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SE Reference Manual CHAPTER 16 Design Requirements

Chapter 16

Chapter 16 of the IBC/CBC prescribes general design requirements for structures regulated by the code. Relevant information from Chapter 16 is presented below: §1604.5 Occupancy Category Per Table 1604.5 (IBC/CBC) or Table 1-1 (ASCE 7), Occupancy Category I II III Description of Hazard Represented by Building Collapse Low All buildings except those in I, III and IV Substantial · Public Assembly > 300 people · Schools, daycares > 250 people · College, adult education > 500 people · Healthcare (no emergency or surgery) > 50 people · Jails, detention centers · Any building with more than 5000 people · Public utility buildings (not in IV) · Buildings containing hazardous materials (not in IV) Essential facilities · Hospitals with emergency and surgery · Fire, rescue, police · Emergency shelters for earthquakes · Power stations, public utility buildings designated for earthquake backup · Aviation towers, control centers · Critical nation defense related building · Buildings containing hazardous materials quantities greater than in Table 307.1.(2).

IV

§1605 ­ Load Combinations Strength Design IBC/CBC 1605.2.1 1. 2. 3. 4. 1.4(D + F) 1.2(D + F + T) + 1.6(L + H) + 0.5(Lr or S or R) 1.2D + 1.6(Lr or S or R) + (f1L + 0.8W) 1.2D + 1.6W + f1L + 0.5(Lr or S or R)

Chapter 16

CH16-1

SE Reference Manual Roof Loads (§1607.11)

Chapter 16

Roof live loads may be reduced per 1607.11.2.1 based on the roof slope and tributary area, except for landscaped roofs (20psf minimum). Special purpose roofs (§1607.11.2.2) shall be treated similar to floors. §1609 ­ Wind Loads · Wind loads are per Section 6 of ASCE 7. See section `Wind Loads'.

§1617 ­ Earthquake Loads The IBC references ASCE 7 for the majority of the earthquake load provisions. IBC (and ASCE 7) assigns a `Seismic Design Category' to each structure. Seismic design categories are used to determine permissible lateral systems, height limitations, type of lateral analysis and seismic detailing requirements. Earthquake loads are described in the section titled Earthquake Loads. Other relevant items are discussed here. The code references are to ASCE 7. The general layout of the seismic provisions of ASCE 7 is as follows: Chapter 11 Description Seismic design criteria - Importance Factor & Seismic Design Category (SDC) - Mapped accelerations etc. Seismic design requirements for buildings - Design basis - Provisions for structural system selection, horizontal and vertical combinations of lateral systems etc. - Seismic load combinations - Equivalent lateral force calculations - Response spectrum analysis - Drift limits - Detailing requirements for different SDC etc. Seismic design requirements for non-structural components, including architectural and MEP components. Seismic design and detailing for different materials ­ Not used by IBC/CBC Seismic design requirements for non-building structures, including those similar to buildings (pipe racks, towers etc.) and those not similar to buildings (tanks, stacks, chimneys etc.). Seismic response history procedures (time history analysis procedures) Design requirements for base isolated structures Design requirements for structures with damping systems. Soil-structure interaction for seismic design Site classification for seismic design

12

13 14 15

16 17 18 19 20

Chapter 16

CH16-5

SE Reference Manual 21 22 Site-specific ground motion procedures for seismic design Seismic ground motions and long-period transition maps

Chapter 16

Relevant Provisions of ASCE 7 Earthquake Design: · §12.2.5.1 Dual Systems Dual systems are defined as a combination, in any given direction of loading, of moment frames (special or intermediate) and shear walls, braced frames (SCBF, EBF, BRBF etc.)--see Table 12.2-1 for a complete listing of allowed dual systems. The moment frames shall be designed to resist a minimum of 25% of the design base shear. The actual seismic force distribution shall be based on the appropriate rigidities of the systems. · §12.2.2 Combinations in Different Directions Different seismic systems can be used in each of the orthogonal directions of the structure. The appropriate values of R, Cd, and o should be used for each system. · §12.2.3 Combinations in the Same Direction For non-dual systems used in combination in the same direction, use the least value of R for any of the systems. The Cd and o values shall correspond to the R factor being used in a given direction and shall not be less than the largest respective values for that R factor. Exception: Different systems in each independent line of lateral system are permitted to be designed for the least value of the R factor in that line if the following conditions are met: 1. Occupancy Category I or II. 2. Height is two stories or less. 3. Light frame construction or flexible diaphragms. · §12.2.3.1 Vertical Combinations of Lateral Systems R used in any story shall not exceed the lowest R value used in any story above. Cd and o shall not be less than the largest value of each factor used in any story above. Exceptions:

Chapter 16

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SE Reference Manual

Chapter 16

Table 1 Structural Design Requirements

Description Building height limits Redundancy/Reliability factor (§12.3.4) SDC `A' Table 12.2-1 SDC B Table 12.2-1 SDC C Table 12.2-1 SDC D Table 12.2-1 & §12.2.5.4 = 1.3 SDC E & F Table 12.2-1 & §12.2.5.4 Same as SDC D

= 1.0

= 1.0

= 1.0

=1.00 permitted if conditions in §12.3.4.2 & Table 12.3-3 are met.

1 (§11.7.2) OC I, II & 3 stories with building frame or bearing wall system ­ 2,3,4,5 All other structures ­ 3,4,5 Any structure with site class E or F ­ 3,4,5 Same as SDC B Same as SDC B & All other light framed structures ­ 3,4,5 Regular with T<3.5Ts ­ 3,4,5, Irregular with T<3.5Ts and irregularities listed in Note 3 - 3,4,5 Any structure with torsional irregularity (Table 12.3-1, Type 1a or 1b) - 4,5 Same as SDC D For SDC F, the simplified design procedure (type 2) is not permitted.

Analysis Procedures1,2 (§12.6 & Table 12.6-1) OC ­ Occupany Category (See Note 2 for a description of analytical procedures 1 through 5)

Chapter 16

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Chapter 16

Description Design & Detailing Load Path Connections (§12.1.3 & 11.7.3)

SDC `A'

SDC B

SDC C

SDC D

SDC E & F

Provide continuous path to the lateral system within the structure. Connection between a smaller portion & main structure shall be for Fp=0.05wp Horizontal force shall be greater of: Fp=0.05Wp & Fp 280plf (§11.7.5)

Connections between a smaller portion & the main structure shall be capable of carrying the greater of: Fp=0.133SDSwp or Fp=0.05wp Horizontal force to be greater of: Fp=0.10Wp & Fp=0.40SDSIWp & Fp=400SDSI & Fp 280plf Wall Design to be based on greater of: Fp=0.10Wp & Fp=0.40SDSIWp If anchor spacing > 4ft, design wall to span between anchors

Same as SDC B

Same as SDC B

Same as SDC B

Anchorage of Concrete or Masonry Walls (§12.11 & 11.7.5)

Minimum requirements as per SDC B For flexible diaphragms, Fp=0.8SDSIWp (§12.11.2.1) Maximum length/width ratio for sub-diaphragms shall be 2.5 to 1.0 (§12.11.2.2.1)

Same as SDC C

Same as SDC C

Chapter 16

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Chapter 16

collectors and connections between diaphragms and collectors to vertical elements. Force increase not required if load combinations with over-strength are used. See also `Collectors ...' above in this table.

Notes: 1. 2. 3. OC ­ Occupancy Group, ASCE 7 Table 1-1, CBC Table 1604.5 and 1604A.5. Analysis Procedures: 1 ­ Minimum Lateral Force (§11.7), 2 ­ Simplified Design Procedure, 3 ­ Equivalent Lateral Force, 4 ­ Response Spectrum, 5 ­ Time History. See Section `Earthquake Loads'. Irregular structures with T < 3.5Ts and having only Horizontal Irregularities (Table 12.3-1) type 2, 3, 4, or 5 or Vertical

Irregularities (Table 12.3-2) type 4, 5a or 5b.

