👋 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 moment resistance (aka capacity) of a RC section with given tension reinforcement 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 shear analysis of the section.

Geometry
Section
	Width	300mm
	Height	500mm
Reinforcement
	Tension Rebar	3T25

Material
Concrete
	Strength	30 MPa
Rebar
	Strength	500 MPa

Assumption
$cover, cc$	=	$50mm$
$shear links dia.$	=	$8mm$

🔢 Calculation Steps

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

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

Neutral Axis x ^ⓘ
$x$	=	$\frac{(f_{yk}/\gamma_{s}) \cdot A_{s}}{\lambda \cdot \eta \cdot \alpha_{cc} \cdot (f_{ck} / \gamma_{c}) \cdot b}$
	=	$\frac{(500MPa/1.15) \cdot 1472mm²}{0.8 \cdot 1 \cdot 0.85 \cdot (30MPa / 1.5) \cdot 300mm}$
	=	$156 mm$

Check Limit of Neutral Axis x
$0.125d ≤$	x	$≤ 0.45d$
$54 ≤$	156	$≤ 193$
$∴ x$	=	$156 mm$

Hence, lever arm ^ⓘ
$z$	=	$d - ( \lambda \cdot x ) / 2$
	=	$429 mm - ( 0.8 \cdot 156 mm ) / 2$
	=	$366 mm$

Moment Capacity
$M_{Ed}$	=	$\frac{f_{yk}}{\gamma_{s}} \cdot A_{s} \cdot z$
	=	$\frac{500MPa}{1.15} \cdot 1472 mm² \cdot 366 mm$
	=	$234kNm$

∴ The Moment Capacity of the Section is 234kN.

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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.