BRACED FRAMES
5.23 COLUMN BASE-PLATE DESIGN The design discussed here involves two issues:
1. Design the base plate for maximum axial compression. The maximum axial design force is 690 kips [12], derived from formula (30-1), CHAP.
16, DIV. IV, 1630.1.1 of the 1997 UBC:
E⫽ Eh ⫹Ev (30-1)
Therefore it includes both lateral and vertical earthquake force com-ponents.
The reader will recall that we had to multiply PE, generated by Eh
and Evearthquake components, by 0.4R to obtain the maximum column design load. Because the column transfers the same axial load to the base plate, we are obliged to design the base plate for an increased earthquake design force (0.4R)PEadded to factored dead and live loads, per formula (6-1), CHAP. 22, DIV. IV.
Because the foundation is part of the load path system, it must safely transfer all gravity and seismic loads to the ground.
2. Design the base plate–footing connection for maximum uplift. The min-imum column reaction will be the governing force for the column
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5.23 COLUMN BASE-PLATE DESIGN 175
plate design against uplift. The maximum uplift force is based on formula (30-1) and, instead of using the fundamental load combinations of 1612.2.1, the formula is derived from the special load combinations of formula (6-2), CHAP. 22, DIV. IV. Formula (6-2) also increases the seismic-caused uplift, 0.4R ⫽ 2.56 times. Only the tributary dead load carried by the frame itself was entered in formula (6-2).
The computed uplift is
Pu ⫽ 634 kips Computer analysis load case [13]
This is an extremely large uplift force demanding an equally large foundation capacity to counteract it, which might not prove practicable. However, CHAP.
22, DIV. IV, 6.1.c, states:
6.1.c. The axial Load Combinations 6-1 and 6-2 are not required to exceed either of the following:
1. The maximum loads transferred to the column, considering 1.25 times the design strengths of the connecting beam or brace elements of the structure.
2. The limit as determined by the foundation capacity to resist overturning up-lift.
The uplift limit for the foundation capacity for this project is Pu⫽ 500 kip / footing. We will use this value for maximum uplift in the column base-plate design.
Design of Base Plate for Compression Design Parameters
Size of footing 10 ft⫻ 10 ft Strength of concrete ƒ⬘ ⫽c 3.0 ksi
Steel plate A36
Bolts A490
Procedure We will follow the procedure outlined in ‘‘Design of Axially Loaded Base Plates,’’ Part 11, Volume II of the LRFD Specification. Following is a brief review of the basic issues.
The compressive strength of both concrete and soil is considerably smaller than the strength of steel. The ƒ⬘cof concrete used for footing is 3.0–4.0 ksi as compared to 36–50 ksi of structural steel, that is just about ––101th. The function of the base plate is to spread the highly concentrated column load over a sufficiently large area to keep the footing from being overstressed. Two
176 SEISMIC STEEL DESIGN: BRACED FRAMES
types of concrete design strength apply depending on the relative geometric relationship of base plate and footing:
(a) Unconfined: LRFD equation (J9-1) (b) Confined: LRFD equation (J9-2)
When the base plate covers the entire concrete support area, we refer to the uniaxial strength of concrete, and the resisting force is expressed as
Pu ⫽cPp⫽ c(0.85 ƒ⬘cA )1 From LRFD equation (J9-1) where A1 ⫽ contact area
c⫽ 0.60 for bearing on concrete from which
Pu
A1 ⫽
c0.85ƒ⬘c
On the other hand, the confined strength of concrete is activated if the load-receiving concrete area—the top surface of the footing—is larger than the A1 contact area. The gross concrete area A2 ⬎ A1 surrounding the contact area gives lateral confinement to the concrete in contact with the base plate. The correction factor to allow increase in bearing strength is given as
A2
by the Specification Limited to maximum value of 2
冪A1
The design strength includes the effect of confinement:
A2
cPp⫽ c(0.85 ƒ⬘cA )1 冪A1 From LRFD equation (J9-2)
Then
A2 A2
A1⫽ P /u c(0.85 ƒ⬘cA )1 冪A1 where 冪A1ⱕ 2
For the actual computation we refer to the procedure outlined by W. A. Thorn-ton16and adopted by the Specification:
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5.23 COLUMN BASE-PLATE DESIGN 177
Figure 5.16 The LRFD design dimensions of the base plate.
Notation
d, bƒ Depth and flange width of column B Width of base plate
N Length of base plate
t Required thickness of base plate
m, n Cantilever overhang dimensions of base plate (Figure 5.16) l Maximum value of m, n, orn⬘
4dbƒ Pu
X 冋(d ⫹b )ƒ 2册cPp
Pp Design strength of concrete bearing area 兹X
2 ⱕ 1
1 ⫹ 兹1 ⫺X
n⬘ 兹db / 4ƒ
The thickness of the plate is determined by 2Pu
t ⫽ l冪0.9F BNy
Steps to Design Column Base Plate of Braced Frame 1. Compute A2.
2. Compute A1 from LRFD equation (J9-2).
3. Select B and N.
178 SEISMIC STEEL DESIGN: BRACED FRAMES
4. Determine values of m, n, andn⬘. 5. Determine the required plate thickness:
2 2
The selection of B and N is also determined by geometric considerations to accommodate connection requirements for uplift:
B⫽ 13.0 in. and N⫽18.0 in.
are chosen with
2 2
A1⫽ 234 in. ⬎ 226 in.
Note that by selecting 13 in. for B, some conventional, although not sacred, rules of the construction industry which favor an even number of inches for plate dimension have been bypassed. However, plate sizes as chosen above can be ordered and delivered to the project site without difficulties.
N⫺0.95d 18.0 ⫺(0.95 ⫻ 12.71)
5.23 COLUMN BASE-PLATE DESIGN 179
Design of Base Plate for Uplift
We will provide four A490 bolts. The design tensile strength of four 1–12 A490 bolts using Table 8-15, Volume II of the Specification, is
tPu⫽ 4(150)⫽ 600 kips⬎500 kips applied Figure 5.17 shows the disposition of the bolts.
The required plate thickness to resist bending caused by the pair of bolts on each side of the column flange is determined as
1 2 1
–4(0.9)(F )(B)(t)y ⫽ –2P (I)u where I is the lever arm in inches. Then
2P Iu 2(500)(1.5)
t ⫽冪0.9F By ⫽ 冪(0.9)(36)(13) ⫽1.887 in.⬍ 2.25 in. Provided Provide two L5 ⫻ 3 ⫻ –58 ⫻ (4 in. long) to act as reinforcement welded to the base plate. This will supply the extra strength needed to improve the response of conventionally designed base plates (as experience has taught us) against stress reversals caused by strong ground motion. The base-plate di-mensions, bolts, and connections are shown in Figure 5.17.
180 SEISMIC STEEL DESIGN: BRACED FRAMES