Chapter 16

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SE Reference Manual LOADS & ANALYSIS EARTHQUAKE LOADS

Loads & Analysis

Per IBC §1613, the earthquake loads shall be per ASCE 7. The relevant provisions are presented below. All references are to ASCE 7, unless otherwise noted. Per IBC and ASCE 7, the earthquake forces and the associated detailing is based on the `Seismic Design Category (SDC)' assigned to the building. Seismic Design Category (SDC), IBC §1613.5.6, ASCE 7 §11.6: The SDC is a function of the `Occupancy Category' (IBC/CBC Table 1604.5 and ASCE 7 Table 1-1) and the mapped accelerations at the site. See IBC/CBC Tables 1613.5.6(1) and 1613.5.6(2) (ASCE 7 Tables 11.6-1 and 11.6-2, respectively) for SDC classification. SDC A and B indicate low seismic risk; SDC C indicates moderate seismic risk; while SDC D, E and F apply to high seismic risk. The detailing requirements as well as construction quality assurance requirements for SDC `D', `E', and `F' are much more stringent than for the lower categories. Earthquake Loads The code permits a variety of analytical procedures ­ see Table 1 in Chapter `Design Requirements'. The Equivalent Lateral Force Procedure per ASCE 7 §12.8 is presented below. Equivalent Lateral (Static) Force Procedure (ASCE 7 §12.8 & 11.4) · Step 1 ­ Obtain Mapped Spectral Accelerations: ASCE 7 §11.4.1 From the maps (IBC Figure 1613.5(1) through 1613.5(14) or ASCE 7 Chapter 22, obtain the following: Ss = Short period earthquake spectral response acceleration, & S1 = 1-second period earthquake spectral response acceleration · Step 2 - Determine Site Coefficients Fa and Fv: ASCE 7 §11.4.3 Determine Site Coefficients Fa and Fv from Tables 11.4-1 & 11.4-2. If site class is not known, assume `D'.

IBC Earthquake Loads

IBCSL1

SE Reference Manual

Loads & Analysis

Note: OSHPD requires that if a structure is not assigned to SDC E of F, it shall be assigned to SDC D (§1613A.5.6) · Step 6 ­ Compute Base Shear: ASCE 7 §12.8 V = CsW (Eqn 12.8-1)

W = Dead load + 25% live load for storage areas + Actual partition load (or 10psf minimum) + weight of permanent equipment + snow load (§12.7.2) · Step 6a ­ Approximate Period Calculation: ASCE 7 §12.8.2.1 T = Ta = CT hn

x

(Eqn 12.8-7)

§12.8.2 If the period is computed from analysis, T CuTa. where, CT & x are given below (Table 12.8-2) hn = Height of building in feet Cu is given below (Table 12.8-1) Structure Type Steel MRF Concrete MRF Steel EBF All others Cu 0.028 0.016 0.03 0.02 x 0.8 0.9 0.75 0.75 SD1 0.4 0.3 0.2 0.15 0.1 Cu 1.4 1.4 1.5 1.6 1.7

Alternative methods for periods for moment frames and shear wall buildings are presented in §12.8.2.1. · Step 6b ­ Cs calculation: ASCE 7 §12.8.1.1

Cs =

( )

S DS R I

(Eqn 12.8-2)

where, R = Response reduction factor, Table 12.2-1 I = Importance factor, IBC Table 1604.5A, ASCE & Table 1-1. I = 1, 1.25 & 1.5 for Occupancy Category I/II, III & IV, respectively.

IBC Earthquake Loads

IBCSL3

SE Reference Manual The value of Cs need not exceed:

Cs =

Loads & Analysis

( ) ( )

S D1 R T I

for T TL

(Eqn 12.8-3)

Cs =

S D1TL R T2 I

for T > TL

(Eqn 12.8-4)

Cs shall not be less than: C s = 0.01 (OSHPD/DSA, C s = 0.03 ) (Eqn 12.8-5)

Where S1 0.6g, Cs shall not be less than:

Cs = 0.5S1 R I

(Eqn 12.8-6)

·

Step 7 ­ Vertical Distribution of Base Shear: ASCE 7 §12.8.3 At each level the seismic force is given as: Fx = C vxV C vx = wx hxk (Eqn 12.8-11) (Eqn 12.8-12)

w h

i =1

n

k i i

If T 0.5 k = 1.0 If T 2.5 k = 2.0 Use k = 2 or linear interpolation between the period limits. · Seismic Load Effect: ASCE 7 §12.4.2 E = Eh ± Ev E = QE + 0.2SDSD E = QE - 0.2SDSD Where, QE = Effect of horizontal seismic forces 0.2 SDSD = Vertical acceleration effect (Eqn 12.4-4) (Eqn 12.4-1)

IBC Earthquake Loads

IBCSL4

SE Reference Manual

Loads & Analysis

Where seismic over strength factor needs to be included in the design, §12.4.3, Em = Emh ± Ev Em = QE ± 0.2SDSD The load combinations with over strength are given in §12.4.3.2. · Redundancy Factor `': ASCE 7 §12.3.4.2 For SDC A, B, or C, For SDC D, E, or F

= 1.0 = 1.3 = 1.0

For all structures, or if one of the following two conditions are met.

a. Each story resisting more than 35% of the base shear (typically the lower stories in a building) shall comply with the following: 1. Loss of one of the following does not result in more than 33% reduction in story strength: i. An individual brace or connection thereto ii. Moment connections at both ends of one beam iii. A shear wall or wall pier with height-to-length ratio > 1.0 iv. Moment resistance at the base of a single cantilever column. 2. Loss of one of the above does not result in an extreme torsional irregularity (Type 1b, Table 12.3-1). b. For structures regular in plan at all levels with at least two perimeter bays of the seismic force-resisting in each direction at each level resisting more than 35% of the base shear. For shear walls: Number of bays = (n*Wall length)/story height Where, n = 2, For shear walls in light framing. n = 1, for all other shear wall building. In addition to the above, = 1.0 is permitted for the following: 1. Drift & P- calculations 2. Design of non-structural components & non-building structures that are not similar to buildings. 3. Design of collectors, splices, their connections etc., for which the load combinations with over-strength as used.

IBC Earthquake Loads

IBCSL5

SE Reference Manual

Loads & Analysis

4. For design of any member or connection for which the load combinations with over-strength are used. · Displacement amplification: ASCE 7 §9.5.5.7 For allowable stress design, displacement is computed for earthquake loads without dividing by 1.4 and using = 1.0. The design deflection at the center of mass at any level is calculated as,

x =

C d xe I

(Eqn 12.8-15)

where, x = Maximum inelastic displacement at level x. Cd = Displacement amplification factor, Table 12.2-1 xe = deflection from an elastic lateral analysis of the building. The deflections/drifts can be determined for the seismic forces at the actual period calculated for the building, without applying the CuTa limit in Step 6a.

Exceptions to Static Force Procedure: Where applicable, the equivalent lateral force procedure may be substituted by one of the procedures below. See Table-1 of `Chapter 16 Design Requirements' for more information. · Minimum Lateral Force: IBC §11.7.1 Applies to SDC A only. At each floor the minimum base shear shall be: Fx = 0.01Wx where, Fx = Design seismic force @ story x Wx = Seismic weight @ story x · Simplified Procedure: §12.14 Note: Not permitted by OSHPD & DSA (§1613A.5.6.2). This procedure can be used in lieu of the other analytical procedures for the analysis/design of simple buildings with bearing walls or building frame systems, if the building meets certain limitations. See §12.14.1.1 for a complete list and below for the major limitations: 1. The building shall be in Occupancy Category I or II and shall not exceed 3 stories in height. IBC Earthquake Loads IBCSL6

