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1. REINFORCED CONRETE (1)
(CE411)
Chapter 3-b
Flexural Analysis and Design of
Beams
Instructor:
Eng. Abdallah Odeibat
Civil Engineer, Structures , M.Sc.
1

2. EXAMPLE
 For concrete section of b= 250 mm, d=435 mm
and h=500mm, find the steel area required to
resist Mu = 350 kN.m, material strength are fc’ =
28MPa and fy=420 MPa ?
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3. SOLUTION
 Since we need to exceed maximum reinforcement
ratio, we need to:
1. Enlarge the cross section, or
2. Use doubly reinforced section (compression
reinforcement).
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4. DOUBLY REINFORCED BEAMS
 If a beam cross section is limited of architectural
or other considerations
Reinforcement is added in the compression zone
resulting in Doubly Reinforced Beams
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5. REASONS FOR PROVIDING
COMPRESSION REINFORCEMENT
 Reduced sustained load deflections.
 Increased Ductility.
 Change failure mode from compression to
tension. When r > rbal addition of As strengthens.
 Eases in Fabrication
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6. ANALYSIS
1. Tension and Compression Steel Yield
2. Compression Steel Below Yield 6

7. 1. TENSION AND COMPRESSION STEEL
YIELD
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8. 8

9. 2. COMPRESSION STEEL BELOW YIELD
 If compression steel is not yielded compression
stress in steel fs’, then
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10. 10

11.  To determine whether compression steel will
have yielded or not , the following equation is
used:
 If , compression steel not yield
 If , compression steel yield
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12. ANALYSIS PROCEDURE
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Given b, d, d’, As, As’,
fy, fc’
Check
No Yes
Analyze As
Singly
Reinforced
(disregard
Compression
Reinforcement)
Analyze As
Doubly
Reinforced
Check
No Yes Compression
Steel not
Yield
Compression
Steel Yield
Slide 9 & 10
Slide 7 & 8

13. EXAMPLE
 Find Nominal moment for
Given:
b= 300 mm
d= 600 mm
d’= 65 mm
As= 4914 mm2
As’= 1020 mm2
fc’= 35 MPa
fy= 420 MPa 13

14. SOLUTION
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15. EXAMPLE
 Find Nominal moment for
Given:
b= 300 mm
d= 550 mm
d’= 65 mm
As= 6ø30 = 4241 mm2
As’= 2 ø25 = 982 mm2
fc’= 35 MPa
fy= 420 MPa 15

16. 16

17. 17

18. DESIGN EXAMPLE
 A rectangular beam with width of 250 mm and
total depth of 500 mm, is to be designed to carry
an ultimate moment of 287.2 kN.m. fy =420 MPa,
fc’ = 28 MPa. Determine Area(s) of reinforcement
steel ?
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19. SOLUTION :
 Check if this beam can be designed as singly
reinforced (using d =400 mm) :
 a = 145.7 mm , c=171.4 mm
 Can not be designed as singly
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20. SOLUTION :
 The remaining moment to be carried by
compression steel couple:
 To check whether compression steel will reach yield
stress (fs’ >fy) or not …
 Calculating fs’
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21. SOLUTION :
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22. SOLUTION :
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Use 4ø30 (in two layers ) , As= 2827 mm2
Use 2ø 20 , As’= 628 mm2