Structural steel designs pdf

Thus, the deviation of the diaphragm from a straight line is 0. Clearly, then, the diaphragm flexibility is negligible and the deck behaves as a rigid diaphragm.

The ratio of maximum to average displacement is 1. The same process needs to be repeated for the E-W direction. The demands from the three-dimensional ELF analysis are combined to meet the orthogonal combination requirement of Standard Section However, there is no story drift limit for single-story structures with interior wall, partitions, ceilings and exterior wall systems that have been designed to accommodate the story drifts.

Detailing for this type of design may be problematic. In the longitudinal direction, the lateral deflection is much smaller and is within the limits of Standard Section The deflection computations do not include the redundancy factor. The P-delta effects on the structure may be neglected in analysis if the provisions of Standard Section First, the stability coefficient maximum should be determined using Standard Equation The stability coefficient is calculated at both the roof and mezzanine levels in both orthogonal directions.

The maximum moments and axial forces caused by dead, live and earthquake loads on the gable frames are listed in Tables 6. The moments are given in Table 6. The moment diagram for the combined load condition is shown in Figure 6.

The load combination is 1. The size of the members is controlled by gravity loads, not seismic loads. The design of connections will be controlled by the seismic loads. Forces in the design of the braces are discussed in Section 6.

Individual maxima are not necessarily on the same frame; combined load values are maximum for any frame. Using the load combinations presented in Section 6. The mezzanine framing, also shown in Figure 6. The diagonal bracing, shown in Figure 6. AISC Table 6. As Designed in. Maximum in. According to Standard Section All P-M ratios combined compression and flexure are less than 1. This is based on proper spacing of lateral bracing. Lateral bracing is provided by the roof joists. The maximum spacing of lateral bracing is determined using beam properties at the ends and AISC , Section F , whichever is greater, in.

Adjacent to the plastic hinge regions, lateral bracing must have additional strength as defined in AISC Instead, tube brace members will be used, but they are not analyzed in this example. At the negative moment regions near the knee, lateral bracing is necessary on the bottom flange of the beams and inside the flanges of the columns Figure 6.

The knee detail is shown in Figures 6. The vertical plate shown near the upper left corner in Figure 6. The beam-to-column connection requires special consideration. The method of AISC for bolted, stiffened end plate connections is used. Refer to Figure 6. Highlights from this method are shown for this portion of the example. Refer to AISC for a discussion of the entire procedure. Determine the maximum moment at the plastic hinge location. Find bolt size for end plates.

Try A bolts. See Figure 6. Use 1 in. Step 3. Use 1. Step 4. Step 5. OK Step 6. Column flange of 2 inches is OK. Step 9. Check local column web yielding strength of the unstiffened column web at the beam flanges by AISC Equations 6. Column stiffeners need to be provided. Step Check the unstiffened column web buckling strength at the beam compression flange by AISC Equations 6. Check the unstiffened column web crippling strength at the beam compression flange by AISC Equation In compression, the continuity plate will be designed to take the full force delivered by the beam flange, Fsu.

In tension, however, the compressive limit states web buckling and web yielding are not applicable and column web yielding will control the design instead.

As it will be shown later, net section rupture not gross yielding will control the design of this plate. Strength in the other direction does not need to be checked because the cruciform section will not buckle in the plane of the column web. The continuity plate had been previously sized for adequacy to tensile yielding of the gross section.

The critical section will be analyzed where the continuity plates are clipped adjacent to the k-region of the column. Although doubler plates can be added to the panel zone to increase strength, this may be an expensive solution.

For simplicity, these changes are not undertaken in this example. The ridge joint detail is shown in Figure 6. An unstiffened bolted connection plate is selected.

Lateral seismic forces produce no moment at the ridge until yielding takes place at one of the knees. Vertical accelerations on the dead load do produce a moment at this point; however, the value is small compared to all other moments and does not appear to be a concern. Once seismic loads produce a plastic hinge at one knee, further lateral displacement produces positive moment at the ridge.

Under the condition on which the AISC design is based a full plastic moment is produced at each knee , the moment at the ridge will simply be the static moment from the gravity loads less the horizontal thrust times the rise from knee to ridge. Analyzing this frame under the gravity load case 1. The design of the framing for the mezzanine floor at the east end of the building is controlled by gravity loads.

The concrete-filled 3-inch, gauge steel deck of the mezzanine floor is supported on steel beams spaced at 10 feet and spanning 20 feet Figure 6. The steel beams rest on three-span girders connected at each end to the portal frames and supported on two intermediate columns Figure 6.

The girder spans are approximately 30 feet each. Those lateral forces that are received by the mezzanine are distributed to the frames and diagonal bracing via the floor diaphragm.

A typical beam-column connection at the mezzanine level is provided in Figure 6. The design of the end plate connection is similar to that at the knee, but simpler because the beam is horizontal and not tapered. Also note that demands on the end-plate connection will be less because this connection is not at the end of the column.

The strength of the members and connections, including the columns in this area but excluding the brace connections, must be based on Standard Section For simplicity, we can assume that the lateral force is equally divided among the roof level braces and is slightly amplified to account for torsional effects. Demand will be taken as either the expected yield strength of the brace or the amplified seismic load. In ordered to calculate U, the weld length along the double angles needs to be determined.

The eave strut, part of the braced frame, also acts as a collector element and must be designed using the overstrength factor per Standard Section Figure 6. There are deviations from simple approximations in both directions. In the E-W direction, the base shear is kips Section 6. The plot shows that the shear in the edge of the diaphragm is significantly higher in the two braced bays.

In the N-S direction, the shear is generally highest in the bay between the mezzanine frame and the first frame without the mezzanine. This is expected given the significant change in stiffness. There is no simple approximation to estimate the shear here without a three-dimensional model. The shear is also high at the longitudinal braced bays because they tend to resist the horizontal torsion.

However, the shear at the braced bays is lower than observed for the E-W motion. This seven-story office building of rectangular plan configuration is feet, 4 inches long in the E-W direction and feet, 4 inches wide in the N-S direction Figure 6.

The building has a penthouse. It is framed in structural steel with foot bays in each direction. The typical story height is 13 feet, 4 inches; the first story is 22 feet, 4 inches high. The penthouse extends 16 feet above the roof level of the building and covers the area bounded by Gridlines C, F, 2 5 in Figure 6. The elevators and stairs are located in the central three bays.

There are five bays of moment frames on each line. The braced frames are in a two-story X configuration. The frames are identical in brace size and configuration, but there are some minor differences in beam and column sizes. Braced frame elevations are shown in Figures 6. The building has no vertical irregularities despite the relatively tall height of the first story.

The exception of Standard Section In the three-dimensional analysis, the first story drift ratio is less than percent of that for the story above. Because the building is symmetrical in plan, plan irregularities would not be expected.

Analysis reveals that Alternative B is torsionally irregular, which is not uncommon for core-braced buildings. A combination of percent of the seismic forces in one direction with 30 percent of the seismic forces in the orthogonal direction is required for structures in Seismic Design Category D for certain elements—namely, the shared columns in the SCBF Standard Sec.

In using modal response spectrum analysis MRSA , the bidirectional case is handled by using the square root of the sum of the squares SRSS of the orthogonal spectra. The effect of seismic load is defined by Standard Section It is assumed that the design would fail the calculation-based requirements of Standard Sec. The allowable story drift per Standard Section Adjust calculated story drifts by the appropriate Cd factor from Standard Table Determine the building period T per Standard Equation The height of the penthouse will be neglected since its seismic mass is negligible.

CuTa, the upper limit on the building period, is determined per Standard Table The seismic response coefficient Cs is determined from Standard Equation Seismic base shear is computed per Standard Equation In evaluating the building in ETABS, twelve modes are analyzed, resulting in a total modal mass participation of 97 percent. The code requires at least 90 percent participation for strength. The method used is as follows: 1. Select preliminary member sizes 2. Check deflection and drift Standard Sec.

Check beam strength 5. The most significant criteria for the design are drift limits, relative strengths of columns and beams the panel-zone shear. Member strength must be checked but rarely governs for this system. Select Preliminary Member Sizes: The preliminary member sizes are shown for the moment frame in the X-direction in Figure 6. Using a ratio of 2. The software used accounts explicitly for the increase in beam flexibility due to the RBS cuts.

Check Drift: Check drift is in accordance with Standard Section Displacements at the building corners under the 5 percent accidental torsion load cases are used here. Calculated story drifts, response spectrum scaling factors Cd amplification factors are summarized in Table 6.

P-delta effects are included. Level 7 2. The expected moment strength of the beams is projected from the plastic hinge location to the column centerline per the requirements of AISC Section 9.

This is illustrated in Figure 6. For the columns, the moments at the location of the beam flanges are projected to the column-beam intersection as shown in Figure 6. These values are for the typical lateral braces. See below for the design of the plates. Therefore, each plate takes 60 kips. The minimum thickness of the plates is the thickness of the beam flanges, 0. Alternatively, a W24x section will work in lieu of adding continuity plates.