SE Reference Manual

Loads & Analysis

SELECTION OF LATERAL SYSTEMS FOR SEISMIC DESIGN CHAPTERS 19 & 22 As with seismic loads and detailing requirements, the IBC/CBC places limits on the type of structural systems that can be used for lateral design based on Seismic Design Category (SDC)--see section `Chapter 16' and `Earthquake Loads' for more information. The brief list below specifies the minimum concrete and steel system requirements for a given SDC. It is always permitted to provide a better lateral system and take advantage of the lower seismic design forces (ACI 318, R21.2.1) For a detailed listing of lateral systems and associated limitations, see ASCE 7 Table 12.2-1. All reference in the following are to IBC/CBC, unless noted otherwise. Concrete (Chapter 19 & ACI 318) Seismic Design Categories A & B (Low Seismic Risk) §1910.2 & 1910.3 · Ordinary Shear Walls Designed using Chapters 1 through 18 of ACI 318. Note: For SDC A, shear walls can be ordinary plan concrete walls per Chapter 22 of ACI 318 or detailed plain concrete walls per IBC §1908.1.14. · Ordinary Precast Concrete Shear Walls Designed using Chapters 1 through 18 of ACI 318. · Ordinary Moment Frames Designed using Chapters 1 through 18 of ACI 318. §108.1.1 ­ Provide at least two reinforcing bars continuously at top and bottom in beams and develop at (or continuous through) the columns. §1908.1.2 ­ Columns with clear height to maximum dimension ratio of five or less shall also be designed for shear. Seismic Design Category C (Intermediate or Moderate Seismic Risk) §1908.1.4 · Ordinary Shear Walls: Designed using Chapters 1 through 18 of ACI 318.

IBC Lateral System Selection

LSS1

SE Reference Manual

Loads & Analysis

Note: Plain concrete shear walls not permitted except as basement (retaining) walls for one or two family dwellings with stud framing above. · Intermediate Precast Concrete Shear Walls: Designed using Section 21.13 in addition to Chapters 1 through 18 of ACI 318. · Intermediate Moment Frames: Designed using Section 21.12 in addition to Chapters 1 through 18 of ACI 318. · Discontinuous Members (§1908.1.12): Columns supporting discontinuous lateral systems above (such as shear walls) shall be designed for the special seismic load combinations (i.e. using o) with appropriate transverse reinforcement, per 21.12.5.2 of ACI 318, over the full height as well as above and below as required.

Seismic Design Categories D, E, F (High Seismic Risk) §1908.1.4 · Special Shear Walls: Cast-in-place walls designed using Sections 21.2 and 21.7 in addition to Chapters 1 through 18 of ACI 318. Precast walls shall also satisfy §21.8 of ACI 318 in addition to the above. · Special Moment Frames: Cast-in-place frames designed using Sections 21.2, 21.3, 21.4 and 21.5 in addition to Chapters 1 through 18 of ACI 318. Precast frames designed per Sections 21.2, 21.3, 21.4 and 21.6 of ACI 318, including all requirements for ordinary moment frames. · Diaphragms and Foundations: Designed using Sections 21.2 and 21.9 for diaphragms and 21.2 and 21.10 for foundations, in addition to Chapters 1 through 18 of ACI 318. · Frame members not part of the lateral system: Designed/checked per section 21.11 to ensure that they can continue to carry the gravity loads at the maximum lateral displacements corresponding to the design level seismic forces.

IBC Lateral System Selection

LSS2

SE Reference Manual

Loads & Analysis

Steel (Chapter 22, AISC Steel Specifications (ASD/LRFD AISC 360) & AISC Seismic Provisions, AISC 341) Seismic Design Categories A, B & C (Low or Moderate Seismic Risk) §2205.2.1 Steel structures may be designed using the following two options: 1. Use R = 3 per ASCE 7, Table 12.2-1, Item H for `Structural Steel Systems Not Specifically Detailed for Seismic Resistance' in conjunction with the typical AISC LRFD or ASD Specifications. 2. Use an R factor per ASCE 7, Table 12.2-1 and design per AISC Seismic Provisions (ASIC 341), Part I.

Seismic Design Categories D, E & F (High Seismic Risk) §2205.2.2 3. Steel structures shall be designed using AISC Seismic Provisions (ASIC 341-02), Part I.

