half of the span, is satisfactory
and conforms with the foregoing results:

Distance from last
stirrup to face of
Quantity Spacing, in. (mm) Total, in. (mm) support, in. (mm)
1 2 (50.8) 2 (50.8) 2 (50.8)
9 4 (101.6) 36 (914.4) 38 (965.2)
2 6 (152.4) 12 (304.8) 50 (1270)
5 9 (228.6) 45 (1143) 95 (2413)

DETERMINATION OF BOND STRESS

A beam of 4000-lb/sq.in. (27,580-kPa) concrete has an effective depth of 15 in. (381 mm)
and is reinforced with four no. 7 bars. Determine the ultimate bond stress at a section
where the ultimate shear is 72 kips (320.3 kN). Compare this with the allowable stress.

Calculation Procedure:

1. Determine the ultimate shear flow h u
The adhesion of the concrete and steel must be sufficiently strong to resist the horizontal
shear flow. Let u u ultimate bond stress, lb/sq.in. (kPa); V u ultimate vertical shear, lb (N);