Page 52 - Demo

CONCRETE TECHNOLOGY50 CPI %u2013 Concrete Plant International %u2013 1 | 2026 www.cpi-worldwide.com(2)(3)(4)Figures 7 and 8 present representative strain distributions over the cross-sectional height at the defined time points. The correlation coefficient lies in the range 0.99 %u2264 |R| %u2264 1, indicating a linear strain distribution across the section height. A summary of the normalized compression zone heights is provided in Tables 4 and 5. For all specimens, the maximum loads are reached within the range 0.06 %u2264 %u03be %u2264 0.1, meaning that near the fracture stress the crack heights amount to approximately 90% of the cross-sectional height. These findings are consistent with [19, 20]. Reference [20] attributes this behaviour to the ratio between compressive and tensile strength. In the DAfStb guideline for steel fibre-reinforced concrete [13], a crack height of 90% of the beam height is likewise assumed. As an approximation, the normalized compression zone height at the point of localization can therefore be taken as 0.1.The normalized mean values are presented in Tables 6 and 7. Crack localization occurs at approximately 90-92 % of Mmax.%ud835%udc53%ud835%udc53!\%ud835%udefd%ud835%udefd $ %u210e100(&,'1 + %ud835%udefd%ud835%udefd $ %u210e100(&,' %ud835%udc53%ud835%udc53(%,$% [%ud835%udc40%ud835%udc40%ud835%udc40%ud835%udc40%ud835%udc40%ud835%udc40] (1)%ud835%udf05%ud835%udf05 =%ud835%udf0b%ud835%udf0b2 %u2212 arctan (%ud835%udc4e%ud835%udc4e) (2)%ud835%udf05%ud835%udf05 =%ud835%udf00%ud835%udf00%! %u2212 %ud835%udf00%ud835%udf00%\70 (3)%ud835%udf09%ud835%udf09 = >%ud835%udf00%ud835%udf00!(>%ud835%udf00%ud835%udf00\(4) %ud835%udf09%ud835%udf09* + 3%ud835%udf09%ud835%udf09+ %u2212 12%ud835%udc40%ud835%udc40$,-%ud835%udc4f%ud835%udc4f%ud835%udc4f%ud835%udc4f%ud835%udc4f%ud835%udc4f%u210e* = 0 (5)(2%ud835%udc38%ud835%udc38%ud835%udc38%ud835%udc38%u210e %u2212 %ud835%udf0e%ud835%udf0e\ + 2%ud835%udf0e%ud835%udf0e\(6)13 %ud835%udc4f%ud835%udc4f%ud835%udc4f%ud835%udc4f%ud835%udc4f%ud835%udc4f%ud835%udf07%ud835%udf07*%u210e*%ud835%udf09%ud835%udf09* +%ud835%udc4f%ud835%udc4f%ud835%udc4f+6 G((1 %u2212 %ud835%udf07%ud835%udf07) $(%ud835%udf07%ud835%udf07 + 2)%ud835%udf0e%ud835%udf0e! + (2%ud835%udf07%ud835%udf07 + 1)%ud835%udf0e%ud835%udf0e!& + C2%ud835%udf0e%ud835%udf0e\ + %ud835%udf0e%ud835%udf0e\%u2212%ud835%udc4f%ud835%udc4f%ud835%udc4f6%ud835%udf05%ud835%udf05 I(4%u210e%ud835%udf05%ud835%udf05 %u2212 %ud835%udf00%ud835%udf00\+%ud835%udc4f%ud835%udc4f6%ud835%udf05%ud835%udf05+ I(2%u210e+%ud835%udf05%ud835%udf05+ %u2212 %u210e%ud835%udf05%ud835%udf05%ud835%udf05%ud835%udf05\+)%ud835%udf0e%ud835%udf0e\(7)%u0009%u0009%u0009%u0009%u0009%ud835%udf07%ud835%udf07 = N%ud835%udf00%ud835%udf00!&%ud835%udf00%ud835%udf00!%u2264 1%u0009%u0009|%ud835%udf00%ud835%udf00!&| %u2264 |%ud835%udf00%ud835%udf00!