04-05-2012, 10:07 AM
SAFE RC Design
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Chapter 1
Introduction
SAFE automates several slab and mat design tasks. Specifically, it integrates
slab design moments across design strips and designs the required reinforcement;
it checks slab punching shear around column supports and concentrated
loads; and it designs beam flexural, shear, and torsion reinforcement. The design
procedures are outlined in the chapter entitled "SAFE Design Features” in
the Key Features and Terminology manual. The actual design algorithms vary
based on the specific design code chosen by the user. This manual describes
the algorithms used for the various codes.
It should be noted that the design of reinforced concrete slabs is a complex subject
and the design codes cover many aspects of this process. SAFE is a tool to
help the user in this process. Only the aspects of design documented in this
manual are automated by SAFE design capabilities. The user must check the
results produced and address other aspects not covered by SAFE.
Notations 2 - 1
Chapter 2
Design for ACI 318-08
This chapter describes in detail the various aspects of the concrete design procedure
that is used by SAFE when the American code ACI 318-08 [ACI 2008]
is selected. Various notations used in this chapter are listed in Table 2-1. For
referencing to the pertinent sections of the ACI code in this chapter, a prefix
“ACI” followed by the section number is used herein.
The design is based on user-specified load combinations. The program provides
a set of default load combinations that should satisfy the requirements for
the design of most building type structures.
English as well as SI and MKS metric units can be used for input. The code is
based on inch-pound-second units. For simplicity, all equations and descriptions
presented in this chapter correspond to inch-pound-second units unless
otherwise noted.
2.1 Notations
Table 2-1 List of Symbols Used in the ACI 318-08 Code
Acp Area enclosed by the outside perimeter of the section, sq-in
Ag Gross area of concrete, sq-in
SAFE Reinforced Concrete Design
2 - 2 Notations
Table 2-1 List of Symbols Used in the ACI 318-08 Code
Al Area of longitudinal reinforcement for torsion, sq-in
Ao Area enclosed by the shear flow path, sq-in
Aoh Area enclosed by the centerline of the outermost closed transverse
torsional reinforcement, sq-in
As Area of tension reinforcement, sq-in
A's Area of compression reinforcement, sq-in
At /s Area of closed shear reinforcement per unit length of member for
torsion, sq-in/in
Av Area of shear reinforcement, sq-in
Av /s Area of shear reinforcement per unit length, sq-in/in
a Depth of compression block, in
amax Maximum allowed depth of compression block, in
b Width of section, in
bf Effective width of flange (flanged section), in
bo Perimeter of the punching shear critical section, in
bw Width of web (flanged section), in
b1 Width of the punching shear critical section in the direction of
bending, in
b2 Width of the punching shear critical section perpendicular to the
direction of bending, in
c Depth to neutral axis, in
d Distance from compression face to tension reinforcement, in
d' Distance from compression face to compression reinforcement, in
Ec Modulus of elasticity of concrete, psi
Es Modulus of elasticity of reinforcement, psi
f 'c Specified compressive strength of concrete, psi
f 's Stress in the compression reinforcement, psi
Chapter 2 - Design for ACI 318-08
Notations 2 - 3
Table 2-1 List of Symbols Used in the ACI 318-08 Code
fy Specified yield strength of flexural reinforcement, psi
fyt Specified yield strength of shear reinforcement, psi
h Overall depth of a section, in
hf Height of the flange, in
Mu Factored moment at a section, lb-in
Nu Factored axial load at a section occurring simultaneously with Vu or
Tu, lb
Pu Factored axial load at a section, lb
pcp Outside perimeter of concrete cross section, in
ph Perimeter of centerline of outermost closed transverse torsional
