Rc Beam Torsion Design (bs8110) 736748

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RECTANGULAR RC BEAM TORSION DESIGN (BS8110-2:1985 (CL. 2.4)) TEDDS calculation version 1.0.01

b

Longitudinal torsion reinf't at max 300 ctrs (but see 3.12.11.2.6 of BS8110-1:1997) is additional to that required for bending.

Perimeter link only is considered in the design. This link to be a closed torsion link. Internal links not included in the design but may be required for spacing rules (see 3.4.5.5 of BS8110-1:1997)

h

D Area of steel at this level includes that required for bending and torsion

L dia c nom c nom

Beam definition Beam width;

b = 230 mm

Overall beam depth;

h = 450 mm

Characteristic strength of concrete;

fcu = 25 N/mm2

Characteristic strength of longitudinal reinf’t;

fy = 500 N/mm2

Characteristic strength of shear reinforcement;

fyv = 500 N/mm2

Nominal cover to all reinforcement (incl. links);

cnom = 25 mm

Longitudinal tension bar diameter (try);

D = 16 mm

Link bar diameter;

Ldia = 8 mm

Number of perimeter link legs at a section;

N=2

Area of longitudinal reinf’t provided for bending;

As = 201 mm2

Effective depth;

d = h - cnom - Ldia - D/2 = 409 mm

Larger dimension of rectangular beam;

hmax = max(h,b) = 450 mm

Smaller dimension of rectangular beam;

hmin =min(h,b) = 230 mm

Larger centre to centre dim. of links;

y1 = hmax - 2cnom - Ldia = 392 mm

Smaller centre to centre dim. of links;

x1 = hmin - 2cnom - Ldia = 172 mm

Design shear force and torsional moment Ultimate shear force;

V = 18.0 kN

Ultimate torsional moment;

T = 6.2 kNm

Check torsional shear stress (cl. 2.4.4, 2.4.5 & 2.4.6) Applied torsional shear stress;

vt = (2  T)/(hmin2  (hmax - hmin/3)) = 0.628 N/mm2

Min torsional shear stress above which reinforcement is required vtmin = min((0.067N1/2/mm)(fcu),0.4N/mm2) = 0.335 N/mm2 Max allowable torsional stress;

vtmax = vtu  min(1,y1/550mm) = 2.851 N/mm2 vt>vtmin - Torsion reinforcement required

Check direct shear stress Applied direct shear stress; From BS8110:Part 1:1997 - Table 3.8

v = V/(bd) = 0.191 N/mm2

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17/01/2017 vc = 0.378 N/mm2 v
Check combined shear stress (cl. 2.4.5) Resultant shear stress; vres = vt + v = 0.819 N/mm2 Max allowable combined direct & torsional shear stress vtu = min((0.8N1/2/mm)(fcu),5.0N/mm2) = 4.000 N/mm2 - vres<=vtu - Resultant shear stress is OK Link design (cl. 2.4.7) Area of shear reinforcement req’d for torsion;

Asvt = max(T/(0.8  x1  y1  0.87fyv),0.4b/(0.87fyv)) = 264 mm2/m

Area of shear reinforcement req’d for direct shear; Asvs = 0 mm2/m Total area of shear reinforcement required;

Asv = Asvt + Asvs = 264 mm2/m

Using 2H8 legs max link spacing;

sv = 1/((4  Asv)/(N    Ldia2)) = 380.5 mm

From BS8110:Part 1:1997 - cl. 2.4.8 Maximum allowable link spacing; Selected link spacing;

svmax = min(x1,y1/2,200mm) = 172 mm sact = 200 mm FAIL - Clause 2.4.8 link spacing is exceeded (link utilisation = 0.526)

Longitudinal torsion reinforcement design (cl. 2.4.7) Area of longitudinal torsion reinf’t required;

Ast = Asvt  fyv  (x1 + y1) / fy = 149 mm2 149 mm2 longitudinal reinforcement required