IBC Lateral System Selection

LSS3

(1) §13.2 Bracing Members §13.2a Braces: KL 4 E r Fy See §13.2a for KL/r greater than above limit. §13.2d Compactness (§8.2b, Table I-8-1): WF & Channels: b 0.30 E t Fy For h/tw under flexure and axial load, see Table I-8-1. Rectangular HSS: b or h 0.64 E tw Fy t Circular HSS: OD 0.044 E t Fy Angles: b 0.30 E t Fy OSHPD/DSA do not permit the use of rectangular HSS sections unless filled with concrete. §13.2c Lateral Force Distribution For a line of bracing: 0.3VTotal Vh tension 0.7Vtotal Vh tension = Horizontal component of axial force for braces in tension. VTotal = Total horizontal force in line of bracing. Note: Exception if all braces are designed to resist the load combinations including o in compression.

(4) §13.2d Columns WF: b 0.30 E t Fy Rectangular HSS: b or h 0.64 E tw Fy t

(2) §13.3 Bracing Connections Same limits as braces, Table I-8-1. §13.3a Tensile strength of connections (including beam-column connection) shall be the lesser of: 1. Pst = RyFyAg (LRFD) or Pst = RyFyAg/1.5 (ASD) 2. Maximum load effect that can be transferred to brace by the system §13.3b Flexural strength of the connection shall be based on 1.1RyMp (LRFD) or (1.1/1.5)RyMp (ASD) of the brace about the critical buckling axis (typically out of plane). This strength requirement does not apply if the connection can accommodate the inelastic rotations due to the brace post-buckling deformations. This can be accomplished by using single plate gussets with a 2t setback from the yield line for out-of-plane rotation to the brace end. The gusset plate shall be designed to resist the compressive strength of the brace without buckling.

Column strength and splice design shall be per §13.5 => See sheet SLRS-Col1&2 for details.

(3) §13.4.a Beam Design for V-Type & Inverted V-Type Bracing 1. Beam shall be continuous between columns and designed to carry all applicable gravity load combinations without braces. 2. For load combinations that include earthquake effects, use the following: a. (1.2 + 0.2SDS)D + Pb + f1L + f2S b. (0.9 - 0.2SDS)D ± Pb where, Pb = unbalanced post-buckling force based on Pst = RyFyAg & Psc = 0.3Pn, where Pn is the nominal compressive capacity of the brace. 3. Both flanges of the beam shall be braced as follows: a. At the point of brace intersection. E r b. At a maximum spacing of Lb = L pd = 0.12 + 0.076 M 1 (A-1-7) M 2 Fy y where, M1 & M2 (k-in) are the smaller and larger moments at the ends of the unbraced length. The ratio is positive for reverse curvature and negative for single curvature. Note: For TS beams, see Appendix 1 §A.1.7. of AISC Specification. Lateral braces shall be per Eqns. A-6-7 & A-6-8 of Appendix 6 of the AISC Spec. with Mr being either RyZFy (LRFD) or RyZFy/1.5(ASD) and Cd = 1.0.

§13.2e Built-up Members: For each individual element between stitches, l/r 0.4l t/r, where lt/r is for whole member. Shear strength of stitches tensile strength of each element. Stitches to be placed uniformly along length. No less than 2 stitches. No bolted stitches within the middle ¼ of the brace clear length.

Net Area: Typical connections use slotted HSS members welded to the gusset. The net area in tension shall be calculated as the gross area minus the slot width times the thickness of the HSS. This area needs to be replaced via a plate welded to the two non-slotted faces of the HSS (curved plates for round HSS). The side plates need to be adequately extended either side of the slot via a shear lag analysis (see §D3 of the AISC Specification).

STEEL SPECIAL CONCENTRIC BRACED FRAMES (AISC 341, §13, ASCE 7, Table 12.2-1) R = 6, = 2, Cd=5

SLRS-SCBF

SE Reference Manual REINFORCED CONCRETE SHEAR WALL DESIGN Referencec: ACI-318 & IBC 2006/CBC 2007. Wall Type Ordinary Shear Wall Special Shear Wall Notes: 1. 2.

