Reinforcement Requirements for Beams of Special Moment Frames

Special Moment Frames

Based on ACI 2.3, special moment frames are beam-column frames assigned to SDC D, E and F and complying with 18.6 through 18.8. ACI 18.6 deals with requirements for beams, while ACI 18.7 deals with columns and ACI 18.8 deals with joints of special moment frames. A- Beams of Special Moment Frames ACI 18.6 applies to beams of special moment frames that form part of the seismicforce-resisting system and proportioned primarily to resist flexure and shear. ACI 318-14 is written with the assumption that special moment frames comprise beams and columns interconnected by beam-column joints. 1- Dimensional Limits: ACI 18.6.2 requires that the following conditions are to be satisfied:  Clear span, ln , shall be at least 4d, where d is effective depth of the beam.  Width, bw , shall be at least the lesser of 0.3 h and 25 cm, where bw is web width and h is overall thickness of beam.  Projection of the beam width beyond the width of the supporting column on each side shall not exceed the lesser of

c2

and 0.75 c1 . Note that

the column dimension in the direction of analysis, and

c1 is

c2 is the column

dimension measured in the direction perpendicular to c1 , as shown in Figure R18.6.2.

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2- Longitudinal Reinforcement: ACI 18.6.3 specifies the following requirements for beam longitudinal reinforcement:  At least two bars are to be provided continuously both top and bottom faces.  At any section, for top as well as for bottom reinforcement, the amount of reinforcement is not be less than the larger 0.80 f ' b d and 14 bw d . c

fy

164

w

fy

   



This requirement needs not to be satisfied if the tension reinforcement provided at every section is 1/3 larger than required by analysis. Maximum reinforcement ratio is not to exceed 0.025. Positive moment strength at joint face is not to be less than ½ of the negative moment strength provided at the face of the joint. Both the negative and positive moment strength at any section along the beam length is not to be less than ¼ the maximum moment strength provided at face of either joint. Lap splices of deformed longitudinal reinforcement are permitted only if hoop or spiral reinforcement is provided over the lap length. Maximum spacing of the transverse reinforcement enclosing the-lap-spliced bars is not to exceed the lesser of d/4 or 10 cm. Lap splices are not to be used; (a) within the joints, (b) within a distance of twice the beam depth from the face of the joint, and (c) within a distance of twice the beam depth from critical sections where flexural yielding is likely to occur as a result of lateral displacements beyond the elastic range of behavior.

Reinforcement Requirements for Beams of Special Moment Frames 3- Transverse Reinforcement: ACI 18.6.4 specifies reinforcement:

the

following

requirements

for

transverse

 Hoops are to be provided in the following regions of a beam: (a) Over a length equal to twice the beam depth measured from the face of the supporting column toward mid span, at both end of the beam.

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(b) Over lengths equal to twice the beam depth on both sides of a section where flexural yielding is likely to occur as a result of lateral displacements beyond the elastic range of behavior.  The first hoop is to be located at a distance not more than 5 cm from the face of a supporting column. Spacing of the hoops is not to exceed the smallest of: (a) d/4, (b) 6 d , where db is the diameter of the smallest primary flexural b

  





reinforcing bars, and (c) 15 cm. Where hoops are required, they are designed to resist shear according to 18.6.5. Where hoops are not required, stirrups with seismic hooks at both ends are to be spaced at a distance not more than d/2 throughout the length of the beam. Where hoops are required, primary longitudinal reinforcing bars closest to the tension and compression faces shall have lateral support in accordance with 25.7.2.3 and 25.7.2.4. The spacing of transversely supported flexural reinforcing bars shall not exceed 35 cm. Hoops in beams are permitted to be made up of two pieces of reinforcement: a stirrup having seismic hooks at both ends and closed by a crosstie. Consecutive crossties engaging the same longitudinal bar shall have their 90 deg hooks at opposite sides of a flexural member. If the longitudinal reinforcing bars secured by the crossties are confined by a slab on only one side of the beam, the 90-degree hooks of the crossties shall be placed on that side. In beams having factored axial compressive force exceeding Ag f c / 10 , hoops satisfying 18.7.5.2 through 18.7.5.4 shall be provided along lengths given in 18.6.4.1. Along the remaining length, hoops satisfying 18.7.5.2 shall have spacing, s not exceeding the lesser of six times the diameter of the smallest longitudinal beam bars and 15 cm. Where concrete cover over transverse reinforcement exceeds 10 cm, additional transverse reinforcement having cover not exceeding 10 cm and spacing not exceeding 35 cm shall be provided.

