The document discusses different types of composite structural systems that combine steel and concrete elements. It describes composite slabs made with metal decking and concrete topping that act as diaphragms transferring shear forces. It also discusses composite girders that use shear stud connectors to increase the moment of inertia of the beam and girder, and composite columns with a steel core encased in concrete or steel tubes filled with concrete. The document emphasizes that composite systems allow for more efficient use of the dissimilar properties of steel and concrete in buildings.

1. 1
Dr Youssef Hammida
SEISMIC DESIGN OF COMPOSITE
SHEAR WALLS & FRAMES
‫ﺟدران‬ ‫واﻟزﻻزل‬ ‫اﻟرﯾﺎح‬ ‫ﻣﻘﺎوﻣﺔ‬
‫ﻗﺻﯾﺔ‬‫ﻣرﻛﺑﺔ‬‫واطﺎرات‬

2. 2
The structural system of a building is a complex three-
dimensional assembly of interconnected discrete or continuous
structural elements.
The primary function of the structural system is to carry all the loads
acting on the building effectively and safely to the foundation.
The structural system is therefore expected to:
 Carry dynamic and static vertical loads.
 Carry horizontal loads due to wind and earthquake effects.
 Resist stresses caused by temperature and shrinkage effects.
 Resist external or internal blast and impact loads.
 Resist, and help damp vibrations and fatigue effects.
 steel-concrete composite systems for buildings are
composed of concrete components that interact with
 structural steel components within the same system
COMPOSITE ACTION BETWEEN STRUCTURAL
ELEMENTS IN BUILDINGS
 Steel and concrete are the major materials used in composite
systems.
 Although they have several dissimilar physical
characteristics, it is possible to use them together,
beneficially, in different ways.
 A number of systems have been developed in the last few
decades which successfully combine steel and concrete. The
following composite systems have been used for a wide
range of buildings: ‫اﻧﻮا‬‫ع‬‫واﻟﺸﺎﻗﻮﻟﯿﺔ‬ ‫اﻷﻓﻘﯿﺔ‬ ‫ﻟﻠﺤﻤﻮﻻت‬ ‫اﻟﻤﺮﻛﺒﺔ‬ ‫اﻟﺠﻤﻞ‬

3. 3
1. Frame structure ‫اﻻطﺎرات‬ ‫ﺟﻣﻠﺔ‬
2. Shear wall structure ‫اﻟﻘص‬ ‫ﺣدران‬ ‫ﺟﻣﻠﺔ‬
3. Staggered shear wall system ‫اﻟﻣ‬ ‫اﻟﻘص‬ ‫ﺟدران‬‫ﺗ‬‫ﻧﺎوﺑﺔ‬
4. Tubular system ‫واﻻﻧﺑوﺑﯾﺔ‬ ‫اﻟﺷﺑﻛﯾﺔ‬ ‫اﻟﺟﻣل‬
‫اﻟﻤﺮﻛﺒﺔ‬ ‫اﻷﺳﻘﻒ‬ ‫ﺑﻼطﺎت‬

4. 4

5. 5

6. 6

7. 7
‫اﻟﻤﺮﻛﺒﺔ‬ ‫واﻟﺒﻼطﺎت‬ ‫اﻟﺠﺎھﺰة‬ ‫اﻟﻤﻘﺎطﻊ‬

8. 8

9. 9
 COMPOSITE MEMBERS ‫اﻟﻣرﻛﺑﺔ‬ ‫اﻟﻣﺟﻣﻌﺔ‬ ‫اﻟﻌﻧﺎﺻر‬
To get an idia into the composite behavior of structural steel and
reinforced concrete systems, it is to study common techniques of
compositing the following structural units:
1. Composite slabs ‫واﻟطواق‬ ‫اﻷﺳﻘف‬ ‫ﺑﻼطﺎت‬
2. Composite beams‫اﻟﻣرﻛﺑﺔ‬ ‫اﻟﻛﻣرات‬
3Composite columns ‫اﻟﻣرﻛﺑﺔ‬ ‫ﻋﻣدة‬ ‫اﻷ‬
4. Composite diagonals ‫اﻟﻣرﻛﺑﺔ‬ ‫اﻟﻣﺎﺋﻠﺔ‬ ‫اﻟﻘطرﯾﺔ‬ ‫اﻟﻌﻧﺎﺻر‬
5. Composite shear walls ‫اﻟﻣرﻛﺑﺔ‬ ‫اﻟﻘص‬ ‫ﺟدران‬
Composite slabs ‫اﻟﻣرﻛﺑﺔ‬ ‫اﻟﺑﻼطﺎت‬
 In steel buildings, the use of high-strength, light-gauge (16–20 gauge)
metal deck with concrete topping has become a standard (see Figure 2.1).
 The metal deck has embossments pressed into the sheet metal to achieve
composite action with concrete slab.
When the concrete hardens, the steel deck becomes the tension reinforcement.
 The resulting composite slab acts as a diaphragm providing for the
horizontal transfer of shear forces to the vertical bracing elements.
Furthermore, it actsas a stability bracing for the compression flange of
steel beams.

10. 10
 The shear forces in the diaphragm mostly occur in the concrete slab
because the in-plane stiffness of concrete slab is significantly more than that
of the metal deck. Thus, the horizontal forces must transfer from the slab to
the beam top flange through welded studs
‫اﻟﻘوى‬‫اﻻ‬‫اﻟﺟﺳور‬ ‫اﻟﻰ‬ ‫اﻟﺑﻼطﺔ‬ ‫ﻣن‬ ‫ﺗﻧﺗﻘل‬ ‫واﻟزﻻزل‬ ‫اﻟرﯾﺎح‬ ‫ﻣن‬ ‫ﻓﻘﯾﺔ‬
‫واﻟﻛﻣر‬‫ا‬‫واﻷﺳﺎس‬ ‫ﻋﻣدة‬ ‫اﻷ‬ ‫ﺛم‬ ‫اﻟﻘص‬ ‫ﺑﺳﺎﻣﯾر‬ ‫ﺑواﺳطﺔ‬ ‫ت‬
‫ﻣﻘ‬ ‫ﻣﺳﺎﻣﯾر‬ ‫ﺗرﻛﯾب‬‫اﻟﻛﻣرة‬ ‫ﺑﯾن‬ ‫اﻟواﺻﻠﺔ‬ ‫اﻟﻘص‬ ‫ﺎوﻣﺔ‬-‫واﻟﺑﻼطﺔ‬ ‫اﻟﺟﺳر‬

