👋 Introduction

Moment design is one of the first essential design in most of the reinforced concrete(RC) beam, as moment existed basically in every siutation. This articles aim to demonstrate the steps involoved in calculating the tension reinforcement of a RC section with given moment through worked numerical examples.

The concept behind and corresponding equations used can be found in other articles What Are the Assumptions of Bending Design in Reinforced Concrete?, What is lever arm? and What is neutral axis?.

📐 Design Data

Below are the design information of the tension reinforcement design of moment analysis of the section.

Geometry
Section
	Width	350mm
	Height	500mm

Material
Concrete
	Strength	30 MPa
Rebar
	Strength	500 MPa

Design Action
	Moment My	185kNm

Assumption
$cover, cc$	=	$50mm$
$shear \ links \ dia., \phi_{shear}$	=	$8mm$
$tension \ reinforcement \ dia., \phi_{tension}$	=	$25mm$

🔢 Calculation Steps

*Unless otherwise specified, all clauses and equations quoted herein are based on BS EN 1992-1-1:2004.

Effective Depth ^ⓘ
$d$	=	$h - cc - \phi_{shear} - \phi_{tension}/2$
	=	$600 mm - 50 mm - 8 mm - 25 mm /2$
	=	$429 mm$

Moment Coeff.
$K$	=	$\frac{M_{Ed}}{b * d^2 * f_{ck}}$
	=	$\frac{185kNm}{350 mm * 429 mm^2 * 30 MPa}$
	=	$0.1$

Check Limit of K Coeff.
$K_{min} ≤$	K	$≤ K'$
$0.05 ≤$	0.1	$≤ 0.17$
$∴ K$	=	$0.1$

Hence, lever arm ^ⓘ
$z$	=	$(0.5 + \sqrt{0.25 - \frac{K}{0.9}} * d)$
	=	$(0.5 + \sqrt{0.25 - \frac{0.1}{0.9}} * 429 mm)$
	=	$160 mm$

Minimum Tension Rebar Area

Minimum Tension Rebar Area
$A_{s,min}$	=	$min(0.26 \cdot \frac{f_{ctm}}{f_{yk}}b \cdot d, 0.0013 \cdot b\cdot d)$
	=	$min(0.26 * \frac{2.9MPa}{434MPa}350mm \cdot 429mm, 0.0013 \cdot 350mm \cdot 429mm)$
	=	$260 mm²$

Tension Rebar Area
$A_{s,req}$	=	$\frac{M_{Ed}}{(f_{yk}/\gamma_{s}) \cdot z}$
	=	$\frac{185kNm}{(500MPa/1.15) \cdot 160mm}$
	=	$2650mm² > 260mm², OK$

Bar Dia.	Number	As Provided	notation	utilization
32	4	3217	4T32	82%
40	3	3770	3T40	70%
16	14*	2814	14T16	94%

[*] Note: Section width is insufficient for a single row of rebars. Multiple rows required.

∴ The tension rebar area need to provided 2650mm² and the Recommend Rebar Arrangement is 4T32.

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#rc design #moment design #work example #structural

CivilSimple Team

The CivilSimple Team writes practical engineering guides for the profession and the curious. All articles are reviewed for technical accuracy before publication.