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Transverse Reinforcement for Beams of Special Moment Frames

Splices and Hoop Reinforcement for Beams of Special Moment Frames

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4- Shear Strength Reinforcement: ACI R18.6.5 states that "Unless a beam possesses a moment strength that is on the order of 3 or 4 times the design moment, it should be assumed that it will yield in flexure in the event of a major earthquake. The design shear force should be selected so as to be a good approximation of the maximum shear that may develop in a member. Therefore, required shear strength for frame members is related to flexural strengths of the designed member rather than to factored shear forces indicated by lateral load analysis. The conditions described by 18.6.5.1 are illustrated in Fig. R18.6.5."

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 The design shear force, Ve , is to be determined from consideration of the forces on the portion of the beam between faces of the joints. It is assumed that moments of opposite sign corresponding to probable flexural moment strength, M pr , act at the joint faces and that the beam is loaded with the factored tributary gravity load along its span. For calculation of M pr it is assumed that tensile strength in the longitudinal bars is 1.25 f y and the strength reduction factor  is equal to 1.0. M pr  As 1.25 f y  d  a / 2

where a

As 1.25 f y  0.85 f 'c b

 Transverse reinforcement over the lengths identified in 3(a) and 3(b) shall be proportioned to resist shear assuming Vc  0 when both of the following conditions occur: (a) The earthquake induced shear force, Ve , represents ½ or more of the maximum required shear strength within those lengths; (b) The factored axial compressive force, Pu , including earthquake effects is less than 0.05 Ag f 'c .

Design Shear Forces for Beams of Special Moment Frames

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Example (8): Design the transverse reinforcement for the potential hinge regions of the earthquake resisting beam in a monolithic reinforced concrete frame shown in the figure. The beam which is part of a special moment resisting frame is subjected to a service dead load of 3.0 t/m and a service live load of 2.0 t/m ( LL  480 Kg / m2 ). Note that f 'c  300 Kg / cm2 and f y  4200 Kg / cm 2 .

Solution: In this example, requirements of sections 18.6 through 18.8 of ACI 318-14 are to be satisfied. A- ACI 18.6.2 "Dimensional Limits":  Clear span of beam is not to be less than four times its effective depth. d  60  4  1 1.25  53.75 cm 930  17.3  4.0 (O.K) 53.75

 The width is not to be less than the smaller of 0.3h and 25 cm. Beam width is 45 cm, which is larger than the greater of 0.3(60) and 25cm. (O.K) 170

 Projection of the beam width beyond the width of the supporting columns is not to exceed the smaller of c2 and 0.75 c1. Width of beam = width of column. (O.K) B- ACI 18.6.3 "Longitudinal Reinforcement":  Minimum ratio of top as well as bottom reinforcement is not to be less than the larger of: 0.80 300 14  0.0033  0.0033 and 4200 4200 9.817  min provided    0.00406  0.0033 (O.K) 45 53.75

 Maximum reinforcement ratio is not to exceed 0.025.  max provided  

29.452  0.01217  0.025 (O.K) 45 53.75

 At least two bars are to be provided continuously top and bottom. 2  25 mm bars are provided throughout the length of the beam on the top side, while 4  25 mm bars are provided continuously on the bottom side. (O.K)  Positive moment strength at joint face is not to be less than 1/2 of the negative moment strength provided at the face of the joint. Positive moment strength at face of joint is evaluated as follows:





M n  ve   A s, ve f y d  a / 2

From equilibrium of forces, C n  ve   Tn  ve  and 0.85300a 45 19.634200 and a  7.18 cm M n  ve  

19.634200 105

53.75  7.18 / 2  41.35

t.m

Negative moment strength at face of joint is evaluated as follows:





M n  ve   A s, ve f y d  a / 2

From equilibrium of forces, Cn  ve   Tn  ve  and 0.85300a 45  29.454200 and a 10.78 cm M n  ve 