The factored shear Ru is determined from the flexural strength of the beams connected to the column. This depends on the style of connection. Previously calculated, this is kips at this location. The column axial force Load Combination: 1. Use four plug welds spaced 12 inches apart.

Seismic base shear is computed using Standard Equation In evaluating the building in ETABS, twelve modes are analyzed, resulting in a total modal mass participation of 99 percent.

The Standard Sec. The method used to size members is as follows: 1. Select brace sizes based on strength 2. Select column sizes based on special seismic load combinations Standard Sec.

Select beam sizes based on the load imparted by the expected strength of the braces 4. Check drift Standard Sec. Design the connection Reproportion member sizes as necessary after each check. After the weight and stiffness have been modified by changing member sizes, the response spectrum must be rescaled.

Torsional amplification is a significant consideration in this alternate. Select Beam Sizes: The beams are sized to be able to resist the expected plastic and post-buckling capacity of the braces. In the computer model, the braces are removed and replaced with forces representing their capacities. These loads are applied for four cases reflecting earthquake loads applied both left and right in the two orthogonal directions T1x, T2x, T1y, T2y. For instance, in T1x, the earthquake load is imagined to act left to right; the diagonal braces expected to be in tension under this loading are replaced with the force RyFyAg and the braces expected to be in compression are replaced with the force 0.

For T2x, the tension braces are now in compression and vice versa. T1y and T2y apply in the other orthogonal direction. The load cases applied are as follows: 1. The results are summarized in Table 6. Level 7 1. All story drifts are within the allowable story drift limit of 0. As shown in the table above, the drift is far from being the governing design consideration.

Design the Connection: Figure 6. The required strength of the connection is to be the nominal axial tensile strength of the bracing member. The thickness of the gusset is chosen to be 1 inch. The gusset plate must be permitted to flex about this hinge, unrestrained by any other structural member.

With such a pinned-end condition, the compression brace tends to buckle out-of-plane. During an earthquake, there will be alternating cycles of compression and tension in a single bracing member and its connections. Proper detailing is imperative so that tears or fractures in the steel do not initiate during the cyclic loading. While the gusset is permitted to hinge, it must not buckle.

To prevent buckling, the gusset compression strength must exceed the expected brace strength in compression per AISC Section Determine the nominal compressive strength of the brace member. The effective brace length kL is the distance between the hinge zones on the gusset plates at each end of the brace member. This length is somewhat dependent on the gusset design. Note that the 0.

By this method, illustrated by Figure 6. The length, from geometry, is The necessary width can be computed from the effective area, but that calculation is not performed here. Grade 50 material is used in order to match or exceed the brace material strength, thus allowing for treatment of the material as homogenous. Thus, the shear lag factor for the reinforced section is: 2. To accomplish this, the reinforcement plate will be 33 inches: 14 inches on each side of the reduced section, 2 inches of anticipated over slot, plus 1 inch to provide erection tolerance.

The takeoffs are based on all members, but do not include an allowance for plates and bolts at connections. Torsional amplification and drift limitations both increased the weight of steel in the bracing.

The weight of the moment-resisting frame is controlled by drift and the strong column rule. The podium is Story heights are 18 feet in the podium and reduce to 15 feet throughout the tower, bringing the total building height to feet.

As the tower is centered horizontally on the podium below, the entire building is symmetric about a single axis. Both the podium and the tower have large roof superimposed dead loads due to heavy HVAC equipment located there.

The combination of a stiff podium structure beneath a more flexible tower results in significant force transfer at the floor level between them. The bay spacing is 30 feet each way. There are three floor beams per bay. All beams and girders are composite. BRBFs have been selected for this building because they provide high stiffness paired with a high degree of ductility and stable hysteretic properties.

The building has a thick mat foundation. The foundation soil is representative of Site Class C conditions identical to those discussed in Section 3.

The lateral force-resisting system throughout the tower consists of BRBFs in the middle bay along each side of the perimeter—Gridlines 3, 6, A D, as can be seen in the representative elevation of Figure 6.

These BRBFs deliver lateral loads to the collectors and diaphragm at the third floor where both in-plane and out-of-plane discontinuities exist. This transfer occurs in-plane along Gridlines A and D to two braced bays nearer the ends of the podium and out-of-plane from a single braced bay in the tower along Gridlines 3 and 6 to braces in the two adjacent bays along Gridlines 2 and 7 in the podium below.