Concrete Design

Axial & Flexural Other SDC Design A, B 14.2, 14.3 11.10 (10.2, 10.3. 10.1010.14, 10.17) A, B, C, 21.7.2 21.7.3, 21.7.5 Boundary D, E, F 21.7.4 (10.2, 10.3. 10.10- Elements 10.14, 10.17) 21.7.6 Provisions 10.10-10.14, 10.17 address slenderness, moment magnification, bearing strength etc. and typically do not govern the design. Precast walls follow similarly to above, except `Intermediate Precast Walls' (permitted in SDC A, B, C) shall also comply with 21.13.

Reinforcement Limits 14.3 11.10.8, 11.10.9

Shear Design

Reinforcement Limits (§11.10.9, 14.3, 21.7.2)

Note: 1.

2.

OSHPD/DSA ­ Minimum reinforcement parallel to all edges of the wall and boundaries of all openings shall be twice the shear reinforcement required per lineal foot of wall (§1908A.1.37). For seismic design reinforcement development lengths (& splices) shall be per 21.5.4 ­ See `Reinforcement Development & Lap Splices', pp. RDL3-RDL5.

Shear Wall Design

CSWD1

SE Reference Manual Boundary element requirements for Special Walls (§21.7.6):

Concrete Design

Boundary element requirements can be evaluated by either one of the two methods described below: a) For walls that are effectively continuous from the base to the top with a single critical section for axial and flexural loads (§21.7.6.2): Provide boundary elements where: where,

c

600( u / hw )

lw

(21-8)

c = neutral axis depth for (1.2 + 0.2SDS)D + QE + f1L u = design displacement at top of wall (i.e. Cdx/I) u/hw 0.007 (§21.7.6.2(a)) For u/hw = 0.007, c = 0.24w.

At some height along the wall, the above requirement will not be applicable Extend the boundary element reinforcing beyond this elevation by a distance not less than the larger of: w or Mu/4Vu. b) For walls not designed per above, provide boundary elements at wall boundaries, and edges of openings where maximum compressive stress exceeds 0.2f'c. Discontinue boundary detailing where the stress is less than 0.15f'c (§21.7.6.3). Pu Mu Shear wall Factored Loads

0.15f'c 0.2f'c

Extend up to and discontinue above Boundary detailing required.

Axial Stress

Use gross section properties with elastic force distribution §21.7.6.3

Flexural Stress If res > 0.2f'c, provide boundary reinforcing.

Resultant Stress

Shear Wall Design

CSWD6

SE Reference Manual REINFORCED CONCRETE BEAM DESIGN

Concrete Design

Reference: ACI 318 General Design Provisions for Beams: Analysis Reinforcement Limits: · Check

min = s min

3 f 'c f

y

bw d §10.5.1

min =

6 f 'c

200 bw d fy

bw d for T-beams with flanges in tension) fy The above limits need not apply if As provided, at each section, exceeds by 1/3rd the steel area required by analysis (§10.5.3). In ACI 318-05, section strength is governed by available ductility (i.e. amount of reinforcement at a given section and tensile stress in the reinforcement) and the strength-reduction factor, , e.g. the higher the ductility, the smaller the strength reduction and vice-versa. Each section is classified as either compression-controlled, tension-controlled or in transition. These categories are based on the net tensile strain (t) in the extreme tension steel and are defined at a concrete ultimate strain (cu) of 0.003. · Balanced strain conditions: @ cu = 0.003, sb = fy/Es sb = 0.002 for fy = 60ksi · · · Compression-controlled: Tension-controlled: Transition-range: @ cu = 0.003, t sb @ cu = 0.003 , t 0.005 @ cu = 0.003 , 0.002 < t 0.005 §10.3.2 §10.3.3 §10.3.3 §10.3.4 §10.3.4

( As min =

Concrete Beam Design

CBD1

SE Reference Manual · Beam Deflection (§9.5.2)

