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Jonathan Gallis [Structural] Final Report

“Building Z” South Halls Dormitory Addition Page 34

The last modification to member forces from the modal analysis is the design for

torsion. Since rigid diaphragms were not used, as discussed later, the ability to automatically

include an eccentricity of the center of mass was lost. Instead, using the torsion spreadsheets

which examined the effects of torsion, the average max design shear can be compared to the

direct shear component to look at the amount of amplification each frame can expect to see onaverage. It was found that BF-1 and BF-12 would on average see about a 20% increase in

design shear from direct shear, and BF-4 and BF-8 would only see about an 8% increase. For

BF-C and BF-H the amplification varied from 3% to 20% depending on the story and frame.

Thus, the design forces were a result several modifications to get the design forcese.

For dead load, the load combination involving earthquake involves a vertical component as

well, effectively making the dead load factor 1.2 + .2(Ss).

Modeling and Member Analysis

Building Properties for Hand Calculations

As discussed in Tech3, a variety of methods could be employed to estimate the effective

center of rigidity. In tech3, it was shown that using the shears was a more effective way of

capturing actual behavior. Thus, it was the method that was used in the “hand calc” method

with the EFM to give an initial sizing of members. Note: the example shown in figure ## has

“dumby” loads, as the handling of forces within the truss was not within the scope of the

redesign.

06N 06S 05 04 03 02 01N 01S dir

BF-1 120 4 32.9 46.7 63.7 76.8 0.0 46.2 x

BF-4 712 4 56.7 74.4 92.4 131.3 245.7 0.0 x

CW-4. 746 0.0 0.0 0.0 0.0 69.4 0.0 x

BF-8 1304 4 55.1 71.8 97.2 99.3 0.0 33.8 x

BF-12 2054 4 38.6 53.0 70.1 94.4 112.2 0.0 x

CW-K 120 0.0 23.6 0.0 0.0 0.0 0.0 0.0 0.0 y

BF-H 402 0.0 22.7 85.1 115.2 150.2 182.4 0.0 110.5 y

CW-F 608 0.0 0.0 0.0 0.0 0.0 0.0 0.0 149.3 yCW-E 712 0.0 0.0 0.0 0.0 0.0 0.0 15.4 0.0 y

BF-C 918 25.6 0.0 98.4 130.9 167.1 200.3 56.9 0.0 y

CW-A 1200 27.1 0.0 0.0 0.0 0.0 0.0 186.2 0.0 y

COR X 1,383 712 1,066 1,062 1,064 1,060 1,070 620

COR Y 1,063 258 679 676 674 672 1,109 520

A X 1.000 1.000 1.000 1.000 1.000 1.000 2.280 1.098

A Y 1.008 1.008 1.000 1.000 1.000 1.000 1.000 1.000

Frame Stiffness

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Tech 3: Computer Model (ETABS)

A Model of Building Z was created in ETABS. It was assumed that the flexural rigidity of

typical gravity columns was a negligible contribution in the overall rigidity of the structure, and

thus only the columns within the braced frames were modeled. Correct sections and properties

were assigned according to the drawings, including the varying thicknesses of concrete shear

walls. Property modifiers were used to set the mass of all elements to 0, and instead an extra

point was added to each floor with assignments of mass and rotational moment of inertia,

whose location was placed at the calculated center of mass. A rigid diaphragm constraint was

used on the points on each floor and the point mass.

ETABS automatically uses insertion point for beams; it aligns the

top of steel (T.O.S.) to the line intersection. However, to effectively adjust

the T.O.S. to be 5.5” lower than the story level to account for the thickness

of the slab the first story height was simply reduced by 5.5”. Rigid end

offsets were used based on connectivity, as shown in figure ## the next

page, and could be as high as a 3’ reduction in overall brace length. The

detailing of the eccentric braces required that the work point (intersection

of line elements, if extended) of the eccentric braces should be located

2’6” above the midpoint of the

centerline of the beams.

Calculations in the appendix show

that for the beams used in the

frames, this results in an effective

spacing of 1.5’ from the centerline if the work points

were moved down to the T.O.S., which is how it is

modeled in ETABS. All braces were given end releases

from moments on both ends, on the assumption that

the connection would not be rotationally restrained.

