Chapter 5-End Zones

Helwan University University F aculty aculty of E ngineering ngineering-Matar -Mataria ia Prof. Dr. Ahmed Moussa Prof. Dr. Alaa Sherif  Dr. Hatem Seliem

Third Y ear Civil E ngineering ngineering E lective lective Course 1: P restressed restressed Concrete Concrete

CHAPTER 5 DESI ESI GN OF ANCHORAGE ANCHORA GE ZON ZONES 5.1 ST RES RE SS DI ST RI BUTI ON AT END ZONES ZONES Stress trajectories

t

Uniform Stress Distribution

Prestressing Force

La

Fig. 1: 1: Ide I dealized stress stress pat paths hs at end end bl block of prestress prestressiing force force

 Ten  Tension sion Stresses

Prestressing t Force

+ -

Compression Stresses

La

Fig. 2: Stress distribution along centerline of an anchorage zone Page 1 of 5

Helwan University Faculty of Engineering-Mataria Prof. Dr. Ahmed Moussa Prof. Dr. Alaa Sherif  Dr. Hatem Seliem

Third Year Civil Engineering Elective Course 1: Prestressed Concrete

5.2 FAIL URE TY PES -

Bearing failure underneath anchorage plate

-

Splitting failure of concrete

Fig. 3: Spiral Reinforcement at the anchorage zone

Page 2 of 5

Helwan University Faculty of Engineering-Mataria Prof. Dr. Ahmed Moussa Prof. Dr. Alaa Sherif  Dr. Hatem Seliem

Third Year Civil Engineering Elective Course 1: Prestressed Concrete

DESIGN FOR BEARI NG f bu ≤ f bcu f bu =applied ultimate bearing stress

f bu =

1.2× P j Aanchor plate

f buc =ultimate bearing stress resistance of the concrete f buc = 0.67×

f cu γ  c

×

A2 A1

where

A1

=area of bearing plate

A2

=maximum area of bearing

A2 ≤ 2.0 A1

A1=axb 2 1

d

A2=(a+4d)x(b+4d)

Page 3 of 5

Helwan University Faculty of Engineering-Mataria Prof. Dr. Ahmed Moussa Prof. Dr. Alaa Sherif  Dr. Hatem Seliem

Third Year Civil Engineering Elective Course 1: Prestressed Concrete

5.3 DESIGN OF SPLITT ING REI NFORCEM ENT 5.4.1 Strut-and-Tie Method

P/2 t

Prestressing Force P

 Ts

h

P/2

t/4 Uniform Stress Distribution t/4 t/4 t/4

t/2

⎛  h ⎞  Ts = 0.25× P⎜1− ⎟ ≅ 0.25P ⎝  t ⎠ 5.4.2 Beam Analogy

P/2 t/2

t/4

P/2 h/4

 Ts

Cs t/2

Mb =

P ⎛  t h ⎞ P × ⎜ − ⎟ = × (t − h) 2 ⎝ 4 4 ⎠ 8

 Ts =

M b P ⎛  h ⎞ = × ⎜1− ⎟ t / 2 4 ⎝  t ⎠

Page 4 of 5

Helwan University Faculty of Engineering-Mataria Prof. Dr. Ahmed Moussa Prof. Dr. Alaa Sherif  Dr. Hatem Seliem

Third Year Civil Engineering Elective Course 1: Prestressed Concrete

EXAMPLE

Reference: “Design of Reinforced Concrete structures”, Volume 3, by Mashour Ghoneim and Mahmoud El-Mihilmy

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