ec2 beam design

8/11/2019 EC2 Beam Design

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Section Sheet no./rev.

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Chk'd by Date App'd by Date

RC BEAM ANALYSIS & DESIGN (EN1992)

RC BEAM ANALYSIS & DESIGN (EN1992-1)

In accordance with Singapore national annex

TEDDS calculation version 2.1.15

Load Envelope - Combination 1

0.0

90.564

mm 5000

1A B

Support conditions

Support A Vertically restrained

Rotationally free

Support B Vertically restrained

Rotationally free

Applied loading

SW Permanent self weight of beam 1

DL Permanent full UDL 30 kN/m

LL Variable full UDL 30 kN/m

Load combinations

Load combination 1 Support A Permanent 1.35

Variable 1.50

Span 1 Permanent 1.35

Variable 1.50


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Support B Permanent 1.35

Variable 1.50

Analysis results

Maximum moment support A; MA_max= 0kNm; MA_red= 0kNm;

Maximum moment span 1 at 2500 mm; Ms1_max= 283kNm; Ms1_red= 283kNm;

Maximum moment support B; MB_max= 0kNm; MB_red= 0kNm;

Maximum shear support A; VA_max= 226kN; VA_red= 226kN

Maximum shear support A span 1 at 450 mm; VA_s1_max= 186kN; VA_s1_red= 186kN

Maximum shear support B; VB_max= -226kN; VB_red= -226kN

Maximum shear support B span 1 at 4550 mm; VB_s1_max= -186kN; VB_s1_red= -186kN

Maximum reaction at support A; RA= 226kN

Unfactored permanent load reaction at support A; RA_Permanent= 84kN

Unfactored variable load reaction at support A; RA_Variable= 75kNMaximum reaction at support B; RB= 226kN

Unfactored permanent load reaction at support B; RB_Permanent= 84kN

Unfactored variable load reaction at support B; RB_Variable= 75kN

Rectangular section details

Section width; b = 300mm

Section depth; h = 500mm

500

300

Concrete details (Table 3.1 - Strength and deformation characteristics for concrete)

Concrete strength class; C40/50

Characteristic compressive cylinder strength; fck= 40N/mm2

Characteristic compressive cube strength; fck,cube= 50N/mm2

Mean value of compressive cylinder strength; fcm= fck+ 8 N/mm2= 48N/mm2

Mean value of axial tensile strength; fctm= 0.3 N/mm2(fck/ 1 N/mm2)2/3= 3.5N/mm2

Secant modulus of elasticity of concrete; Ecm= 22 kN/mm2[fcm/10 N/mm2]0.3= 35220N/mm2

Partial factor for concrete (Table 2.1N); C= 1.50

Compressive strength coefficient (cl.3.1.6(1)); cc= 0.85

Design compressive concrete strength (exp.3.15); fcd= ccfck/ C= 22.7N/mm2

Maximum aggregate size; hagg= 20mm

Reinforcement details

Characteristic yield strength of reinforcement; fyk= 460N/mm2

Partial factor for reinforcing steel (Table 2.1N); S= 1.15

Design yield strength of reinforcement; fyd= fyk/ S= 400N/mm2


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Nominal cover to reinforcement

Nominal cover to top reinforcement; cnom_t= 35mm

Nominal cover to bottom reinforcement; cnom_b= 35mm

Nominal cover to side reinforcement; cnom_s= 35mm

Mid span 1

;

500

300

2 x 8 shear legs at 300 c/c

4 x 25 bars

4 x 25 bars

Rectangular section in flexure (Section 6.1) - Positive midspan moment

Design bending moment; M = abs(Ms1_red) = 283kNm

Depth to tension reinforcement; d = h - cnom_b- v- bot/ 2 = 444mm

Percentage redistribution; mrs1= Ms1_red/ Ms1_max- 1 = 0%

Redistribution ratio; = min(1 - mrs1, 1) = 1.000

K = M / (b d2fck) = 0.119

K' = 0.598 - 0.181 2- 0.21 = 0.207

K' > K - No compression reinforcement is required

Lever arm; z = min((d / 2) [1 + (1 - 3.53 K)0.5], 0.95 d) = 391mm

Depth of neutral axis; x = 2.5 (d - z) = 133mm

Area of tension reinforcement required; As,req= M / (fydz) = 1808mm2

Tension reinforcement provided; 4 25bars

Area of tension reinforcement provided; As,prov= 1963mm2

Minimum area of reinforcement (exp.9.1N); As,min= max(0.26 fctm/ fyk, 0.0013) b d = 264mm2

