Design for shear

Figure 3.14 Section through rib

Support A (and D) at solid/rib interface

Shear at solid/rib interface = 29.3 kN / rib

Taking solid area as the support, at d from face of support <6.2.1(8)> VEd = 29.3 - 0.232 x 0.90 x 13.38 = 26.5 kN / rib

where

fttt Both Asprov / Asreq and any adjustment to N obtained from Exp. (7.16a) or Exp. (7.16b) is restricted to 1.5 by Note 5 to Table NA.5 in the UK NA.

d k = 1 + (200 / d)05 < 2 = 1 + (200 / 257)05 = 1.88

= assume only 1 H20 anchored = 314 mm2 = min. width between tension and compression chords.

At bottom assuming 1 / 10 slope to rib: = 150 + 2 x (25 + 8 + 20 / 2) / 10 = 159 mm

= 257 mm as before p = 314 / (159 x 257) = 0.0077 fck = 35

. VRdc = (0.18 / 1.5) 1.88 (100 x 0.0077 x 35)0333 x 159 x 257 = 0.68 x 159 x 257 = 27.8 kN / rib

. No shear links required <6.2.1(5)> But use nominal links to allow prefabrication.

Support B (and C) at solid/rib interface

Shear at solid/rib interface = 40.9 kN / rib [max(BA, BC)] At d from face of support VEd = 40.9 - 0.245 x 13.38 x 0.9

37.9 kN/rib

Resistance

Y = 1.5 k = 1 + (200 / d)05 < 2 = 1 + (200 / 245)05 = 1.90

Pi = where

Asl = 2 H16 = 402 mm2 bw = 159 mm as before d = 245 mm as before = 0.0103 = 35

.•. VRdc = (0.18 / 1.5) 1.9 (100 x 0.0103 x 35)0333 x 159 x 245 = 0.75 x 159 x 245 = 29.2 kN / rib

.'. Shear links required

Shear links required for a distance:

(37.9 - 29.2) / (13.38 x 0.9) + 245 = 722 + 245 = 967 mm from interface Check shear capacity

= 0.6 (1 - fck / 250) = 0.528 = 35 / 1.5 = 23.3 MPa = angle of inclination of strut. Rearranging formula above:

bw z

fcd e bwd

41.6 x 103

By inspection, cot 0 << 21.8. But cot 0 restricted to 2.5 and . tan 0= 0.4.

VRd.max= 1.0 x 159 x 0.9 x 245 x 0.528 x 20 / (2.5 + 0.4) = 127.6 kN

Shear links: shear resistance with links VRd.s = (Asw / s) z fywd cot 0 < VRd.max where

Asw / s = area of legs of links/link spacing z = 0.9d as before fywd = 500 / 1.15 = 434.8 cot 0 = 2.5 as before

> 37.9 x 103 / (0.9 x 245 x 434.8 x 2.5) > 0.158 Maximum spacing of links = 0.75d = 183 mm

. Use H8 @ 175 cc in 2 legs (A^ / s = 0.57) for min. .967 mm into rib

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