11. 11
‫اﻟﻘص‬ ‫وﻣﺳﺎﻣﯾر‬ ‫اﻟﺻﺎج‬ ‫اﻟواح‬ ‫ﺗرﻛﯾب‬

12. 12
Composite Girders ‫اﻟﻣرﻛﺑﺔ‬ ‫اﻟﻛﻣرات‬ -‫اﻟﺟﺳور‬
Consider a typical steel moment frame consisting of beams rigidly connected to
columns.
 Therefore, to limit the sway under lateral loads, it is more prudenteffecting
to increase the girder stiffness rather than the column stiffness.
 Although frame beams are designed as non-composite, it is a usual
practice to use shear studs at a nominal spacing of say, 12 in.
 The shear connectors primarily provided for the transfer of diaphragm
shear also increase the moment of inertia of the girder.
 The increase, however, is not for the entire length of the girder because
under lateral load sit bends in a reverse curvature.
 Since concrete is ineffective in tension, the increase in the moment
of inertia can be counted on only in the positive moment region.

13. 13
‫ﺑﺎﻟﺧرﺳﺎﻧﺔ‬ ‫ﻣدﻓوﻧﺔ‬ ‫ﺗﻛون‬ ‫اﻟﻣرﻛﺑﺔ‬ ‫اﻟﻛﻣرات‬
‫ﺻﻠﺑﺔ‬ ‫ﺗﻛون‬ ‫ان‬ ‫وﯾﺣب‬ ‫اﻟﺑﻼطﺔ‬ ‫اﺳﻔل‬ ‫ظﺎھرة‬ ‫او‬
‫اﻟﺑﻼطﺔ‬ ‫ﻣﻊ‬ ‫اﺳﺎﺗﺎدھﺎ‬ ‫ﻧﻘﺎط‬ ‫ﻋﻧد‬
‫ﻣﻌدﻧﻲ‬ ‫دك‬ ‫ﯾﺗواﺟد‬ ‫ﻗد‬‫اﻟﺑﻼطﺔ‬ ‫اﺳﻔل‬
‫اﻟﻣﻌدﻧﯾﺔ‬ ‫اﻟﻛﻣرة‬ ‫ﻣﻊ‬ ‫ﺳﻼب‬ ‫ﺳوﻟد‬ ‫او‬

14. 14

15. 15

16. 16
‫اﻟﻛﻣرات‬ ‫اﺳﺗﻧﺎد‬ ‫ﺗﻔﺎﺻل‬–‫اﻟﻔوﻻذﯾﺔ‬ ‫اﻷﻋﻣدة‬ ‫ﻣﻊ‬ ‫اﻟﺟﺳور‬

17. 17
‫اﻟﻘص‬ ‫ﺟدار‬ ‫ﻣﻊ‬ ‫اﻟﻣﻌدﻧﻲ‬ ‫اﻟﺟﺳر‬ ‫اﻟﻛﻣرة‬ ‫اﺗﺻﺎل‬ ‫ﺗﻔﺎﺻﺑل‬‫اﻟﺟدار‬ ‫ﻓﻲ‬ ‫ﻣﺛﺑﺗﺔ‬ ‫ﺑزواﯾﺎ‬

18. 18

19. 19
‫ﺻﻼﺑﺔ‬ ‫زﯾﺎدة‬‫ﻋﻘدة‬‫اﻟﻌﺎﻣود‬‫ﺑﺎﻟدﻋﻣﺎت‬

20. 20
‫اﻟﺟﺳر‬ ‫ﻣﻊ‬ ‫اﻟﺷﺑﻛﻲ‬ ‫اﻟﺟﺎﺋز‬ ‫اﺗﺻﺎل‬-‫ﻛﻣرة‬‫ﻣﺣﯾطﯾﺔ‬‫ﺧرﺳﺎﻧﺔ‬
 Composite Columns ‫اﻟﻣرﻛﺑﺔ‬ ‫اﻷﻋﻣدة‬
Two types of composite columns are used in buildings (see Figure 2.2a
and b).
The first, commonly referred to as encased composite column, consists of a
steel core surrounded by a reinforced concrete envelope.
 The second referred to as filled composite column consists of a steel pipe or
tube filled with high-strength concrete.

21. 21

 In the first type, the steel core, most usually a wide flange section
placed within the reinforced concrete column is designed as an erection
column to carry construction loads only.
 Conceptually the behavior of a composite column is similar to a reinforced
concrete column, if the steel section is analytically replaced with an
equivalent mild steel reinforcement.
 In fact, this concept provides the basis for generating the interaction
diagram for the axial load and moment capacities of composite columns.
 Compositing of exterior columns by encasing steel sections with concrete is
by far the most frequent application of composite columns. The reasons are
entirely economic, because forming around interior columns is quite
involved and is not readily applicable to jump forms.

22. 22
 Exterior columns, on the other hand, are relatively open-faced: formwork
can be “folded” around steel columns for placement of concrete, then
unfolded and jumped to the next floor..
‫ﻣﻌدﻧﻲ‬ ‫ﻋﻣود‬‫ﻣرﻛب‬‫اﻟﺧرﺳﺎن‬ ‫ﻓﻲ‬ ‫ﻣﻌدﻧﯾﺔ‬ ‫وﺗﺷﺎرﯾك‬‫ة‬

23. 23
‫ﻣرﻛﺑﺔ‬ ‫اﻋﻣدة‬ ‫اﻟﻣﻌدﻧﻲ‬ ‫اﻟﺧﺎرﺟﻲ‬ ‫اﻟﻐﻼف‬

24. 24
‫اﻟﻣرﻛﺑﺔ‬ ‫اﻷﻋﻣدة‬ ‫اﺷﻛﺎل‬‫وﺗﺻﻣﯾم‬ ‫اﻻطﺎرات‬ ‫ﻣﻊ‬
‫اﻟﺿﻌﯾف‬ ‫واﻟﺟﺎﺋز‬ ‫اﻟﻘوي‬ ‫اﻟﻌﺎﻣود‬