Concrete Design

Per Table 9.5(a), deflections need not be computed if the following minimum depths are provided (for normal weight concrete & 60ksi reinforcement): Beams Slabs - Simple span: L/16 L/20 - Cantilever: L/8 L/10 - One end continuous: L/18.5 L/24 - Both ends continuous: L/21 L/28 Deflection Calculation (§9.5.2.3): Deflection is to be based on beam formulas and Ie shown below,

M I e = cr M a

M cr =

3 M I g + 1 - cr Ma

3

I cr

D 2

(Eqn 9-8)

fr I g yt

where, f r = 7.5 f ' c & y t =

(Eqn 9-9)

Ma is the service level moment (if Ma < Mcr=> No cracking =>Ie = Ig)

I cr

b(kd ) 3 = + nAs (d - kd ) 2 3 Using transformed section from working stress design. PCA Notes on ACI 318-95, pg. 8-3

b 2 d + 1 - 1 nAs kd = b nA s Long-term deflection factors (§9.5.2.5):

=

1 + 50 '

(Eqn 9-11)

where, ' = compressive steel ratio = 2.0 for 5 years or more, 1.4 for 12 months or more etc. Notes: 1. See ACI 318, Table 9.5(a) for quick estimates of slab/beam thickness. 2.See ACI 318, Table 9.5(b) or UBC/CBC Table 19-C-2 for permissible deflections (typically use D+L L/240 & L L/360). Concrete Beam Design CBD5

SE Reference Manual Non-Seismic Beam Reinforcement Detailing (§12.10, 12.11, & 12.12): Positive Moment Reinforcement: · · ·

Concrete Design

Distance to extend reinforcement past where it is no longer required = MAX(d,12db) ­ except at supports of simple spans and ends of cantilevers. Extend bars at least d past the critical section. Minimum reinforcement to be extended at least 6" into support (Bars `B'): 1 Simple span beams: As + 3 §12.11.1 1 Continuous beams: As + 4 At simple supports & points of inflection, bar size shall be limited such that d satisfies the following:

·

Mn §12.11.3 + la Vu Mn = Nominal flexural capacity of beam Vu = Factored shear at the section la = Embedment length beyond center of support or maximum of beam effective depth & 12db at an inflection point. Ld

Notes: 1. This provision limits the bar size to ensure adequate Ld is available. 2. Use 1.3(Mn/Vn) in above equation if a compressive reaction confines the end of the bars.

Concrete Beam Design

CBD8

SE Reference Manual Seismic Provisions for Special Moment Frame (SMRF) Beams: · · Pu 0.10Agf'c

ClearSpan 4 d

Concrete Design

§21.3.1.1 §21.3.1.2

· · ·

Width 0.3 Depth Width 10" As top & As bot 3 f 'c fy bw d & 200bw d fy

§21.3.1.3 §21.3.1.4 §21.3.2.1

max = 0.025 , where =

As bw d

Provide 2 continuous bars top and bottom, typical.

· · ·

At face of joint,

As min bot = ½ As top

§1921.3.2.2

Anywhere along the beam length, Mn min at top & bottom ¼ Mn max. Lap splices permitted only if confined over full length by hoop or spiral reinforcement (see figure below). §21.3.2.3 Beam shear demand, Ve =

·

(M

prA

+ M prB )

Lclr

+

wg Lclr 2

§21.3.4.1

Where, MprA & MprB = Moment capacities @ beam ends using 1.25fy & =1.0 Wg = Factored gravity load Lclr = Clear span · If

Vu & §21.3.4.2 Pu < 0.05 Ag f ' c 2 Ve = seismic shear demand from analysis. Assume Vc = 0 & design stirrups to carry entire shear demand, Ve (shear from analysis)--see CBD4 for Vs. Ve

Concrete Beam Design

CBD11

SE Reference Manual

Concrete Design

Since Ve approximates the maximum shear that can develop in a member, use = 0.75 (§21.3.4.1 & 9.3.4).

Detailing Requirements for SMRF Beams Note: For development lengths, splices etc. see `Concrete Column Design' section.

Concrete Beam Design

CBD12

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