reinforcement, in
s Spacing of shear reinforcement along the beam, in
Tcr Critical torsion capacity, lb-in
Tu Factored torsional moment at a section, lb-in
Vc Shear force resisted by concrete, lb
Vmax Maximum permitted total factored shear force at a section, lb
Vs Shear force resisted by transverse reinforcement, lb
Vu Factored shear force at a section, lb
αs
Punching shear scale factor based on column location
βc
Ratio of the maximum to the minimum dimensions of the punching
shear critical section
β1
Factor for obtaining depth of the concrete compression block
εc
Strain in the concrete
εc max Maximum usable compression strain allowed in the extreme
concrete fiber, (0.003 in/in)
εs
Strain in the reinforcement
SAFE Reinforced Concrete Design
2 - 4 Design Load Combinations
Table 2-1 List of Symbols Used in the ACI 318-08 Code
εs,min Minimum tensile strain allowed in the reinforcement at nominal
strength for tension controlled behavior (0.005 in/in)
φ Strength reduction factor
γf
Fraction of unbalanced moment transferred by flexure
γv
Fraction of unbalanced moment transferred by eccentricity of shear
λ Shear strength reduction factor for lightweight concrete
θ Angle of compression diagonals, degrees
2.2 Design Load Combinations
The design load combinations are the various combinations of the load cases
for which the structure needs to be designed. For ACI 318-08, if a structure is
subjected to dead load (D), live load (L), pattern live load (PL), snow (S), wind
(W), and earthquake (E) loads, and considering that wind and earthquake
forces are reversible, the following load combinations may need to be considered
(ACI 9.2.1):
1.4D (ACI 9.2.1)
1.2D + 1.6L (ACI 9.2.1)
1.2D + 1.6 (0.75 PL) (ACI 13.7.6.3)
0.9D ± 1.6W
1.2D + 1.0L ± 1.6W (ACI 9.2.1)
0.9D ± 1.0E
1.2D + 1.0L ± 1.0E (ACI 9.2.1)
1.2D + 1.6L + 0.5S
1.2D + 1.0L + 1.6S
1.2D + 1.6S ± 0.8W
1.2D + 1.0L + 0.5S ± 1.6W
1.2D + 1.0L + 0.2S ± 1.0E
(ACI 9.2.1)
The IBC 2006 basic load combinations (Section 1605.2.1) are the same. These
Chapter 2 - Design for ACI 318-08
Limits on Material Strength 2 - 5
also are the default design load combinations in SAFE whenever the ACI 318-
08 code is used. The user should use other appropriate load combinations if
roof live load is treated separately, or if other types of loads are present.
2.3 Limits on Material Strength
The concrete compressive strength, f 'c , should not be less than 2500 psi (ACI
5.1.1). The upper limit of the reinforcement yield strength, fy, is taken as 80 ksi
(ACI 9.4) and the upper limit of the reinforcement shear strength, fyt, is taken as
60 ksi (ACI 11.5.2).
SAFE enforces the upper material strength limits for flexure and shear design
of beams and slabs or for torsion design of beams. The input material strengths
are taken as the upper limits if they are defined in the material properties as
being greater than the limits. The user is responsible for ensuring that the minimum
strength is satisfied.
2.4 Strength Reduction Factors
The strength reduction factors, φ, are applied to the specified strength to obtain
the design strength provided by a member. The φ factors for flexure, shear, and
torsion are as follows:
φ = 0.90 for flexure (tension controlled) (ACI 9.3.2.1)
φ = 0.75 for shear and torsion (ACI 9.3.2.3)
These values can be overwritten; however, caution is advised.
2.5 Beam Design
In the design of concrete beams, SAFE calculates and reports the required areas
of reinforcement for flexure, shear, and torsion based on the beam moments,
shear forces, torsion, load combination factors, and other criteria described in
this section. The reinforcement requirements are calculated at each station
along the length of the beam.
SAFE Reinforced Concrete Design
2 - 6 Beam Design
Beams are designed for major direction flexure, shear, and torsion only. Effects
resulting from any axial forces and minor direction bending that may exist in
the beams must be investigated independently by the user.
The beam design procedure involves the following steps: