RC Beam Torsion Design (BS8110)

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

L dia c nom c nom

Beam Beam definitio n Beam width; width;

230 mm b = 230 mm

Overall beam depth; depth;

450 mm h = 450 mm

Characteristic strength of concrete; concrete;

25 N/mm2 f cu cu = 25 N/mm

Characteristic strength of longitudinal reinf’t; reinf’t;

500 N/mm2 f y = 500 N/mm

Characteristic strength of shear reinforcement; reinforcement;

500 N/mm2 f yv yv = 500 N/mm

Nominal cover to all reinforcement (incl. links); links);

25 mm cnom = 25 mm

Longitudinal tension bar diameter (try); (try);

16 mm D = 16 mm

Link bar diameter ;

Ldia = 8 mm

Number of perimeter link legs at a section; section;

N=2

 Area of longitudinal reinf’t provided for bendi ng; ng;

201 mm2  As = 201 mm

Effective depth; depth;

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

Larger dimension of rectangular beam; beam;

450 mm hmax = max(h,b) = 450 mm

Smaller dimension of rectangular beam; beam;

230 mm hmin =min(h,b) = 230 mm

Larger centre to centre dim. of links; links;

392 mm y1 = hmax - 2 2cnom - Ldia = 392 mm

Smaller centre to centre dim. of links; links;

172 mm x1 = hmin - 2 2cnom - Ldia = 172 mm

Design Design sh ear ear force and t orsional moment Ultimate shear force; force;

18.0 kN V = 18.0 kN

Ultimate torsional moment; moment;

6.2 kNm T = 6.2 kNm

Check tor sio nal sh ear stress (cl. 2.4.4, 2.4.4, 2.4.5 2.4.5 & 2.4.6) 2.4.6)  Applied torsional shear stress; stress;

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

Min torsional shear stress above which reinforcement is required 2 0.335 N/mm2 vtmin = min((0.067N1/2/mm) /mm)(f  (f cu cu),0.4N/mm ) = 0.335 N/mm

Max allowable torsional stress; stress;

2.851 N/mm2 vtmax = vtu  min(1,y1/550mm) = 2.851 N/mm v t>v tmin - Torsion reinforc ement ement required

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

0.191 N/mm2 v = V/(b V/(bd) = 0.191 N/mm

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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)(f cu),5.0N/mm2) = 4.000 N/mm2 PASS - v res <=v tu  - Resultant shear stress is OK Link design (cl. 2.4.7)  Area of shear reinforcement req’d for torsion;

 A svt = max(T/(0.8

x1

y1  0.87 f yv ),0.4 b/(0.87 f yv )) = 264 mm2/m

 Area of shear reinforcement req’d for direct shea r ;  Asvs  = 0 mm 2/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;

svmax = min(x1,y1/2,200mm) = 172 mm

Selected link spacing;

sact = 200 mm FAIL - Clause 2.4.8 link sp acing i s exceeded (link uti lis ation = 0.526)

Longitu dinal tor sion reinfo rcement design (cl. 2.4.7)  Area of longitudinal torsion reinf’t requ ired;

 Ast = Asvt  f yv  (x1 + y1) / f y = 149 mm2 149 mm 2 longitu dinal reinforcement required