|1%u0009%u0009%u0009%u0009%u0009%u0009%u0009%u0009%u0009%u0009%u0009%u0009|%ud835%udf00%ud835%udf00!&| %u2265 |%ud835%udf00%ud835%udf00!|(8)%ud835%udf09%ud835%udf09 =%u2212%ud835%udf0e%ud835%udf0e\2%ud835%udc38%ud835%udc38%ud835%udc38%ud835%udc38%u210e %u2212 %ud835%udf0e%ud835%udf0e\%ud835%udc5a%ud835%udc5a%ud835%udc5a%ud835%udc5a%ud835%udc5a%ud835%udc5a %ud835%udf0e%ud835%udf0e\(9)%ud835%udf0e%ud835%udf0e\+(1 %u2212 %ud835%udf09%ud835%udf09) %u2212 %ud835%udf0e%ud835%udf0e\%ud835%udc38%ud835%udc38%ud835%udc38%ud835%udc38%u210e90 %u2212 %ud835%udf0e%ud835%udf0e\ (10)%ud835%udf00%ud835%udf00\(11)%ud835%udc53%ud835%udc53!\%ud835%udefd%ud835%udefd $ %u210e100(&,'1 + %ud835%udefd%ud835%udefd $ %u210e100(&,' %ud835%udc53%ud835%udc53(%,$% [%ud835%udc40%ud835%udc40%ud835%udc40%ud835%udc40%ud835%udc40%ud835%udc40] (1)%ud835%udf05%ud835%udf05 =%ud835%udf0b%ud835%udf0b2 %u2212 arctan (%ud835%udc4e%ud835%udc4e) (2)%ud835%udf05%ud835%udf05 =%ud835%udf00%ud835%udf00%! %u2212 %ud835%udf00%ud835%udf00%\70 (3)%ud835%udf09%ud835%udf09 = >%ud835%udf00%ud835%udf00!(>%ud835%udf00%ud835%udf00\(4) %ud835%udf09%ud835%udf09* + 3%ud835%udf09%ud835%udf09+ %u2212 12%ud835%udc40%ud835%udc40$,-%ud835%udc4f%ud835%udc4f%ud835%udc4f%ud835%udc4f%ud835%udc4f%ud835%udc4f%u210e* = 0 (5)(2%ud835%udc38%ud835%udc38%ud835%udc38%ud835%udc38%u210e %u2212 %ud835%udf0e%ud835%udf0e\ + 2%ud835%udf0e%ud835%udf0e\(6)13 %ud835%udc4f%ud835%udc4f%ud835%udc4f%ud835%udc4f%ud835%udc4f%ud835%udc4f%ud835%udf07%ud835%udf07*%u210e*%ud835%udf09%ud835%udf09* +%ud835%udc4f%ud835%udc4f%ud835%udc4f+6 G((1 %u2212 %ud835%udf07%ud835%udf07) $(%ud835%udf07%ud835%udf07 + 2)%ud835%udf0e%ud835%udf0e! + (2%ud835%udf07%ud835%udf07 + 1)%ud835%udf0e%ud835%udf0e!& + C2%ud835%udf0e%ud835%udf0e\+%u2212%ud835%udc4f%ud835%udc4f%ud835%udc4f6%ud835%udf05%ud835%udf05 I(4%u210e%ud835%udf05%ud835%udf05 %u2212 %ud835%udf00%ud835%udf00\+%ud835%udc4f%ud835%udc4f6%ud835%udf05%ud835%udf05+ I(2%u210e+%ud835%udf05%ud835%udf05+ %u2212 %u210e%ud835%udf05%ud835%udf05%ud835%udf05%ud835%udf05\ %u2212 %ud835%udf00%ud835%udf00\+)%ud835%udf0e%ud835%udf0e\(7)%u0009%u0009%u0009%u0009%u0009%ud835%udf07%ud835%udf07 = N%ud835%udf00%ud835%udf00!&%ud835%udf00%ud835%udf00!%u2264 1%u0009%u0009|%ud835%udf00%ud835%udf00!&| %u2264 |%ud835%udf00%ud835%udf00!|1%u0009%u0009%u0009%u0009%u0009%u0009%u0009%u0009%u0009%u0009%u0009%u0009|%ud835%udf00%ud835%udf00!&| %u2265 |%ud835%udf00%ud835%udf00!|(8)%ud835%udf09%ud835%udf09 =%u2212%ud835%udf0e%ud835%udf0e\2%ud835%udc38%ud835%udc38%ud835%udc38%ud835%udc38%u210e %u2212 %ud835%udf0e%ud835%udf0e\%ud835%udc5a%ud835%udc5a%ud835%udc5a%ud835%udc5a%ud835%udc5a%ud835%udc5a %ud835%udf0e%ud835%udf0e\(9)%ud835%udf0e%ud835%udf0e\+(1 %u2212 %ud835%udf09%ud835%udf09)%u2212 %ud835%udf0e%ud835%udf0e\90 %u2212 %ud835%udf0e%ud835%udf0e\ (10)%ud835%udf00%ud835%udf00\(11)%ud835%udc53%ud835%udc53!