Openings in the shear walls were also roughly

included. This is a level of detail not necessarily

required for this stage of analysis; however the holes

reduced the stiffness of the shear walls significantly,

and it was decided to incorporate them. A smaller max

mesh size of 16” was used to handle the openings.

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The shear walls also “brace” the frames in with differing connecting details ways

depending on the frame. For frames BF-C and BF-H, the shear wall attaches with shear studs to

a WT shape at the top of the wall, which in turn is connected to a beam of the frame through

an angle. In the model, this is accomplished by connecting the shear wall (membrane element)

to the above beam and keeping a gap (~6” as detailed in the drawings) between the columnsand the wall.

A second type of connection is found in frame BF-12. The connection is similar; however

the wall is offset to the side as seen in figure 23. An additional column line was added for this

shear wall, and the “connection” to the frame was simply through the rigid diaphragm. Lastly,

frame BF-4 effectively had the columns embedded in the wall, which was modeled by ending

the column in a moment connection to the wall. The brace, however, was given a moment

release.

A major aspect of the model is the splitting of the first floor slab into two separate slabs,

as the slab is detailed to have a 1” expansion joint to divide itself in two. Thus the model had

two different diaphragm constraints on the first floor, each including their own point mass with

their own mass and inertia values. For hand calculations, this affected the torsion checks were

applied, since the effective width changes and only certain frames participate in the resistance

of each slab half from rotating

In reality the fixity of the column lies

somewhere between fixed and pinned. A

pinned connection was chosen for the model

to be conservative for deflection values. A

fixed connection could also be used to be

conservative for determining forces – as a

stiffer structure will incur higher shears under

seismic loading. However, HSS columns have

significantly less flexural stiffness than

traditional wide flange columns of the same weight, and would thus suffer a smaller penalty for

having a fixed base. A pinned connection was therefore used.

Columns were spliced at 48” above the second floor using a reference plane. In ETABS,

this allowed for a full transfer of moment between columns. Although the connection is only a

partial penetration weld, as discussed previously, the column would not likely experience high

moments in a braced frame. Thus, actual behavior of a “partial” moment connection would

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resemble that of a “fully restrained” moment connection, which was modeled. Since no

moment connections existed between columns and beams, panel zones were not used.

Lastly, since the roof is composed almost entirely of diagonal bracing, and a strict limit

of h/600 on deflections in cold-formed members, it was assumed the roof was rigid and moved

with the roof level. Thus the ETABS frame only goes to the ceiling of the 4th story, referred to as

the roof level for this report, since the attic was not incorporated, as in the SAP2000 model.

This was also done since the details of the cold-formed structure were not able to be obtained

at the time of the study.

Thesis Redesign: Computer Model (SAP2000)

For the spring redesign it was chosen to use a SAP model instead of an ETABS model for

a few reasons. A few reasons were mistakenly perceived shortcomings of ETABS3 Another

perceived issue was the lack of plastic, non-linear analysis, which was considered initially as an

an analysis, but difficulty in finding a correctly scaled earthquake precluded that analysis type

from being used to size members. Finally, since SAP is a more generic modeling program, the

author wished to demonstrate the ability to model a building and how to deal with unique

oddities when they appear.

The general basic modeling techniques were used the same way as in the Tech3 model:rigid end offsets to the columns with adjusted insertion points, the separation of the first floor

slab into two areas (for a more detailed expiation, see the slab discussion in the introduction)

and a reduction of the first floor level to effectively bring the top of slab elevation to the correct

3 For example, a vertical levels cutting columns into different “pieces”. When creating a new level in ETABS, it

makes a cut through every member at that elevation, which created difficulty in creating the column splices.)

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height from the column restraint level. Where moment connections were used (used in the

R=8 design), panel zones assignments were included to include the extra flexibility when

considering deflection checks.