25. 25
‫اﻷﻋﻣدة‬‫ﻟﻸﻋﻣدة‬ ‫اﻟﺷﺎﺋﻌﺔ‬ ‫اﻷﻧﻣﺎ‬ ‫اﺣد‬ ‫ﻫﻲ‬ ‫اﻟﻣﻐﻠﻔﺔ‬ ‫ﺔ‬ ‫اﻟﻔوﻻذ‬‫ﺔ‬ ‫اﻟﻣر‬.‫ﺔ‬ ‫اﻟﺻﻼ‬ ‫ﺑﯾن‬ ‫ﯾﺟﻣﻊ‬ ‫اﻟﻧظﺎم‬ ‫ﻫذا‬
‫وﻗﺎﺑﻠ‬‫ﺔ‬‫اﻹﻧﺷﺎﺋﻲ‬ ‫ﻟﻠﻔوﻻذ‬ ‫اﻹﻧﺷﺎء‬ ‫ﻋﺔ‬‫وﺳر‬ ‫اﻟﻘوة‬ ‫ﯾن‬ ‫و‬ ‫اﻟﻣﺳﻠﺣﺔ‬ ‫ﻟﻠﺧرﺳﺎﻧﺔ‬ ‫ﯾﻞ‬ ‫اﻟﺗﺷ‬
‫ﻟﻠوﺻول‬‫اﻟﻰ‬‫ﻣﻧﺷﺄ‬‫اﻗﺗﺻﺎد‬‫وﻣﻘﺎوم‬

26. 26
‫اﻟﻣﺻري‬ ‫اﻟﻛود‬‫ﺗﺻﻣﯾم‬‫اﻋﻣدة‬‫اطﺎرات‬‫ﻣرﻛﺑﺔ‬

27. 27

28. 28

29. 29
‫ﺗﺻﻣﯾم‬‫اﻟﻣرﻧﺔ‬ ‫اﻟطرﯾﻘﺔ‬ ‫اﻟﻣرﻛﺑﺔ‬ ‫اﻷﻋﻣدة‬

30. 30

31. 31
‫اﻣرﯾﻛﻲ‬ ‫ﻛود‬ ‫اﻟﻣرﻛﺑﺔ‬ ‫اﻷﻋﻣدة‬ ‫ﺗﺻﻣﯾم‬

32. 32

33. 33

34. 34
‫ا‬‫اﺗﺟﺎھﯾن‬ ‫اﻧﻌطﺎف‬ ‫ﻋزم‬ ‫ﻣرﻛﺑﺔ‬ ‫ﻋﻣدة‬‫ﻋﻠﻰ‬‫ﻣﺣورﯾن‬

35. 35

36. 36

37. 37
‫اﻵﺑﺎك‬ ‫ﻣﺧطط‬ ‫ﻣن‬ ‫اﻟﻣرﻛب‬ ‫اﻟﻌﺎﻣود‬ ‫ﺗﺻﻣﯾم‬‫ﺑﺎﺗﺟﺎھﯾن‬ ‫ﻋزم‬

38. 38

39. 39

40. 40
Composite diaGonals ‫اﻟﻣرﻛب‬ ‫اﻟﻣﺎﺋل‬ ‫اﻟﻘطري‬ ‫اﻟﻌﻧﺻر‬
As a part of a vertical truss, diagonals in a braced frame resist lateral forces
primarily through axial stresses.
 As a result, braced frames are more economical than moment-resisting
frames.
 However,their use is often limited, because of potential interference with
architectural planning concerns

41. 41
FIGURE 2.3 Japanese composite construction details: (a) beam column
intersection; (b and c) composite column with welded ties;
‫ﻣرﻛب‬ ‫اطﺎر‬ ‫ﻋﻘدة‬ ‫ﺗﻔﺻﯾل‬‫ﻟﻠﻌزوم‬ ‫ﻣﻘﺎوم‬

42. 42
Composite shear Walls ‫اﻟﻣرﻛﺑﺔ‬ ‫اﻟﻘﺻﯾﺔ‬ ‫اﻟﺟدران‬
 One of the most common uses of composite shear walls is in steel frame
buildings, in which selected bays are infilled with a reinforced concrete wall.
 In essence, this results in a reinforced concrete
shear wall with structural steel boundary elements and coupling beams (see
Figure 2.5). ‫ا‬‫اﻟﻣﻌدﻧﻲ‬ ‫اﻷﺑﻧﯾﺔ‬ ‫ﻓﻲ‬ ‫اﻟﻣرﻛﺑﺔ‬ ‫اﻟﻘﺻﯾﺔ‬ ‫اﻟﺟدران‬ ‫ﺳﺗﻌﻣﺎل‬‫ة‬
 If the coupling beams were pin-connected at each end to the boundary
elements, they would be ineffective in improving the lateral resistance of the
wall.
 This is because the two wall piers would
resist lateral loads independently.
 On the other hand, if the coupling beams are infinitely stiff, they
would fully couple the two piers coercing them to work as a single unit. If the
coupling beam stiffness is in between the two extremes, as is the case in most
buildings, the corresponding response will also be in between the two limits.
 Composite steel plate diaphragms are appropriate when extremely high
shear forces must be transferred from one system to another at the base of
the building.
 An example of this use may be
found again in the Bank of China Tower, Hong Kong, in which the entire

43. 43
base shear is transferred from the building perimeter to the building core at
the base, via a steel-plated floor diaphragm.
 Possible details of composite shear plate walls are shown in Figure 2.6. In
these details, structural steel framing surrounds the steel plates with the
entire steel assembly encased in reinforced
‫ﻟﻠﻌزوم‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫ﺳﺗﯾل‬ ‫ﻓوﻻذﯾﺔ‬ ‫ﻣﻌدﻧﯾﺔ‬ ‫اطﺎرات‬ ‫ﺿﻣن‬ ‫ﻣرﻛﺑﺔ‬ ‫اﻋﻣدة‬ ‫اﺳﺗﻌﻣﺎل‬

44. 44
‫ﺟدار‬‫وﺟ‬ ‫ﻋﻠﻰ‬ ‫ﻓوﻻذﯾﺔ‬ ‫ﺑﺻﻔﺎﺋﺢ‬ ‫ﻣرﻛب‬ ‫ﻗﺻﻲ‬‫ووﺟﮭﻲ‬ ‫واﺣد‬ ‫ﮫ‬‫ن‬

45. 45
‫اﻟﻧﮭﺎﯾﺎت‬ ‫ﻓﻲ‬ ‫اﻟﻣطﺎوﻋﺔ‬ ‫زﯾﺎدة‬ ‫اﻋﻣدة‬ ‫ﻣﻊ‬ ‫ﻣرﻛب‬ ‫ﻗﺻﻲ‬ ‫ﺟدار‬‫واﻟوﺳط‬
‫اﻟﻘص‬ ‫ﺗﺷﺎرﯾك‬ ‫ﻟﺣﺎم‬