\%ud835%udefd%ud835%udefd $ %u210e100(&,'1 + %ud835%udefd%ud835%udefd $ %u210e100(&,' %ud835%udc53%ud835%udc53(%,$% [%ud835%udc40%ud835%udc40%ud835%udc40%ud835%udc40%ud835%udc40%ud835%udc40] (1)%ud835%udf05%ud835%udf05 =%ud835%udf0b%ud835%udf0b2 %u2212 arctan (%ud835%udc4e%ud835%udc4e) (2)%ud835%udf05%ud835%udf05 =%ud835%udf00%ud835%udf00%! %u2212 %ud835%udf00%ud835%udf00%\70 (3)%ud835%udf09%ud835%udf09 = >%ud835%udf00%ud835%udf00!(>%ud835%udf00%ud835%udf00\(4) %ud835%udf09%ud835%udf09* + 3%ud835%udf09%ud835%udf09+ %u2212 12%ud835%udc40%ud835%udc40$,-%ud835%udc4f%ud835%udc4f%ud835%udc4f%ud835%udc4f%ud835%udc4f%ud835%udc4f%u210e* = 0 (5)(2%ud835%udc38%ud835%udc38%ud835%udc38%ud835%udc38%u210e %u2212 %ud835%udf0e%ud835%udf0e\ + 2%ud835%udf0e%ud835%udf0e\(6)13 %ud835%udc4f%ud835%udc4f%ud835%udc4f%ud835%udc4f%ud835%udc4f%ud835%udc4f%ud835%udf07%ud835%udf07*%u210e*%ud835%udf09%ud835%udf09* +%ud835%udc4f%ud835%udc4f%ud835%udc4f+6 G((1 %u2212 %ud835%udf07%ud835%udf07) $(%ud835%udf07%ud835%udf07 + 2)%ud835%udf0e%ud835%udf0e! + (2%ud835%udf07%ud835%udf07 + 1)%ud835%udf0e%ud835%udf0e!& + C2%ud835%udf0e%ud835%udf0e\+%u2212%ud835%udc4f%ud835%udc4f%ud835%udc4f6%ud835%udf05%ud835%udf05 I(4%u210e%ud835%udf05%ud835%udf05 %u2212 %ud835%udf00%ud835%udf00\+%ud835%udc4f%ud835%udc4f6%ud835%udf05%ud835%udf05+ I(2%u210e+%ud835%udf05%ud835%udf05+ %u2212 %u210e%ud835%udf05%ud835%udf05%ud835%udf05%ud835%udf05\ %u2212 %ud835%udf00%ud835%udf00\+)%ud835%udf0e%ud835%udf0e\(7)%u0009%u0009%u0009%u0009%u0009%ud835%udf07%ud835%udf07 = N%ud835%udf00%ud835%udf00!&%ud835%udf00%ud835%udf00!%u2264 1%u0009%u0009|%ud835%udf00%ud835%udf00!&| %u2264 |%ud835%udf00%ud835%udf00!|1%u0009%u0009%u0009%u0009%u0009%u0009%u0009%u0009%u0009%u0009%u0009%u0009|%ud835%udf00%ud835%udf00!&| %u2265 |%ud835%udf00%ud835%udf00!|(8)%ud835%udf09%ud835%udf09 =%u2212%ud835%udf0e%ud835%udf0e\2%ud835%udc38%ud835%udc38%ud835%udc38%ud835%udc38%u210e %u2212 %ud835%udf0e%ud835%udf0e\%ud835%udc5a%ud835%udc5a%ud835%udc5a%ud835%udc5a%ud835%udc5a%ud835%udc5a %ud835%udf0e%ud835%udf0e\(9)%ud835%udf0e%ud835%udf0e\+(1 %u2212 %ud835%udf09%ud835%udf09)%u2212 %ud835%udf0e%ud835%udf0e\90 %u2212 %ud835%udf0e%ud835%udf0e\ (10)%ud835%udf00%ud835%udf00\(11)Fig. 7: Strain distribution V1-B3. Fig. 8: Strain distribution V2-B3.Table 4: Normalized compression zone height V1.Table 6: Normalized mean values of moment, curvature, and strain for V1.Table 5: Normalized compression zone height V2.Table 7: Normalized mean values of moment, curvature, and strain for V2.((Tab. 4)) ((Tab. 5)) ((Tab. 6)) ((Tab. 7)) ((Tab. 8)) ((Tab. 9)) !!\!$%!# !\!()*# !(+\!${body.pageText}-,#./ !\!\!\.0 !\!\!\!\.1 !\!\!\!\!\.2.3 !\!\!\!\.4 !\!\!\!\56 78/4 78/0 7879 7879 787:- 7870 7870 7870 7870 7870;<= /7> /:> /9> /:> 0/>!!\!$%!# !\!()*# !(+\!${body.pageText}-,#./ !\!\!\!\.0 !\!\!\!\.1 !\!\!\!\.2 !\!\!\!\.3.4 !\!\!\!\56 78/3 78// 7879 7879- 7870 7871 787/ 787/:;< //= 02= /4= />=! ! \$%&$ !\$%&# $%!#