The weight was accounted for by adding mas/area assignments to the floor slabs

(65psf), roof deck (35 psf), and to the exterior beams as mass/length assignments. The exterior

beams were assumed to be the first item in the load path emanating from the inertial forces

generated by the brick cladding and were thus given extra mass, according the dead load

calculations covered in the intro. However, since the areas modeled are rectangular and do not

contain the extensions in plan, or the folds of the wall, the mass assignments were modified to

make it heavier to account for the smaller geometry in the computer model. Below is a sample

calculation of the mass/length assignments

The new model also includes the effects of the basement retaining wall. Since the tech3

analysis, it was discovered through a conversation with Nich Umosella, a project engineer from

Barton Malow, that the shear walls in the basement were used as a way to reduce the torsion

effects that would be induced from the retaining wall’s influence on the center of rigidity. As a

simplifying assumption, the effects of the walls were not included in the lateral analysis for

Tech3.

For the thesis re-design, many simplifying assumptions are replaced with more detailed

modeling in an attempt to better model uncommon details. Thus, it was decided that the

inclusion of the retaining walls as part of the lateral system should be included. The stiffness of

the all the basement walls (both shear and retaining) for deflection calculations used cracked

section properties of .35 for the bending stiffness, as required by ACI 318, and a .4 reduction of

8.15E-05

9.78E-05

9.78E-05

9.78E-05

1.18E-04

mass to frame (386.4 in/s2

→ mass/ft)

081

097

097

097

117

532

839

839

839

529

attic 60

roof top 76roof top

parpet top9.45 0.113

Level Bounds

Story

Level

Wall wt

(psf)

Height

(ft)

Wall wt

(klf) klf toframe

kli toframe

parpet top 64 0.123 0.000 026 498

4th 48 0.454 0.0378 0.000

attic

4th37.81 0.454

parpet top

attic37.81 0.151

3rd 36 0.454 0.0378 0.000

0.378 0.0315 0.000

3rd

2nd37.81 0.454

4th

3rd37.81 0.454

1st

ground 53.02 0.636

1st 12 0.545

2nd

1st37.81 0.454

2nd 24 0.454

ground 0

0.0454 0.000

0.0378 0.000

0.0102 2.65E-05

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stiffness for the shear stiffness. The walls also varied in height, as the foundation plan showed

various depths required for the footers.

Perhaps the most obvious difference in comparing the two models the inclusion of the

rest of the building. The rest of the slab and beams and columns were included for several

reasons. First and foremost, a semi flexible diaphragm would reduce the effect of the retaining

wall in inducing large torsion by considering the diaphragm flexible. Since this is closer to actual

behavior, the “simplifying” assumption becomes too conservative, and an uneconomical

solution will be designed. Secondly, and more simply, the author’s interest in modeling was a

driving factor as well, and to explore the old modeling issue of balancing time and effort with

accuracy (the sap model was to explore the time/effort intensive end of the spectrum).

To accomplish this, a shell element was used with the average thickness of the concrete.

Although The reduction of torsion effects is similar to the issue of shear reversal when modeling

tall structures with a sudden and severe change in stiffness near the basement – the effect is

significantly reduced by allowing non-zero strain to form throughout the slab.

Figure 23: flexibility of first floor slab

Although the slab can distort and deflect as a “flexible” diaphragm, its relative stiffness

compared to the steel frames can still be accurately approximated as rigid. The only

appreciable difference can be seen on the first floor, where the LRFS is composed of shearwalls, which contain stiffness values similar to the stiffness of the slab. Below, the large

stiffness of the concrete walls can be seen inducing rotation on the first floor as a reaction to a

NS lateral load. Note: this deflection scale is 1:1000 for a NS loading.

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The modeling of the roof truss was perhaps the largest challenge for the new model.

For tech3 a simplifying assumption was that the truss was perfectly rigid and the mass was

lumped with the attic (ceiling of fourth floor). However, this created a non-conservative

estimate of the overturning moment, and thus the resulting forces in members. The actual

response of the structure changes as well when considering the flexibility of the roof trusses,instead of an assumption of rigidity. This added flexibility changes the behavior of the building,

and since the analysis to be performed is a modal analysis, it may increase the base shear by

modeling the flexibility of the frame

Figure 24: location of roof LFRS

Shop drawings for both the trusses and the bracing of the trusses were obtained, and

the model could be made. Section properties were found online from various cold-formed

steel fabricators. Although the actual roof contained 7 different truss types, only 2 were used

as a simplification since the same stiffness and strength criteria were used. One truss type was

used for end of each roof (as shown above) and one for the intermediate trusses, which

contained fewer and smaller diagonal members. The interior trusses were spaced at 48.” All

members are pin connected.

