Crack width, deflection, and strain limits of concrete beams with unstressed seven-wire steel strands as longitudinal reinforcement

ABSTRACT

This study designed and tested six prototype beams longitudinally reinforced with either SD420 deformed steel bars, unstressed 1860-MPa seven-wire steel strands, or a combination of these. The experiment revealed that the displacement, crack width, and crack spacing increased with the increasing number of strands used to replace deformed bars as longitudinal reinforcement. Crack width was estimated using Frosch’s equation, which conservatively predicted the maximum crack width for beams with deformed bars and those with both strands and deformed bars; a modified version of the equation yielded more accurate values for the beams reinforced with strands only. A bond coefficient for strands was used in the modified equation. Strain limits for the tension- and compression-controlled sections of the beams with strands were determined to be 0.0145 and 0.0115, respectively. The deflection of the beams was well estimated using the ACI 318–19 equation.

COEDITOR-IN-CHIEF:

• Su, Shun-Feng

ASSOCIATE EDITOR:

• Chen, Jeng-Tzong

KEYWORDS:

• Unstressed seven-wire steel strand
• crack width
• strain limits
• deflection

Nomenclature

$a$	=	shear span
$A_s$	=	area of longitudinal tension reinforcement
$A{{ }^{\mathrm{\prime }}}_s$	=	area of longitudinal compression reinforcement
$b$	=	width of the beam
$d$	=	distance from extreme compression fiber to centroid of longitudinal tension reinforcement
$d^{\ast }$	=	controlling cover distance
$d_c$	=	concrete cover to the centroid of the reinforcement
$E_c$	=	modulus of elasticity of concrete
$E_{ps}$	=	modulus of elasticity of strand
$f_c$	=	stress in concrete
$f{{ }^{\mathrm{\prime }}}_c$	=	specified compressive strength of concrete
$f{{ }^{\mathrm{\prime }}}_{ca}$	=	actual compressive strength of concrete
$f_{p,avg}$	=	stress in strands, obtained from test result by taking the average
$f_{p,max}$	=	stress in strands, obtained from test result by taking the maximum
$f_{ps}$	=	stress of strand
$f_{pu}$	=	specified tensile strength of strands
$f_{pua}$	=	actual tensile strength of strands
$f_{py}$	=	specified yield strength of strands
$f_{pya}$	=	actual yield strength of strands
$f_r$	=	modulus of rupture of concrete
$f_{s,avg}$	=	stress in deformed bars, obtained from test result by taking the average
$f_{s,max}$	=	stress in deformed bars, obtained from test result by taking the maximum
$f_{ua}$	=	actual tensile strength of deformed bars
$f_y$	=	specified yield strength of deformed bars
$f_{ya}$	=	actual yield strength of deformed bars
$f_{yt}$	=	specified yield strength of transverse reinforcement
$f_{yta}$	=	actual yield strength of transverse reinforcement
$h$	=	depth of the beam
$I_{cr}$	=	cracking moment of inertia
$I_e$	=	effective moment of inertia
$I_g$	=	specimen gross moment of inertia
$k_b$	=	bond coefficient
$L$	=	beam span, the distance between two supports
$M_{0.53}$	=	moment corresponding to maximum crack width of 0.53 mm
$M_{cr}$	=	cracking moment
$M_n$	=	nominal moment capacity
$M_{n,exp}$	=	nominal moment capacity calculated from the test result
$M_{na}$	=	moment capacity estimated with actual material strength
$M_{ser}$	=	moment corresponding to service loading
$P_{0.53}$	=	force corresponding to maximum crack width of 0.53 mm
$P_{max}$	=	maximum shear force obtained from the test result
$P_y$	=	idealized yield force
$S_{c,avg}$	=	average crack spacing
$S_{c,max}$	=	maximum crack spacing
$V_{Mn}$	=	maximum shear force corresponding to $M_n$
$V_n$	=	nominal shear strength
$w$	=	crack width
$\delta$	=	midspan displacement
${\delta }_{ana}$	=	estimated deflection
${\delta }_u$	=	idealized ultimate displacement of midspan
${\delta }_y$	=	idealized yield displacement of midspan
${\epsilon }_c$	=	average tensile strain of concrete
${\epsilon }_{ps}$	=	strain of strand
${\epsilon }_t$	=	net tensile strain in the extreme layer of longitudinal tension reinforcement at nominal strength
${\epsilon }_{ty}$	=	strain corresponding to $f_y$
$\rho$	=	ratio of $A_s$ to $bd$
$\rho { }^{\mathrm{\prime }}$	=	ratio of $A{{ }^{\mathrm{\prime }}}_s$ to $bd$

Acknowledgments

The authors would like to thank the National Science and Technology Council of Taiwan under Contract Nos. 106-2221-E-002-233-MY3 and Ruentex Engineering and Construction in Taiwan for providing financial support.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work was supported by the National Science and Technology Council of Taiwan [106-2221-E-002-233-MY3]; Ruentex Engineering and Construction, Taiwan