Maximum area of reinforcement (cl.9.2.1.1(3)); As,max= 0.04 b h = 6000mm2

PASS - Area of reinforcement provided is greater than area of reinforcement required

Rectangular section in shear (Section 6.2)

Shear reinforcement provided; 2 8legs at 300 c/c

Area of shear reinforcement provided; Asv,prov= 335mm2/m

Minimum area of shear reinforcement (exp.9.5N); Asv,min= 0.08 N/mm2b (fck/ 1 N/mm2)0.5/ fyk= 330mm2/m

PASS - Area of shear reinforcement provided exceeds minimum required

Maximum longitudinal spacing (exp.9.6N); svl,max= 0.75 d = 333mm

PASS - Longitudinal spacing of shear reinforcement provided is less than maximum

Design shear resistance (assuming cot() is 2.5); Vprov= 2.5 Asv,provz fyd= 131.1kN

Shear links provided valid between 1100 mm and 3900 mm with tension reinforcement of 1963 mm2

Crack control (Section 7.3)

Maximum crack width; wk= 0.3mm

Design value modulus of elasticity reinf (3.2.7(4)); Es= 200000N/mm2

Mean value of concrete tensile strength; fct,eff= fctm= 3.5N/mm2

Stress distribution coefficient; kc= 0.4


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Non-uniform self-equilibrating stress coefficient; k = min(max(1 + (300 mm - min(h, b)) 0.35 / 500 mm, 0.65), 1) = 1.00

Actual tension bar spacing; sbar= (b - 2 (cnom_s+ v) - bot) / (Nbot- 1) = 63mm

Maximum stress permitted (Table 7.3N); s= 350N/mm2

Concrete to steel modulus of elast. ratio; cr= Es/ Ecm= 5.68

Distance of the Elastic NA from bottom of beam; y = (b h2/ 2 + As,prov(cr- 1) (h - d)) / (b h + As,prov(cr- 1)) =

239mm

Area of concrete in the tensile zone; Act= b y = 71633mm2

Minimum area of reinforcement required (exp.7.1); Asc,min= kck fct,effAct/ s= 288mm2

PASS - Area of tension reinforcement provided exceeds minimum required for crack control

Quasi-permanent value of variable action; 2= 0.30

Quasi-permanent limit state moment; MQP= abs(Ms1_c21) + 2abs(Ms1_c22) = 134kNm

Permanent load ratio; RPL= MQP/ M = 0.47

Service stress in reinforcement; sr= fydAs,req/ As,provRPL= 174N/mm2Maximum bar spacing (Tables 7.3N); sbar,max= 250mm

PASS - Maximum bar spacing exceeds actual bar spacing for crack control

Minimum bar spacing

Minimum bottom bar spacing; sbot,min= (b - 2 cnom_s- 2 v- bot) / (Nbot- 1) = 63mm

Minimum allowable bottom bar spacing; sbar_bot,min= max(bot, hagg+ 5 mm, 20 mm) + bot= 50mm

Minimum top bar spacing; stop,min= (b - 2 cnom_s- 2 v- top) / (Ntop- 1) = 63mm

Minimum allowable top bar spacing; sbar_top,min= max(top, hagg+ 5 mm, 20 mm) + top= 50mm

PASS - Actual bar spacing exceeds minimum allowable

Deflection control (Section 7.4)

Reference reinforcement ratio; m0= (fck/ 1 N/mm2)0.5/ 1000 = 0.006

Required tension reinforcement ratio; m= As,req/ (b d) = 0.014

Required compression reinforcement ratio; 'm= As2,req/ (b d) = 0.000

Structural system factor (Table 7.4N); Kb= 1.0

Basic allowable span to depth ratio (7.16b); span_to_depthbasic= Kb[11 + 1.5 (fck/ 1 N/mm2)0.5m0/ (m- 'm)

+ (fck/ 1 N/mm2)0.5('m/ m0)0.5/ 12] = 15.425

Reinforcement factor (exp.7.17); Ks= min(As,prov/ As,req, 1.5) 500 N/mm2/ fyk= 1.180

Flange width factor; F1 = 1.000

Long span supporting brittle partition factor; F2 = 1.000

Allowable span to depth ratio; span_to_depthallow= span_to_depthbasicKsF1 F2 = 18.207

Actual span to depth ratio; span_to_depthactual= Ls1/ d = 11.249PASS - Actual span to depth ratio is within the allowable limit

ec2 beam design

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