In the design of structural members in buildings that are not subjected to signifi- cant wind or earthquake forces the factored loads are computed from either Eq. (2-5) or Eq. (2-6):
(2-5) (ACI Eq. 9-1) whereDis the specified dead load. Where a fluid load,F, is present, it shall be included with the same load factor as used for Din this and the following equations.
For combinations including dead load; live load,L; and roof loads:
(2-6) (ACI Eq. 9-2) where
L = live load that is a function of use and occupancy Lr = roof live load
S = roof snow load R = roof rain load
The terms in Eqs. (2-5) through (2-11) may be expressed as direct loads(such as distrib- uted loads from dead and live weight) or load effects (such as moments and shears caused by the given loads). The design of a roof structure, or the columns and footings supporting a roof and one or more floors, would take the roof live load equal to the largest of the three loads ( or SorR), with the other two roof loads in the brackets taken as zero. For the common case of a member supporting dead and live load only, ACI Eq. (9-2) is written as:
(2-4) If the roof load exceeds the floor live loads, or if a column supports a total roof load that exceeds the total floor live load supported by the column:
(2-7) (ACI Eq. 9-3) The roof loads are principal variable loads in ACI Eq. (9-3), and they are companion variable loadsin ACI Eq. (9-4) and (9-2).
(2-8) (ACI Eq. 9-4) Wind load,W, is the principal variable load in ACI Eq. (9-4) and is a companion variable load in ACI Eq. (9-3). Wind loads specified in ASCE/SEI 7-10 represent strength-level winds, as opposed to the service-level wind forces specified in earlier editions of the minimum load standards from ASCE/SEI Committee 7. If the governing building code for the local jurisdiction specifies service-level wind forces, 1.6Wis to be used in place of 1.0W in ACI Eqs. (9-4) and (9-6), and 0.8W is to be used in place of 0.5W in ACI Eq. (9-3).
Earthquake Loads
If earthquake loads are significant:
(2-9) (ACI Eq. 9-5) where the load factor of 1.0 for the earthquake loads corresponds to a strength-level earthquakethat has a much longer return period, and hence is larger than a service-load
U = 1.2D + 1.0E + 1.0L + 0.2S U = 1.2D + 1.0W + 1.0L + 0.51Lr or S or R2 U = 1.2D + 1.61Lr or S or R2 + 11.0L or 0.5W2
U = 1.2D + 1.6L Lr
U = 1.2D + 1.6L + 0.51Lr or S or R2 U = 1.4D
earthquake. If the loading code used in a jurisdiction is based on the service-load earth- quake, the load factor on Eis 1.4 instead of 1.0.
Dead Loads that Stabilize Overturning and Sliding
If the effects of dead loads stabilize the structure against wind or earthquake loads, (2-10) (ACI Eq. 9-6) or
(2-11) (ACI Eq. 9-7) Load Factor for Small Live Loads
ACI Code Section 9.2.1(a) allows that the load factor of 1.0 for Lin ACI Eqs. (9-3), (9-4), and (9-5) may be reduced to 0.5 except for
(a) garages,
(b) areas occupied as places of public assembly, and (c) all areas where the live load is greater than 100 psf.
Lateral Earth Pressure
Lateral earth pressure is represented by the letter H. Where lateral earth pressure adds to the effect of the principal variable load, H should be included in ACI Eqs. (9-2), (9-6), and (9-7) with a load factor of 1.6. When lateral earth pressure is permanent and reduces the affect of the principal variable load,Hshould be included with a load fac- tor of 0.9. For all other conditions,H is not to be used in the ACI load combination equations.
Self-Straining Effects
ACI Code Section 9.2.3 uses the letter Tto represent actions caused by differential settlement and restrained volume change movements due to either shrinkage or thermal expansion and contraction. Where applicable, these loads are to be considered in combination with other loads. In prior editions of the ACI Code,Twas combined with dead load, D, in ACI Eq.
(9-2), and thus, the load factor was 1.2. The 2011 edition of the ACI Code states that to es- tablish the appropriate load factor for Tthe designer is to consider the uncertainty associated with the magnitude of the load, the likelihood that Twill occur simultaneously with the max- imum value of other applied loads, and the potential adverse effects if the value of Thas been underestimated. In any case, the load factor for Tis not to be taken less than 1.0. In typical practice, expansion joints and construction pour strips have been used to limit the effects of volume change movements. A recent study of precast structural systems [2-13] gives recom- mended procedures to account for member and connection stiffnesses and other factors that may influence the magnitude of forces induced by volume change movements.