46. 46
‫ا‬‫ﻓوﻻذي‬ ‫ﺑروﻓﯾل‬ ‫ﻣﻊ‬ ‫ﻣرﻛﺑﺔ‬ ‫اﻟﻘﺻﻲ‬ ‫اﻟﺟدار‬ ‫ﻧﮭﺎﯾﺎت‬ ‫ﻋﻣدة‬

47. 47
‫ج‬‫ﻓوﻻذﯾﺔ‬ ‫ﻛﻣرة‬ ‫ﻣﻊ‬ ‫ﻣرﻛب‬ ‫ﻗﺻﻲ‬ ‫دار‬‫اﻟﻠدن‬ ‫اﻟﻣﻔﺻل‬ ‫وﺗﺷﻛل‬ coupling Beam

48. 48
‫اﻟﻣﺳﻠﺣﺔ‬ ‫اﻟﺧرﺳﺎﻧﺔ‬ ‫ﻣﻊ‬ ‫ﻣدﻓوﻧﺔ‬ ‫ﻓوﻻذﯾﺔ‬ ‫ﺑروﻓﯾﻼت‬ ‫ﻣﻊ‬ ‫اﻟﻣرﻛﺑﺔ‬ ‫اﻟﻘﺻﯾﺔ‬ ‫اﻟﺟدران‬
 The concrete advantages in terms of higher stiffness, good fire protection,
buckling prevention, recommends composite elements made by steel and
concrete to be used in high-rise buildings placed in seismic areas.
 The steel concrete composite shear walls are used as lateral loads resisting
systems for high-rise buildings as an alternative to reinforced concrete
shear walls.
 Composite steel concrete shear walls are structural walls where at the
boundary elements of the wall are encased steel profiles.
 ‫واﺑﻧﯾﺔ‬ ‫اﻟﺧرﺳﺎﻧﺔ‬ ‫اﺑﻧﯾﺔ‬ ‫ﻣﻊ‬ ‫اﻟﻣرﻛﺑﺔ‬ ‫اﻟﻘﺻﯾﺔ‬ ‫اﻟﺟدران‬ ‫ﺗﺳﺗﻌﻣل‬
 ‫ﺑﺎﻻﺿﺎﻓ‬ ‫ﺷﺎﻗوﻟﯾﺔ‬ ‫ﺣﻣوﻻت‬ ‫ﻟﻣﻘﺎوﻣﺔ‬ ‫اﻟوﻗت‬ ‫ﺑﻧﻔس‬ ‫ﻓوﻻذﯾﺔ‬‫ﺔ‬
 ‫واﻟزﻻزل‬ ‫اﻟرﯾﺎح‬ ‫ﻟﺣﻣوﻻت‬
 Composite Shear Walls with
 Encased Profiles

49. 49
‫ﻣﺣﺎط‬ ‫ﻣﺳﻠﺣﺔ‬ ‫ﺧرﺳﺎﻧﺔ‬ ‫ﻣرﻛب‬ ‫ﻗﺻﻲ‬ ‫ﺟدرار‬‫ﻓوﻻذ‬ ‫ﺑروﻓﯾل‬‫ي‬
‫ﻗﺻﯾﺔ‬ ‫وﺻل‬ ‫وﺑﺳﺎﻣﯾر‬

50. 50
‫اﻟﻔوﻻذي‬ ‫اﻟﺑروﻓﯾل‬ ‫اﻧواع‬ ‫ﻣﻊ‬ ‫ﻣرﻛﺑﺔ‬ ‫ﻗﺻﯾﺔ‬ ‫ﺧرﺳﺎﻧﺔ‬ ‫ﺟدران‬ ‫اﺷﻛﺎل‬ ‫ﺗﻔﺎﺻﯾل‬

51. 51
‫اﻟﻣرﻛﺑﺔ‬ ‫اﻟﻣﺳﻠﺣﺔ‬ ‫اﻟﺧرﺳﺎﻧﺔ‬ ‫ﺟدران‬ ‫واﺷﻛﺎل‬ ‫اﻧواع‬
‫اﻟﻣﻌدﻧﻲ‬ ‫واﻟﺑروﻓﯾل‬ ‫اﻟﺻﻔﺎﺋﺢ‬ ‫وﺗﻣوﺿﻊ‬

52. 52
‫اﻟﺻﻧﻊ‬ ‫ﻣﺳﯾﻘﺔ‬ ‫اﻟﻣرﻛﺑﺔ‬ ‫اﻟﻘﺻﯾﺔ‬ ‫اﻟﺟدران‬

53. 53

54. 54
‫اﻟﺻﻧﻊ‬ ‫وﻣﺳﺑﻘﺔ‬ ‫اﻟﻣرﻛﺑﺔ‬ ‫اﻟﻘﺻﯾﺔ‬ ‫اﻟﺣدران‬
‫ﺿﻣن‬‫ﻟﻠﻌزو‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫ﺧﺎﺻﺔ‬ ‫ﻓوﻻذﯾﺔ‬ ‫اطﺎرات‬‫م‬

55. 55
‫واﻟﻔوﻻذﯾﺔ‬ ‫اﻟﺧرﺳﺎﻧﯾﺔ‬ ‫اﻟﻣرﻛﺑﺔ‬ ‫اﻟﺣدران‬ ‫اﺗﺻﺎل‬ ‫ﺗﻔﺎﺻﯾل‬
‫اﻟﻔوﻻذي‬ ‫اﻟﺑروﻓﯾل‬ ‫ﻣن‬ ‫اﻟﻧﮭﻠﯾﺎت‬ ‫ﻋﻧﺎﺻر‬ ‫ﻣﻊ‬

56. 56
Composite shear wall assembly could speed
construction of steel frames
 The sandwich, called a dual-plate composite shear wall
because its steel-plate walls are filled with lightly reinforced
concrete, is not for use only in seismic zones.
 “It is a great system for multihazard mitigation because it is
good for seismic, wind and gravity loads as well as blast
resistance,
 ”‫ﺧﺎرﺟﯾﺔ‬ ‫ﻓوﻻذﯾﺔ‬ ‫ﺻﻔﺎﺋﺢ‬ ‫ﺑروﻓﯾل‬ ‫اﻟﻣرﻛب‬ ‫اﻟﻘﺻﻲ‬ ‫اﻟﺟدار‬
 ‫ﻣﺳﻠﺣﺔ‬ ‫وﺧرﺳﺎﻧﺔ‬

