HORIZONTAL SHEAR [LRFD ART. 5.8.4]

The LRFD code does not give any guidance for computing horizontal shear. The procedure outlined in Chapter 8 of the PCI Design Handbook will be used with one modification that total Vu shall be used, which is a conservative approach.

V_{u h} = \frac{V_{u}}{d_{v}}

where:

V_uh = horizontal factored shear force per unit length of the beam, kN

V_u = factored shear force, kN

d_v= distance between resultants of tensile and compressive forces, mm

The LRFD code does not identify the location of the critical section. We shall perform the computations at 0.1L.

V_u = 1.25(161.4 + 214.7 + 11.1 + 30.8) + 1.50(52.2) + 1.75(536.8)= 1540.2 kN

d_v= 1678.73 mm

V_{n h} = \frac{1540.2}{1678.73} = 0.9175 k N / m m = 917.50 N / m m

V_{n} = \frac{V_{u h}}{0.9} = \frac{0.9175 k N / m m}{0.9} = 1.02 k N / m m = 1020 N / m m

The nominal shear resistance of the interface plane is:

V_{n i} = c A_{c v} + μ (A_{v f} f_{y} + P_{c})

LRFD Eq. 5.8.4.1-3

Where:

c = cohesion factor, MPa [LRFD Art. 5.8.4.3]

μ = friction factor [LRFD Art. 5.8.4.3]

A_cv = area of concrete engaged in shear transfer, mm²

A_vf = area of shear reinforcement crossing the shear plane, mm²

P_c = permanent net compressive force normal to the shear plane, N

f_y = shear reinforcement yield strength, MPa

Precast/Prestressed Girder calculates the steel for two cases. For concrete placed against clean, hardened concrete with surface intentionally roughened and for concrete placed against clean, hardened concrete with surface not intentionally roughened (smooth). Computations for both of these cases are given here.

For concrete placed against clean, hardened concrete with surface intentionally roughened:[LRFD Art. 5.8.4.2]
c = 1.9 MPa

μ= 1.0: K₂ = 12.4 for normal weight concrete; K₁ = 0.3

The actual contact width, b_v, between the slab and the beam is 1225 mm. Therefore,

A_cv = (1225 mm)(1 mm) = 1225 mm²

$V_{n i} = 1020 = 1.9 \times 1225 + 1.0 (A_{v f} (413.7) + 0)$

Since V_ni is less than cA_cv, A_vf = mm²/m.

A_vf = 0.0 mm²/m
For concrete placed against clean, hardened concrete with surface not intentionally roughened (smooth) [LRFD Art. 5.8.4.2]:
c = 0.52 MPa

μ= 0.6: K₁ = 0.2; K₂ = 5.5MPa

The actual contact width, b_v, between the slab and the beam is 1225 mm. Therefore,

A_cv = (1225 mm)(1 mm) = 1225 mm²

$V_{n i} = 1020 = 0.52 \times 1225 + 0.6 (A_{v f} (413.7) + 0)$

A_vf = 1540.63 mm²/m [less than Vni (5.8.4.1-4, 5.8.4.1-5)]

Compute Minimum Shear Reinforcement:

[LRFD Eq. 5.8.4.1-4]

A_{v f} \geq \frac{0.35 b_{v} s}{f_{y}}

If the spacing (s) is 1000 mm, then minimum A_vf is:

A_{v f} = \frac{0.35 \times 1225 \times 1000}{413.7} = 1036.42 {m m}^{2}

Check the maximum nominal shear resistance (for surface intentionally roughened)

Provided that:

V_{n} = 0.7 \times 1225 + 1.0 (1036.42 (413.7) 10^{- 3}) = 1286.09 N / m m

0.2 {f `}_{c} A_{c v} = 0.2 \times 45 \times 1225 = 11025 N / m m

5.5 A_{c v} = 5.5 \times 1225 = 6737 N / m m

Since V_n provided

\leq 0.2 {f `}_{c} A_{c v}

LRFD Eq. 5.8.4.1-2

\leq 5.5 A_{c v}

LRFD Eq. 5.8.4.1-3

Maximum Spacing= 600 m [LRFD Art. 5.8.4.1]

b_v=1225mm

Therefore, consider providing at least 4 bars per row. [LRFD Art. 5.8.4.1]