In the analysis of a building frame, it is frequently best to analyze the structure elastically for each load to be considered and to combine the resulting moments, shears, and so on for each member according to Eqs. (2-4) to (2-11). (Exceptions to this are analyses of cases in which linear superposition does not apply, such as second-order analyses of frames. These must be carried out at the factored-load level.) The procedure used is illustrated in Example 2-1.
U = 0.9D + 1.0E U = 0.9D + 1.0W
EXAMPLE 2-1 Computation of Factored-Load Effects
Figure 2-7 shows a beam and column from a concrete building frame. The loads per
foot on the beam are dead load, and live load, Addition-
ally, wind load is represented by the concentrated loads at the joints. The moments in a beam and in the columns over and under the beam due to 1.0D, 1.0L, and 1.0W are shown in Figs. 2-7b to 2-7d.
Compute the required strengths, using Eqs. (2-4) through (2-11). For the moment at sectionA, four load cases must be considered
(a) (2-5)
(ACI Eq. 9-1)
•
Because there are no fluid or thermal forces to consider,= -54.6 k-ft.
U = 1.4 * -39 U = 1.4D
L = 0.75 kip/ft.
D = 1.58 kips/ft,
.
Fig. 2-7
Moment diagrams—
Example 2-1.
(b) (2-6) (ACI Eq. 9-2)
•
Assuming that there is no differential settlement of the interior columns rela- tive to the exterior columns and assuming there is no restrained shrinkage, the self- equilibrating actions,T, will be taken to be zero.•
Because the beam being considered is not a roof beam, S,andRare all equal to zero. (Note that the axial loads in the columns support axial forces from the roof load and the slab live load.)ACI Eq. 9-2 becomes
(2-4) (c) Equation (2-7) does not govern because this is not a roof beam.
(d) For Eq. (2-8), assume service-level wind forces have been specified, so the load factor of 1.6 is used for W.
(2-8) where ACI Code Section 9.2.1(a) allows 1.0Lto be reduced to 0.5, so,
The positive and negative values of the wind-load moment are due to the possibility of winds alternately blowing on the two sides of the building.
(e) The dead-load moments can counteract a portion of the wind- and live-load moments. This makes it necessary to consider Eq. (2-10):
(2-10)
Thus the required strengths, at section A–Aare k-ft and k-ft. ■ This type of computation is repeated for a sufficient number of sections to make it possible to draw shearing-force and bending-moment envelopes for the beam.
Strength-Reduction Factors, , ACI Code Section 9.3
The ACI Code allows the use of either of two sets of load combinations in design, and it also gives two sets of strength-reduction factors. One set of load factors is given in ACI Code Section 9.2.1, with the corresponding strength-reduction factors, given in ACI Code Section 9.3.2. Alternatively, the load factors in Code Section C.9.2.1 and the corresponding strength-reduction factors in ACI Code Section C.9.3.1 may be used.
This book only will use the load factors and strength-reduction factors given in Chapter 9 of the ACI Code.
f, f
-191 +98.9
Mu,
= +98.9 or -169 k-ft
= 0.9 * -39 ; 1.6 * 84 = -35.1 ; 134 U = 0.9D + 1.6W
= -191 or +78.1 k-ft
= -56.3 ; 134.4
= 1.2 * -39 ; 1.6 * 84 + 0.5 * -19 U = 1.2D + 1.6W + 0.5L
U = 1.2D + 1.6W + 0.5L + 1.01Lr or S or R2
= 1.2 * -39 + 1.6 * -19 = -77.2 k-ft U = 1.2D + 1.6L
Lr, U = 1.2D + 1.6L + 0.51Lr or S or R2
Flexure or Combined Flexure and Axial Load Tension-controlled sections
Compression-controlled sections:
(a) Members with spiral reinforcement (b) Other compression-controlled sections
There is a transition region between tension-controlled and compression-controlled sec- tions. The concept of tension-controlled and compression-controlled sections, and the resulting strength-reduction factors, will be presented for beams in flexure, axially loaded columns, and columns loaded in combined axial load and bending in Chapters 4, 5, and 11.
The derivation of the factors will be introduced at that time.
Other actions Shear and torsion Bearing on concrete Strut-and-tie model