57. 57

COMPOSITE SUBSYSTEMS
 These systems may be categorized as follows:
 ‫واﻟﻣرﻛﺑﺔ‬ ‫اﻟﻔوﻻذﯾﺔ‬ ‫اﻟﻘﺻﯾﺔ‬ ‫اﻟﺟﻣل‬ ‫اﻧواع‬
1. Composite moment frames
2. Composite braced frames
3. Composite eccentrically braced frames
4. Composite shear wall-frame interacting systems
5. Composite tube systems
6. Vertically mixed systems
7. Mega frames with super columns
8. High-efficiency structures
Composite moment Frames‫م‬‫ﻟﻠﻌزو‬ ‫اﻟﻣﻘﺎوﻣﺔ‬ ‫اﻟﺧﺎﺻﺔ‬ ‫اﻟﻣرﻛﺑﺔ‬ ‫اﻻطﺎرات‬
 Refer to Figure 2.9 for schematics of a composite moment frame
consisting of steel beams and composite columns.
 The columns may consist of either concrete encased or filled composite
columns, with moment connected steel beams.

58. 58
‫ﻣرﻛﺑﺔ‬ ‫واﻋﻣدة‬ ‫ﻟﻠﻌزوم‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫ﺧﺎﺻﺔ‬ ‫ﻓوﻻذﯾﺔ‬ ‫اطﺎرات‬
‫اﻟﺿﻌﯾف‬ ‫واﻟﺟﺎﺋز‬ ‫اﻟﻘوي‬ ‫اﻟﻌﺎﻣود‬ ‫وﺗﺣﻘﯾﻖ‬
 Intermediate and special moment frames must satisfy detailing
requirements that are more stringent than those for ordinary moment
frames
 The reason is to assure a ductile response when these buildings are
pushed beyond elastic limit in a major seismic even

59. 59
‫ﻣرﻛب‬ ‫وﻋﺎﻣود‬ ‫ﻓوﻻذﯾﺔ‬ ‫ﻛﻣرات‬ ‫و‬ ‫ﻟﻠﻌزوم‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫اﻧﺻﺎل‬ ‫ﻋﻘدة‬
‫اﻟﻘوي‬ ‫اﻟﻌﺎﻣود‬ ‫ﺗﺣﻘﺑﻖ‬

60. 60
Seismic provisions of AISC 341-05 recognize three types of
composite moment frames:
1. Ordinary moment frames
2. Intermediate moment frames
3. Special moment frames
‫اﻻطﺎرات‬ ‫واﻧواع‬ ‫اﻷﻣرﯾﻛﻲ‬ ‫اﻟﻛود‬‫اﻟﻣرﻛﺑﺔ‬‫ﻟﻠﻌزوم‬ ‫اﻟﻣﻘﺎوﻣﺔ‬
Special Moment Frames- ‫ة‬‫اﻟﺧﺎص‬ ‫اﻟﻣرﻛﺑﺔ‬ ‫اﻻطﺎرات‬
 The term “special” refers to the characteristics of the frame in which the
members and connections are designed and detailed to provide maximum
ductility and toughness, implying excellent energy dissipation and
seismic performance during severe earthquake shaking.
 In recognition of the ductility, seismic provisions allow a maximum
reduction in the design base shear.
 Because of the recognized ductility and the limited interference with
architectural planning, special moment frames are one of the most
commonly used lateral systems.
‫اﻻط‬ ‫اﺷﺗراطﺎت‬ ‫ﻧﻔس‬ ‫ﺗطﺑﻖ‬‫ﺎ‬‫واﻟﺧرﺳﺎﻧﯾﺔ‬ ‫اﻟﻔوﻻذﯾﺔ‬ ‫رات‬‫اﻟﻣرﻛﺑﺔ‬ ‫اﻻطﺎرات‬ ‫ﻋﻠﻰ‬
‫اﻟﻠدن‬ ‫اﻟﻣﻔﺻل‬ ‫وﺗﺷﻛل‬ ‫اﻟﻣطﺎوﻋﺔ‬ ‫ﺣﯾث‬ ‫ﻣن‬

61. 61
‫اﻟﺿﻌﯾف‬ ‫واﻟﺟﺎﺋز‬ ‫اﻟﻘوي‬ ‫اﻟﻌﺎﻣود‬ ‫وﻗﺎﻋدة‬
‫اﻟﻣطﺎوﻋﺔ‬ ‫ﻋﺎﻣل‬ ‫وﯾؤﺧذ‬R‫اﻟﺟداول‬ ‫ﻣن‬ ‫اﻟﻣﻘﺎوﻣﺔ‬ ‫زﯾﺎدة‬ ‫او‬
 Composite special moment frames are similar in configuration to
ordinary moment-resisting frames.
 As in steel or concrete systems, more stringent detailing provisions are
required to increase the system’s ductility and toughness.
 The commensurate reduction in design lateral force is very
similar to that in steel or concrete special moment frames.
 The design intent is to confine inelastic hinging in beams, while the
columns and connections remain essentially elastic.
 The design base shear prescribed for this system is similar to the special
moment-resisting frame systems of steel or reinforced concrete.
 Likewise, no limitations have been placed on their usage in buildings
assigned
to a higher SDC.
 special moment-resting frames attempts to provide the maximum
possible frame ductility, toughness, and energy-dissipation capacity.
 This requirement results in more stringent provisions for member and
joint detailing.
 Generally these frames are designed to limit inelastic action to the
beams, with the intent of preventing potential yielding in columns and
connections.

62. 62
 The design should include the strong column-weak beam concept. For
composite columns, transverse reinforcement requirements should be
equivalent to those required for reinforced concrete columns in special
moment-resisting frames.
 Special details are required to satisfy closed-hoop and cross-tie
requirements for encased composite columns.
‫ﻗﻲ‬ ‫اﻟﻣطﺎوﻋﺔ‬ ‫ﻟزﯾﺎدة‬ ‫ﺧﺎﺻﺔ‬ ‫ﺗرﺗﯾﺑﺎت‬‫اﻋﻣدة‬‫اﻟﻣرﻛﺑﺔ‬ ‫اﻻطﺎرات‬
 and lateral torsional buckling, allowing the beams to develop their full
plastic flexural capacity.
 However, steel flanges connected to concrete slabs with shear
connectors are exempted from this provision. This is because lateral
torsion and local buckling are inhibited by the shear connectors and
concrete slab.

63. 63
 he design of composite frames is not significantly different from the
procedures for structural steel or reinforced concrete moment frames
‫اﻻط‬ ‫وﻣﻣطوﻟﯾﺔ‬ ‫ﻣطﺎوﻋﺔ‬‫ﺎ‬‫اﻟﻣرﻛﺑﺔ‬ ‫اﻟﺧﺎﺻﺔ‬ ‫رات‬
 Encased composite columns should have a minimum ratio of structural steel gross
column area of 4%.
 The shear strength of columns generally ignores the contribution of concrete.
However, the contribution of the shear strength of the reinforcing ties
based on an effective shear width bf of the section, as noted in Figure 2.12, is
permitted. For filled composite columns; it is conservative to neglect the
contribution of concrete to the shear strength of the column.

64. 64
 Where shear strength becomes critical, the composite column may be treated as a
reinforced concrete column with the steel considered as shear einforcement.
 Transfer of forces between structural steel and reinforced concrete should be made
through shear connectors, ignoring the contribution of bond or friction.
 ‫ﻓﻲ‬ ‫ﻟﻠﻘص‬ ‫اﻟﺧرﺳﺎﻧﺔ‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫ﻻﺗؤﺧذ‬‫اﻟﻣﺗﺷﻘﻖ‬ ‫اﻟﻣﻘطﻊ‬
 ‫اﻟﻠدن‬ ‫اﻟﻣﻔﺻل‬ ‫ﺗﺷﻛل‬ ‫وﻣﻧطﻘﺔ‬

65. 65
Composite Braced Frames‫اﻟﻣرﻛﺑﺔ‬ ‫واﻟﻘطرﯾﺔ‬ ‫اﻟﻣﺎﺋﻠﺔ‬ ‫اﻟدﻋم‬ ‫ﻋﻧﺎﺻر‬
 two types of composite braced frames are recognized in AISC 341-
05/10:
 (1) Concentric bracing, where various bracing members meet at a
common point;
 and (2) a relatively new form of braced frame called eccentric brace.
 this system combines the ductility of moment frames with the high
stiffness of concentrically braced frames ‫ﻋﻧﺎﺻر‬‫واﻟﻘ‬ ‫اﻟﻣﺎﺋﻠﺔ‬ ‫اﻟدﻋم‬‫اﻟﻔوﻻذﯾﺔ‬ ‫طرﯾﺔ‬
‫اﻟﻣرﻛﺑﺔ‬ ‫واﻷﻋﻣدة‬


66. 66
 Composite brace design in concentrically braced frames must recognize
that these elements are expected to provide for the inelastic action during
large seismic overloads.
 Braces consisting of concrete encased steel elements should include
reinforcing and confinement steel sufficient to provide the intended
stiffening effect even after the brace has buckled during multiple cycles
of seismic motion.
 As a result, it is recommended that these elements should meet detailing
requirements similar to those for composite columns.
 Composite braces in tension should be designed considering the
resistance provided only by the steel. ‫اﻟﻣﺎﺋل‬ ‫اﻟﺗدﻋﯾم‬ ‫ﺣﺎﻻت‬ ‫ﺟﻣﯾﻊ‬‫اﻟﺧرﺳﺎﻧﺔ‬ ‫اﻟﻣرﻛب‬
‫اﻟﺷد‬ ‫ﻓوى‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫ﻓﻲ‬ ‫ﺗﺷﺎرك‬ ‫ﻻ‬-‫اﻟﻠدن‬ ‫اﻟﻣﻔﺻل‬ ‫ﺗﺷﻛل‬ ‫ﻣﻧﺎطﻖ‬ ‫ﻓﻲ‬ ‫ﺗواﺟدھﺎ‬ ‫ﻋﻧد‬ ‫اﻻﻧﺗﺑﺎه‬ ‫وﯾﺟب‬
‫اﻟﻠدوﻧﺔ‬ ‫ﻣﺟﺎل‬ ‫ﻓﻲ‬ ‫واﻟﻌﻣل‬

67. 67
 Brace buckling and the resulting large rotation demands at the brace ends
should be considered in connection detailing.
 Schematic details of brace to encased composite column are
shown in Figure 2.14a and b.

68. 68
Composite Eccentrically Braced Frames
‫اﻟﻼ‬ ‫اﻟﻣرﻛﺑﺔ‬ ‫اﻟﻣﺎﺋﻠﺔ‬ ‫اﻻطﺎرات‬ ‫ﻋﻧﺎﺻر‬‫ﻣرﻛزﯾﺔ‬
 figure 2.15. In general, beams in composite eccentrically braced frames
consist of structural steel sections.
 Any concrete encasement of the beam should not extend into the link
regions where large inelastic action is expected to develop
 (see Figure 2.16a). Columns and braces can be of either structural steel or
composite construction.
 The analysis, design, and detailing of the system is similar to that for steel
eccentrically braced frames
since the force transfer mechanisms between the steel and concrete rely on
bearing and shear friction, special attention must be paid to the design of
connections to realize the intended inelastic action intheductile links

69. 69
.
‫ﻣرﻛزﯾﺔ‬ ‫اﻟﻼ‬ ‫اﻟﻣﺎﺋﻠﺔ‬ ‫اﻟدﻋم‬ ‫ﻋﻧﺎﺻر‬

70. 70
Composite brace design in eccentrically braced frames must recognize that
these members are intended to remain essentially elastic during large seismic
overloads.
The design strength must consider the yielding and significant strain
hardening that can occur in properly designed and detailed
link elements.
Both axial and bending forces generated in the braces by the strain-hardened
link‫اﻟﻣرﻧﺔ‬ ‫اﻟﻣﻧطﻘﺔ‬ ‫ﺿﻣن‬ ‫ﻋﻣﻠﮭﺎ‬ ‫ﯾﺑﻘﻰ‬ ‫واﻟﻘطرﯾﺔ‬ ‫اﻟﻣﺎﺋﻠﺔ‬ ‫اﻟدﻋم‬ ‫ﻋﻧﺎﺻر‬
‫وﻣﻧطﻘﺔ‬ ‫اﻟﻌﺎﻣود‬ ‫ﻣﺣورﻋﻘدة‬ ‫ﻋن‬ ‫ﺑﻌﯾد‬ ‫اﺗﺻﺎﻟﮭﺎ‬ ‫وﯾﺑﻘﻰ‬ ‫ﻟدﻧﺔ‬ ‫ﻣﻔﺎﺻل‬ ‫ﻓﯾﮭﺎ‬ ‫وﻻﯾﺗﺷﻛل‬
‫ﺗﺷﻛ‬‫اﻟﺷﻛل‬ ‫ﻓﻲ‬ ‫ﻛﻣﺎ‬ ‫اﻟﻠدن‬ ‫اﻟﻣﻔﺻل‬ ‫ل‬

71. 71
beams must be considered.
‫اﻟﻠد‬ ‫اﻟﻣﻔﺻل‬ ‫ﺗﺷﻛل‬ ‫ﻋن‬ ‫ﺑﻌﯾدة‬ ‫وﻧﻘﺎط‬ ‫اﻣﺎﻛن‬ ‫ﻓﻲ‬ ‫واﻟﻣﺎﺋﻠﺔ‬ ‫اﻟﻘطرﯾﺔ‬ ‫اﻟﻌﻧﺎﺻر‬ ‫وﺻل‬‫ن‬

72. 72
Reinforced Concrete Core With steel surrounding
‫واﻟﻣرﻛﺑﺔ‬ ‫اﻟﻔوﻻذﯾﺔ‬ ‫واﻻطﺎرات‬ ‫اﻟﺧرﺳﺎﻧﻲ‬ ‫اﻟﻛور‬ ‫ذات‬ ‫اﻷﺑﻧﯾﺔ‬
Core walls enclosing building services such as elevators, mechanical and
electric rooms, and stairs have been used extensively to resist lateral
loads in tall concrete buildings.
 The use of simple shapes such as C and I shaped walls around elevators
interconnected with coupling beams constitutes one of the most typical
methods of providing resistance to lateral loads.
 In the composite version of this system, a central concrete shear wall core is
designed to resist the entire lateral load while the remainder of framing
surrounding the core is designed for gravity loads using structural steel, metal
deck and concrete topping (see Figure 2.18)
 concrete core is built first, using jump or slip forms, followed by erection
of steel surround, as shown in Figure 2.19.
 Although structural steel erection may not proceed as fast as in
a conventional steel building, the overall construction time is likely to be
less because the building’s vertical transportation, consisting of stairs and
elevators and mechanical and electrical services can
be installed with in the core while erection of steel outside of the core is
still in progress The only nonstandard connection is between shear walls
and floor beams.

73. 73
 Various techniques have been developed for this connection, chief among
them, are the embedded plate and pocket details, as shown in Figure 2.20.
The floor construction invariably consists
of composite metal deck with concrete topping
 The floor within the core may be constructed either in concrete or structural
steel. The connection between the floor slab and core walls is often project
 specific. ‫ﻣﺳﻠﺣﺔ‬ ‫ﺧرﺳﺎﻧﺔ‬ ‫ﺟدران‬ ‫ﯾﻛون‬ ‫ان‬ ‫ﻟﻠﻛور‬ ‫ﯾﻣﻛن‬‫ﻓوﻻذي‬ ‫ﺑروﻓﯾل‬ ‫او‬
 The weld plate detail shown in Figure 2.20a is, however, the most popular,
particularly in a slip-formed construction.

74. 74
 The weld plates are set with the outer surface flush with the wall surface.
The plate is anchored to the wall by shear connectors welded to the plate.
‫ﻣﺳﻠﺣﺔ‬ ‫ﺧرﺳﺎﻧﺔ‬ ‫ﺟدران‬ ‫ﻣﻊ‬ ‫اﻟﻔوﻻذﯾﺔ‬ ‫اﻟﻛﻣرات‬ ‫اﻧﺻﺎل‬
‫ﻣﺛ‬ ‫ﻗوﻻدﯾﺔ‬ ‫ﺻﻔﺎﺋﺢ‬ ‫ﺑواﺳطﺔ‬‫ﺑ‬‫اﻟﺣﺟرﻟن‬ ‫ﻓﻲ‬ ‫ﺑراﻏﻲ‬ ‫ﻣﻊ‬ ‫ﺗﺔ‬


75. 75


76. 76
shear Wall-Frame interactinG systems
 This system has applications in buildings that do not have sufficiently large
cores to resist the entire lateral loads.
 This may require interaction of shear walls with moment frames to
supplement the lateral stiffness of the shear cor
‫واﻟﺟدراﻧ‬ ‫اﻻطﺎرات‬ ‫ﺑﯾت‬ ‫اﻟﺗﻔﺎﻋﻠﻲ‬ ‫اﻟﻧظﺎم‬ ‫ﺟﻣﻠﺔ‬‫اﻟﻘﺻﯾﺔ‬ ‫ﺎ‬

77. 77
Composite tube systems
‫اﻻﻧﺑوﺑﯾﺔ‬ ‫اﻻطﺎرات‬ ‫ﺟﻣﻠﺔ‬
The key to the success of tube construction as noted earlier, lies in the
rigidity of closely spaced exterior composite columns and deep spandrels. This
results in an exterior façade that behaves more like a bearing wall than as a moment
frame.

78. 78
VertiCally mixed systems
‫ا‬‫ﻟﺟﻣل‬‫اﻟﻔﺻﯾﺔ‬‫اﻟﻣﺧﺗﻠط‬‫ة‬
 Mixed-use buildings are thos

 e that provide for two or more types of occupancies in a single building.

