b) The rectangular section shown below is subjected to a moment of M=257kN.m. Assume a cracked section and calculate the elastic stresses in the concrete and reinforcement at loading Cross-section: width height Modulus of elasticity: concrete reinforcement Reinforcement: depth area b:= 406-mm h := 793-mm Ec := 26.6-GPa Es := 200-GPa d:= 721 mm A, 3039-mm 2 h b - A's A₂ d':= 72 mm A's= 1548-mm 2 d

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
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b) The rectangular section shown below is subjected to a moment of M=257kN.m. Assume a cracked
section and calculate the elastic stresses in the concrete and reinforcement at loading
Cross-section:
width
height
Modulus of elasticity:
concrete
reinforcement
Reinforcement:
depth
area
b:= 406-mm
h := 793-mm
Ec
:= 26.6-GPa
Es := 200-GPa
d:= 721 mm
A, 3039-mm
2
h
b
-
A',
A₂
d':= 72 mm
A's= 1548-mm
2
d
Transcribed Image Text:b) The rectangular section shown below is subjected to a moment of M=257kN.m. Assume a cracked section and calculate the elastic stresses in the concrete and reinforcement at loading Cross-section: width height Modulus of elasticity: concrete reinforcement Reinforcement: depth area b:= 406-mm h := 793-mm Ec := 26.6-GPa Es := 200-GPa d:= 721 mm A, 3039-mm 2 h b - A', A₂ d':= 72 mm A's= 1548-mm 2 d
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Follow-up Question

Please explain why we say (2n -1)As'

(721-x)
K-406mm
On
A₁ = 1548 mm²
A₁ = 3039 mm²
n =
*
Es
E
Neutral
I.
200 G Pa
26.6 GPa
203x²
axis
Locating
(b) (x) (²/2) + (2n-1) A's (x-d') = n As (d-x)
K-406mm
= 7.519
solving above
(406) (x))+ (2x 7.519 -1) (1548) (x - 72) = (7-519) (3039) (721-x)
+ 21730 824 (x-72). = 22850241 (721-x)
equation,
get
x = 207.88 mm
-(2n-1) As
we
-nA₂
Transcribed Image Text:(721-x) K-406mm On A₁ = 1548 mm² A₁ = 3039 mm² n = * Es E Neutral I. 200 G Pa 26.6 GPa 203x² axis Locating (b) (x) (²/2) + (2n-1) A's (x-d') = n As (d-x) K-406mm = 7.519 solving above (406) (x))+ (2x 7.519 -1) (1548) (x - 72) = (7-519) (3039) (721-x) + 21730 824 (x-72). = 22850241 (721-x) equation, get x = 207.88 mm -(2n-1) As we -nA₂
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