RC Structures and Moment of Resistance Calculations

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Questions and Answers

Match the following types of failure with their corresponding condition:

Balanced failure = p = p_b Compression failure = p > p_b Tension failure = p < p_b No failure = p = 0

Match the following reinforcement ratios with their respective reactions:

p = 0.01 = Tension failure p = 0.013 = Balanced failure p = 0.01611 = Tension failure p = 0.02 = Balanced failure

Match the following concrete grades with their corresponding $f_{cd}$ values:

C16 = $1.25$ C20 = $1.25$ C25 = $1.56$ C30 = $1.75$

Match the concepts with their definitions or characteristics:

$M_r$ = Moment resistance $p_b$ = Balanced reinforcement ratio $f_{yd}$ = Design yield strength of steel $f_{cd}$ = Design compressive strength of concrete Signup and view all the answers

Match the materials with their strengths:

B420C = $f_{yk} = 420 N/mm^2$ C16 = $f_{cd} = 16.7 N/mm^2$ C20 = $f_{cd} = 20 N/mm^2$ C25 = $f_{cd} = 25 N/mm^2$ Signup and view all the answers

Match the following formulas with their application:

$M_r = p_b.b.w.d^2.f_{yd}(1-0.599.rac{p.f_{yd}}{f_{cd}})$ = For calculating moment resistance $A_{st} = 0.85 f_{cd} b.w.a$ = For calculating reinforcement area $σ_s = 600 k_1 rac{d-a}{a}$ = To determine stress in steel $p_b = 0.85 k_1 rac{f_{cd}.600}{f_{yd}.600+f_{yd}}$ = To find balanced reinforcement ratio Signup and view all the answers

Match the following structural elements with their components:

RC-section = Reinforced concrete section Bending = Moment applied shear = Force applied perpendicular Axial load = Load along the axis Signup and view all the answers

Match the following failure types with their characteristic strains:

Balanced failure = $ε_s= ε_{sgd} = rac{f_{yd}}{ε_s}$ Compression failure = $ε_{cu} = 0.003$ Tension failure = $ au_s < f_{yd}$ No failure = None of the above Signup and view all the answers

Match the types of steel processing with their characteristics:

Hot rolled = Processed at high temperatures Cold worked = Processed at room temperature Signup and view all the answers

Match the concrete mix related terms with their definitions:

Ecu = Strain limit for concrete p = Ratio of tensile reinforcement area to the beam dimensions Signup and view all the answers

Match the properties of reinforcement with the appropriate values:

$φ_{min}$ = $7-12mm$ minimum diameter $S_{max}$ = $0.85p rac{f_{yd}}{f_{cd}}$ Signup and view all the answers

Match the failure modes with their criteria:

Tension failure = $p < p_b$ Compression failure = $σ_s = f_{yd}$ at failure point Signup and view all the answers

Match the minimum spacing criteria for reinforcement with the specific terms:

$S_{min}$ = $0.8 rac{f_{yd}}{f_{cd}}$ $S_{max}$ = Up to $0.02$ Signup and view all the answers

Match terms related to stress distribution in beams with their symbols:

$A_{sfyd}$ = Area of effective tensile reinforcement $M_r$ = Moment capacity Signup and view all the answers

Match the parameters related to the tension failure with their descriptions:

$ε_s ≥ ε_{syd}$ = Steel strain exceeds yield strain $A_{sfyd}$ = Calculated using $A_{sfyd} = 0.85 f_{cd} a.b.w$ Signup and view all the answers

Match the strain characteristics of concrete with their limits:

$Ecu$ = $0.003$ strain limit $p_b$ = Critical point of reinforcement ratio Signup and view all the answers

Match the definitions to the terms used in beam reinforcement:

$a$ = Depth of neutral axis related to tensile area $d$ = Effective depth of the beam Signup and view all the answers

Match the terms of tension reinforcement configuration with their values:

$p$ = Concrete tensile reinforcement ratio $A_s$ = Tensile area of reinforcement Signup and view all the answers

Match the failure modes in beams with their explaining factors:

Tension failure = Corresponds with $p < p_b$ Compression failure = Involves excessive stress on compressive components Signup and view all the answers

Match the reinforcement design parameters with their formulas:

$M_r$ = $p_b.b.w.d^2.f_{yd}(1-0.599)$ $S_{min}$ = $0.8 rac{f_{yd}}{f_{cd}}$ Signup and view all the answers

Match the reinforcement spacing descriptions with their criteria:

$S_{min}$ = Minimum distance between reinforcement $S_{max}$ = Maximum allowable distance for effective stress distribution Signup and view all the answers

Study Notes

Advantages and Drawbacks of RC

Steel is hot rolled and cold worked.
Concrete mix is used.

Stress Distribution in a Beam

Ecu = 0.003
0.85 fed
Fc = 0.85fcd. a. bw
2 = yd (Lever arm)
FS = As.

TS500 and TS500

Smin = 0.8 fyd
Smax = 0.85 fyd
≤0.02

Tension Failure

p < Pb
Es > Eaydos = fyd
Asfyd = 0.85 fcd abw

Balanced Failure

Es = Esyd = fyd
Mb = 0.85 k₁fcd bwd² (1-0.599 fyd)

Compression Failure

Ecu = 0.003
Ts < fyd
Asfyd = 0.85 fcd bwd
a = 600 k₁ d -a
< fyd

Moment of Resistance (Mr)

Mr = Fo.2 = Fs. 2
p=0.85fcd.k1.600
fyd

Example Calculations (Page 3)

Calculate Mr and reinforcement quantity for rectangular-section with dimensions of 25x55cm and reinforcement ratio p=0.01.
Given different reinforcement types (C16, C20, C25).
Results are presented for each type and failure condition.

Concrete and Steel Strength Effect on Moment (Page 4)

Concrete strength has less effect on moment of resistance compared to steel.

Example Calculation (Page 4)

Examine a reinforced concrete section for conformance with TS500
Define the type of failure.
Parameters include fck, fyk, ym, and fcd.
Tensile and compressive reinforcement are calculated, and stirrup parameters are considered.

Reinforcement Ratio Check (Page 5)

Calculating specific reinforcement ratios (p and pw).
Checking these ratios against specific limits to ensure compliance with standards, for tensile or compression failure.
Includes calculations checks (p < 0.85pb, p <0.02, etc.).
Values to ensure compliance.

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Description

This quiz explores the advantages and drawbacks of reinforced concrete (RC), focusing on stress distribution in beams and different failure modes. It includes practical calculations for the moment of resistance and the effect of concrete and steel strength on structural integrity.