79. 79
 For example, lower levels of the building may be for parking; middle
levels for office floors; and the top levels for residential units, such as
apartments and hotel rooms.
 Therefore, it makes economical sense to stack up different systems
vertically up the building height using a system that
is most logical for the particular occupancy.
 For example, beamless flat ceilings with a minimum
of floor-to-floor height are preferred in residential occupancies

80. 80
‫ﺳﻔﻠﯾﯨﺔ‬ ‫طواﺑﻖ‬ ‫ﺧرﺳﺎﻧﺔ‬ ‫ﺟدران‬ ‫ﻛور‬
‫اﻋﻠﻰ‬ ‫ﻓوﻻذﯾﺔ‬ ‫ﺳﺗﯾل‬ ‫ﺟدران‬ ‫ﻛور‬

81. 81
meGa Frames With super Columns
‫اﻟﻛﺑﯾر‬ ‫اﻟﻌﻣﻼق‬ ‫اﻟﻣرﻛب‬ ‫اﻟﻌﺎﻣود‬‫واﻟﺷﺎﻗوﻟﯾﺔ‬ ‫اﻷﻓﻘﯾﺔ‬ ‫اﻟﻘوى‬ ‫ﻣﻘﺎوﻣﺔ‬
‫ﺷﺑﻛﯾﺔ‬ ‫ﯾﺟواﺋز‬‫ﻣﺣﯾطﯾﺔ‬ ‫واﺣزﻣﺔ‬
 One of the methods resisting lateral loads in tall buildings to provide big
columns placed as far as possible at the perimeter of building, and
interconnect the columns with a shear-resisting system such as Vierendeel
frames, or super diagonals.
 The construction of super columns can take on many forms system uses
large-diameter steel pipes filled with high-strength concrete.
 Generally, neither longitudinal nor transverse reinforcement is used in the
columns,.
 Another method to encase steel columns using conventional forming
techniques.

82. 82

83. 83
‫ﻓوﻻذي‬ ‫ﻋﺎﻣود‬ ‫ﻣﻊ‬ ‫ﻣرﻛب‬ ‫ﺟﺎﺋز‬ ‫اﺗﺻﺎل‬ ‫ﺗﻔﺎﺻﯾل‬

84. 84
(A) Plastic stress distribution for negative moment: (a) composite beam section; (b)
plastic neutral axis, PNA, in steel beam web; (c) PNA in beam flange. (B) Plastic stress
distribution for positive moment:
(a) plastic neutral axis, PNA, in concrete slab; (b) PNA in steel beam flange; (c) PNA in
steel beam web.

85. 85
AISC Design encased composIte columns
Limitations ‫اﻟﻣرﻛﺑﺔ‬ ‫اﻷﻋﻣدة‬ ‫وﺗﺻﻣﯾم‬ ‫اﻷﻣرﯾﻛﻲ‬ ‫ﻟﻛود‬‫ا‬
To qualify as an encased composite column, the following limitations
shall be met:
1. The cross-sectional area of the steel core shall comprise at least 1% of
the total composite
cross section.
2. Concrete encasement of the steel core shall be reinforced with
continuous longitudinal
bars and lateral ties or spirals.
3.The minimum transverse reinforcement shall be at least
0.009 in.2 per in. of tie spacing

86. 86

87. 87

88. 88

89. 89

90. 90

91. 91

92. 92
‫اﻟﻣﺑﺎﻧﻲ‬ ‫وﺗﺻﻣﯾم‬ ‫اﻷورﺑﻲ‬ ‫اﻟﻛود‬‫و‬ ‫اﻟﻔوﻻذﯾﺔ‬‫اﻟﻣرﻛﺑﺔ‬
TYPES OF CROSS-SECTION FOR COMPOSITE COLUMNS
AND THEIR ADVANTAGES
Figure 1 shows typical cross-sections of composite columns together with
the dimensional notation used in Eurocode 4 [1]. The sections can be
classified into two groups:
 concrete filled sections in which the concrete is hidden
 totally and partly encased sections.
Eurocode 8 rules on steel & composite structures

93. 93

94. 94

95. 95

96. 96

97. 97

98. 98

99. 99

100. 100

101. 101

102. 102

103. 103

104. 104

105. 105

106. 106

107. 107

108. 108

109. 109

110. 110

111. 111
Establishing Earthquake Loads for Composite
Shear Walls Using US Codes
‫اﻟﺣﻣوﻻت‬ ‫ﻣن‬ ‫اﻟزﻻزل‬ ‫ﺣﻣوﻟﺔ‬ ‫ﻣﻌﺎدﻟﺔ‬ ‫ﺣﺳﺑﺎب‬

112. 112
‫ﻣرﻛﺑﺔ‬ ‫ﻗﺻﯾﺔ‬ ‫ﺟدران‬ ‫اﺟل‬ ‫ﻣن‬ ‫اﻟزﻻزل‬ ‫ﻗوة‬ ‫ﺣﺳﺎب‬

113. 113
‫اﻟﻣطﺎوﻋﺔ‬ ‫ﻋﺎﻣل‬ ‫اﺳﺗﻌﻣﺎل‬ ‫ﺟدول‬R‫اﻟﻣﻘﺎوﻣﺔ‬ ‫زﯾﺎدة‬

114. 114
‫ا‬‫اﻟﻣﺳﻣوح‬ ‫اﻟﻣروﻧﺔ‬ ‫ﺣد‬ ‫ﺟﮭﺎد‬

115. 115
Design of Composite Wall Element
‫ﺗواﺟد‬‫اﻟﻣﺳﻣوح‬ ‫واﻟﻘص‬ ‫اﻟدﻋﻣﺔ‬

116. 116
‫اﻟﻣرﻛب‬ ‫اﻟﻘص‬ ‫ﺟدار‬ ‫ﺣول‬ ‫اﻟﻛود‬ ‫اﺷﺗراط‬

117. 117
‫اﻻﻧﻘﻼب‬ ‫وﻋزم‬ ‫اﻟﻘﺎﻋدي‬ ‫اﻟﻘص‬ ‫ﺗﺻﻣﯾم‬

118. 118
‫اﻟﻛﻣرة‬ ‫ﻣﻊ‬ ‫اﻟﻣﻌدﻧﯾﺔ‬ ‫اﻟﺻﻔﯾﺣﺔ‬ ‫اﻧﺻﺎل‬‫واﻟﻌﺎﻣود‬

119. 119
‫واﻟﻌﺎﻣود‬ ‫اﻟﻛﻣرة‬ ‫ﻣن‬ ‫اﻻطﺎر‬ ‫ﺗﺻﻣﯾم‬

120. 120
‫واﻟﺟﻧﺎح‬ ‫اﻟﺟﺳد‬ ‫وﺗﺣﻧﯾب‬ ‫اﻟﻣﺳﻣوﺣﺔ‬ ‫اﻻﺟﮭدات‬

121. 121
‫ﻧ‬‫ﻓﻲ‬ ‫اﻟﻣرﻛب‬ ‫اﻟﻘﺻﻲ‬ ‫اﻟﺟدار‬ ‫ﻣذﺟﺔ‬‫ﺑرﻧﺎﻣﺞ‬‫اﻟﺣﺎﺳب‬

122. 122