There were also transfer trusses in the E-W direction, as can be seen in figure above, as

seen in figure ##. The taller trusses in the E-W direction connect directly to BF-C and BF-H. The

two shorter trusses are there to prevent excessive torsion. However, the rotational resistance

from the sum of all the intermediate trusses would sum up to make the effects of torsion

practically negligible. Underneath the short, outermost EW transfer trusses are struts to

effectively give the columns below a moment connection to the beams, as can be seen in figure

##. For the SAP model, a rigid moment connection was used instead, with a 2 ft. rigid offsets

(about the size of the strut as highlighted in red in figure ##). The force transfer in theses

frames quickly “leaks” to other frames through the floor slabs as the frame does not contain

moment frames nor braced frames underneath.

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Figure 25: location of lateral braces

Initially, the biggest issue for modeling the roof trusses was the amount of flexibility.

Since Tech3, it was discovered that there was no slab on the attic level, as can be seen in figure

above. Instead, a large amount of bracing was used for the bottom of the trusses by other cold

formed steel struts, and when enough bracing was modeled, the area behaved closer to a

diaphragm.

Figure 26: Actual construction: no roof slab

The roof deck was modeled as a shell element. Since the roof deck had no concrete on

it, some creativity had to be applied to model its behavior accurately. From vulcraft’s catalog, a

similar deck section was found to the one prescribed by the structural engineer, and an

equivalent thickness of a shell was calculated to match the same moment of inertia per foot of

width. Comparing the resulting thickness of the shell to the actual thickness of the metal plate

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the deck was composed of, a ratio was computed to find the necessary reduction in axial

stiffness for shell modifiers. Similarly, bending in one direction was also reduced significantly to

reflect that deck only has significant stiffness in one direction. To ensure that the correct

direction was modified, both directions (parallel and perpendicular to roof truss direction) were

modified and deflections were observed to double check (the deck “oriented” in the wrongdirection gave a deflection nearly an order of magnitude larger.

The amount of flexibility affected the natural periods of vibration, or mode shapes, as

the algorithm would often result with SAP thinking the most important mode shapes were the

roof structure vibrating by itself, rather than the building as a whole. This was a good indicator

to signal that the roof truss was modeled incorrectly. Many of these shapes were a function of

the trusses falling over at the same time. Using the same tool, once the bracing from the shop

drawings were modeled, the mode shapes showed the deformation of the building as a whole

rather than just the roof truss deflecting, resulting in a more accurate base shear value.

Finally, P-Δ effects must be included by code, or at least a check must be performed to

see if P- Δ effects need to be considered at all. It was chosen to include P- Δ effects. Unlike

Etabs, P- Δ cannot be included at the expense of just a simple click. Instead, a non-linear static

load case must be applied that is representative of the deadload first. There are several types

of nonlinearity for static cases; if the P- Δ effect is selected, the program will iterate until the

solution converges on an stable, deflected shape. This deflected shape essentially has a

different lateral stiffness as secondary moments are added and amplified and the structure

deflects more.

The modal analysis then uses this modified stiffness of the structure to compute mode

shapes for analysis. Finally, a spectral analysis load case uses the spectral acceleration

parameters (calculated previously) to conduct a dynamic analysis by modifying the mode

shapes that were computed from the P- Δ dead loads by said spectral parameters. In the end,

the P- Δ amplifications affected the OCBF minimally, as the braces prevent significant

translation, relative to the flexibility of moment frames or the EBF frame.

Proposed Structural Changes

Although the focus of the thesis redesign is in the structural steel frame, other elements

can have a significant impact on the design of those frames, specifically with respect to any

added torsion the steel frames may see. Thus, several changes to the structure, whose

detailing is beyond to scope of the thesis redesign, were implemented in order to design an

effective structure to resist the lateral loads.