29.454200 53.75 10.78 / 2 59.82 t.m 105

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Thus, M n  ve  

M n  ve  at face of joint. (O.K) 2

 The negative or positive moment at any section along the beam is not to be less than 1/4 the maximum moment strength provided at face of either joint. At section of least reinforcement moment strength is evaluated as follows: From equilibrium of forces, C n  Tn and 0.85300a 45  9.8174200 and a  3.59 cm Mn 

9.8174200 53.75  3.59 / 2 21.42 105

t.m 

59.82 t.m (O.K) 4

 Lap splices of flexural reinforcement are permitted only if hoop or spiral reinforcement is provided over the lap length. Maximum spacing of the transverse reinforcement in the lap region is not to exceed the smaller of d/4 or 10 cm. Thus, maximum spacing is not to exceed 10 cm within the lap length.  Lap splices are not to be used (a) within the joints; (b) within a distance of twice the beam depth from the face of the joint and (c) at locations where analysis indicates flexural yielding caused by inelastic lateral displacements of the frame. Development length of top bars (in tension):       f    y t e s d l    b d c K   3.5   b tr  f '    d  c  b    

 t  1.3 ,  e  1 ,  s  1 , and   1 cb = 4.0 + 1.0 + 1.25 = 6.25 cm

or cb = [(45 – 4 (2) – 2 (1) – 2.5]/ (2) = 16.25 cm

i.e., cb is taken as 6.25 cm K tr 

40 Atr 40 ( 2)(0.785)   3.14 cm sn (10) 2 

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cb  K tr 6.25  3.14   3.756  2.5 , taken as 2.5. db 2 .5  4200 1.3   2.5  90.07 l d     3.5 2.5 300 

Required development length l d  90 cm Development length of bottom bars (in tension):   f y  t  e s  ld     3.5   cb  K tr  f 'c  d   b   

    db   

 t  1 ,  e  1 ,  s  1 , and   1 cb = 4.0 + 1.0 + 1.25 = 6.25 cm

or cb = [(45 – 4 (2) – 2 (1) – 2.5]/ (6) = 5.42cm

i.e., cb is taken as 5.42 cm K tr 

40 Atr 40 ( 2)(0.785)   1.57 cm sn (10) 4 

cb  K tr 5.42  1.57   2.79  2.5 , taken as 2.5. db 2 .5   4200  2.5  69.28 ld     3.5 2.5 300 

Required development length l d  70 cm C- ACI 18.6.4 "Transverse Reinforcement":  Hoops are to be provided in the following regions of beams: (a) Over a length equal to twice the beam depth measured from the face of the supporting member (column) toward mid span, at both end of the beam; (b) Over lengths equal to twice the beam depth on both sides of a section where flexural yielding is likely to occur in connection with inelastic lateral displacements of the frame.  The first hoop is to be located at a distance not more than 5 cm from the face of the supporting member. Maximum spacing of such reinforcement is not to

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exceed the smallest of: d/4, 6 d where d b

b

is the diameter of the smallest

longitudinal bars and 15 cm. Hoops are to be provided over a distance of 2h = 120 cm from faces of joints. d / 4  53.75 / 4 13.44 cm Maximum hoop spacing   6 db  6 2.5 15 cm , taken as 12.5 cm.  15 cm 

 Where hoops are required they are arranged in away similar to that of column ties.  Where hoops are not required, stirrups with seismic hooks at both ends are to spaced at a distance not more than d/2 throughout the length of the beam. Maximum spacing = d/2 = 53.75/2 = 26.875 cm, taken as 25 cm. D- ACI 18.6.5 "Shear Strength Requirements":  The design shear force Ve is to be determined from consideration of the static forces on the portion of the member between faces of the joint. It is assumed that moments of opposite sign corresponding to probable flexural moment strength M pr act at the joint faces and that the beam is loaded with the factored tributary gravity load along its span. For calculation of M pr it is assumed that tensile strength in the longitudinal bars is 1.25 f y and a strength reduction factor  of 1.0.

w u 1.2 3  0.5 2  4.6 t / m w u lc  4.6 9.3 / 2  21.39 t 2 M pr  ve  1.25 A s  ve  f y d  a / 2