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By allowing the first floor to be flexible, a resulting issue can be seen in figure ##, which

shows the shear wall of braced frame 12 rotating out of plane due to the eccentricity of the

connection, which is discussed in the introduction. For the Tech3 model, the assumption of a

rigid diaphragm prevented such a distortion. However, by modeling the slab as flexible, it can

be seen there is no lateral restraint for most of the shear wall sincethere is a large opening for the stairwell, and the much larger shear

forces that are induced in the thesis redesign can cause the wall to bend

out of plane enough to cause unwanted behavior and weakness.

Again, this was a small scale deflection and is not an issue for

concern for the design that would exist in PA, which are found in tech3.

The eccentricity of the connection may have been due to an

architectural constraint as well. If the building was building in Berkley,

CA to force a seismic design category of “D” instead of “A”, thestructural engineer may have had enough reason to force the wall to be

directly under the frame, or alternatively, the shear wall may have been designed differently or

to a higher stiffness.

For the first floor, a large issue with torsion existed in both models, even with the

reduced stiffness of the floor slab. In addition, BF-4 attracted a seemingly disproportionate

amount of force. This was due to the fact that BF-4 sits on top of a larger concrete wall

compared to the analysis performed in tech3. Thie effect is worsened by the fact that that the

other center frame, BF-8, lacked a shear wall at all. To combat this, it is recommended that a

shear wall are to be added at the basement level of BF-8.

From figure ##, the wall contained no windows with the existing design, so no major

architectural conflicts would happen, and a talk with the architect to put a wall in place of the

basement brace may be seem reasonable. To reduce the slab rotation to eliminate code-

amplified torsion, it is also recommended that the shear walls at the basement level of BF-C and

BF-H are increased from 8” to 16” thick to give enough stiffness to bring the center or rigidity

away from the retaining wall.

These changes were applied to both the R=8 and R=3.25 model during analysis.Additionally, for the OCBF frame, it was determined that the shear was great enough that the

axial force developed in the brace was too large. For OCBF, it is required that a brace be

seismically compact, which is a stricter limit on section proportioning to prevent local buckling

than the regular specifications. However, for the HSS shapes, the largest seismically compact

shape, an HSS10x10x5/8 did not provide adequate strength during the analysis iterations, and

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thus it was chosen to use X-bracing rather than the existing bracing for the N-S frames. In the

E-W directions, an additional frame location was needed, as discussed earlier for the new

seismic loading discussion.

Structural Re-design

For the frame re-design, BF-4 was chosen as the frame to examine in detail, since it

contained the braces with the highest design forces throughout the building. All braces, beams

and columns will be sized, and the connection for the braced between the second floor and 3

floor will be detailed, as the connection to the first floor involved a base-plate connection.

Low-Ductile Option: R=3.25

As mentioned previously X-frames were chosen, as a single brace was unable to be used

without resorting to wide-flange shapes for higher capacity. HSS tubes provide great economyfor simple pin-ended compression elements with similar unbraced lengths since the radius of

gyration is the same for both orthogonal directions, and rather large. Thus two braces were

designed per story with HSS shapes instead of a single larger WF brace.

The same train of thought was used with the columns, as no moment connections were

used to the columns to incur moments, assuming the eccentricities of the shear connections

provide minimal eccentricities. Thus the goal was to use HSS tubes as well. However, a

HSS12x12 column had to be used in order to resist the design loads, which is larger in plan that

the standard column size for wide flanges, the W14.

Sizing the beams became an issue due to modeling technique. Since the floor slab was

modeled as a shell element, it had some bending stiffness that made examining the design

forces in the beams complicated and a function of the slab mesh size. Instead, the design

forces were used from the forces found in the beams and columns and applying statics.

Assuming that the concrete could not be relied on in an earthquake, which induces loads of

alternating directions, the beams were sized in order to resist the bending as if it were non-

composite. The earthquake loading could also induce a large axial force within the beams as

the frame acts as a truss, which forces a check for combined load as well, although the bracing

of intermediate beams to these girders gave a graciously small KL value.

Both columns and braces were checked for combined loading of axial and bending. For

P-delta effects, checks were used to examine if B1 > 1. However, since end moments were

often close to equal and in opposite directions, B1 was often below 1. The B2 modifier for the

approximate method was not needed as Sap included PΔ effects. Pδ are not included by

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