0.85300a 45 1.2519.634200 or a  8.98 cm 174

1.25 19.634200

53.75  8.98 / 2 50.77 t.m 105 M pr  ve  1.25 A s  ve  f y d  a / 2 M pr  ve  

0.85300a 45 1.2529.454200 or a 13.47 cm 1.25 29.454200 53.75 13.47 / 2 72.69 t.m M pr  ve   105  M pr  ve   M pr  ve   50.77  72.69    13.27 t   lc 9. 3   Ve, max  13.27  21.39  34.66 t

For sway to the right Ve, max occurs at the right side, while it occurs at the left side for sway to the left.  Transverse reinforcement over the lengths identified in C(a) and C(b) shall be proportioned to resist shear assuming Vc  0 when both of the following conditions occur: (a) The design shear force represents ½ or more of the maximum required shear strength within these lengths; (b) The factored axial compressive force including earthquake effects is less than 0.05 A g f 'c . Seismic induced shear  13.27 tons  34.66 / 2 tons and the above-mentioned requirement is not applicable. Vc  0.53 f 'c b d  0.53 300 4553.75 / 1000 22.20 tons V Vs  Vn  Vc and Vs  u  Vc  34.66 Vs   22.20  24.01 tons 0.75

For two-legged 10 mm transverse reinforcement, Vs 

Av fy d S



2 0.785420053.75  24.01(1000) and S 14.76 cm S

Use two-legged 10 mm stirrups @ 12.5 cm. Stirrups at other locations: At the end of the hoop region,

Vu  8.12 8.1  and Vu  29.14 tons 34.66  8.12 9.3

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Vs  Vn  Vc and Vs  Vs 

Vu  Vc 

29.14  22.20 16.65 tons 0.75

For two-legged 10 mm transverse reinforcement, Vs 

Av fy d S



2 0.785420053.75  16.65 (1000) and S 21.28 cms < 53.75/2 cm S

Use 10 mm stirrups @ 20 cm.

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Requirements for Intermediate Moment Resisting Frames A- Beams 1- Scope: Requirements of ACI 18.4.2 are applicable for beams of intermediate moment frames forming part of the seismic-force-resisting system and assigned to SDC C. 2- Longitudinal Reinforcement:  Beams shall have at least two continuous bars at both top and bottom faces.  Continuous bottom bars shall have area not less than one-fourth the maximum area of bottom bars along the span. These bars shall be anchored to develop f y in tension at the face of support.  The positive moment strength at the face of the joint is not to be less than 1/3 of the negative moment strength provided at that face of the joint.  Neither the negative nor the positive moment strength at any section along the length of the beam shall be less than 1/5 the maximum moment strength provided at the face of either joint. 3- Transverse Reinforcement:  At both ends of the beam, hoops shall be provided over a length equal of at least 2 h measured from the face of the supporting member toward midspan.  The first hoop is to be located at a distance not more than 5 cm from the face of the supporting member. Maximum hoop spacing is not to exceed the smallest of: d/4, 8 d b where db is the diameter of the smallest longitudinal bars, 24 times the diameter of the hoop bar, and 30 cm.  Transverse reinforcement spacing shall not exceed d/2 throughout the length of the beam.  In beams having factored axial compressive force exceeding 0.10 Ag f 'c , transverse reinforcement shall conform to 25.7.2.2 and either 25.7.2.3 or 25.7.2.4 (column tie requirements).

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4- Shear Strength Reinforcement:  Design shear strength,  Vn shall be at least the lesser of (a) and (b): (a) The sum of the shear associated with development of nominal moment strengths of the beam at each restrained end of the clear span due to reverse curvature bending and the shear calculated for factored gravity loads. (b) The maximum shear obtained from design load combinations that include earthquake effect E, with E taken as twice that prescribed by the general building code.

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Requirements for Ordinary Moment Resisting Frames A- Beams

1- Scope: Requirements of ACI 18.3 are applicable for beams of ordinary moment frames forming part of the seismic-force-resisting system and assigned to SDC B. 2- Longitudinal Reinforcement:  Beams shall have at least two continuous bars at both top and bottom faces.  Continuous bottom bars shall have area not less than one-fourth the maximum area of bottom bars along the span. These bars shall be anchored to develop f y in tension at the face of support.

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