The podium bracing configuration is illustrated in Figure 6. A typical bracing elevation in the transverse direction of the podium illustrating the out-of-plane offset is shown in Figure 6. Each BRB is designed for its share of percent of the horizontal component of the earthquake lateral load without considering additional tributary vertical loads.

This is done to encourage distributed yielding of braces up the height of the structure and is justified because the braces will shed any gravity load upon first yield and transfer it to the connecting beams and columns, which are designed to accommodate gravity loads without support provided by the braces. Beams, columns collectors are preliminarily sized using capacity design principles considering plastic mechanisms that develop based on the brace sizes determined using elastic MRSA. The details of this design procedure are summarized in Table 6.

Section 3. Modifications to Section The later compliance path is selected for this design example. This requirement effectively amounts to a braced frame with simple beam-to-column connections per AISC Section B3. A standard detail illustrating this connection is presented in Figure 6. Floor dead load includes lightweight concrete-filled metal deck, ponding allowance, framing, mechanical and electrical equipment, ceiling and fireproofing.

Due to potential for rearrangement, partition loads are considered live loads per Standard Section 4. The hospital building does not possess any stiffness, strength, or weight irregularities despite the relatively tall height of the podium stories. At the podium levels, the two braced bays corresponding to each line of single-bay chevron bracing in the tower above provide more than enough additional strength to compensate for the slight increase in floor-to-floor height.

The story drift ratio increases up the full height of the structure, meeting the exception of Standard Section However, the structure does possess both a vertical geometric irregularity Type 3 and an in-plane discontinuity in vertical lateral force-resisting element irregularity Type 4 since the lateral force-resisting system transitions from a single chevron braced bay in the tower to two chevron braced bays at the podium levels.

The two chevron braced bays in the podium occur two bays away from the tower braced bay in the longitudinal direction. The Type 4 vertical irregularity triggers an increase in certain design forces per Standard Sections Together, the Type 3 and Type 4 vertical irregularities preclude the use of an equivalent lateral force analysis as defined in Standard Section Note that this analysis prohibition is also triggered by the flexibility of the structure, as its fundamental period see Sec.

Nevertheless, the design base shear still must be determined using the equivalent lateral force analysis procedures to ensure that the design base shear for a modal response spectrum analysis meets the requirements of Standard Section Analysis reveals that the structure is torsionally regular the only horizontal structural irregularity present is an out-of-plane offset irregularity Type 4 triggered by the shift in the vertical lateral force-resisting system from Gridlines 3 and 6 in the tower to Gridlines 2 and 7 in the podium structure below.

The only additional provisions triggered by the Type 4 horizontal structural irregularity relate to three-dimensional modeling requirements. Because there are only two BRBF chevrons in each direction throughout the tower, removal of a single brace would dramatically increase flexural demands in the beam at that location and would certainly result in at least a 33 percent reduction in story strength even if the resulting system does not have an extreme torsional irregularity.

The 1. Standard Section In the context of NRHA, orthogonal pairs of ground motion acceleration histories are applied simultaneously in accordance with the requirements of Standard Section The effect of seismic load as defined by Standard Section The seismic load is combined with the gravity loads in elastic analyses as shown in Standard Section The braces are designed without considering additional tributary vertical loads to encourage distributed yielding up the height of the structure.

However, the surrounding beams and columns that are part of the lateral force-resisting system are designed for the above gravity loads in conjunction with the earthquake effect as specified in AISC Section In a NRHA, the structure is analyzed for the effects of the scaled pairs of ground motions simultaneously with the effects of dead load and 25 percent of the required live loads per Standard Section The calculated design story drifts are amplified by the appropriate Cd factor from Standard Table This same figure extracted from a nonlinear response history analysis cannot exceed 1.

In a subsequent section Section 6. Compliance with story drift limits is also evaluated using the results of the nonlinear response history analyses.

First, the ELF base shear will be determined, followed by its vertical distribution up the height of the building. Compute the approximate building period, Ta, using Standard Equation Thus the upper limit on the fundamental period Tmax applies.

The seismic response coefficient, Cs, is computed in accordance with Standard Section Equation The seismic base shear is computed per Standard Equation The redundancy factor is not applicable to the determination of deflections. The floor force, Fx, is calculated using Standard Equation The seismic design shear in any story is computed as follows per Standard Eq.

Standard Sec. Since the floor span-to-depth ratio is a maximum of 1. However, Standard Sec. Due to the out-of- plane offsets irregularity Type 4 in the transverse lateral frames at the podium-to-tower interface, the hospital does not meet this restriction.

As such, the effect on the vertical lateral force distribution of explicitly considering the stiffness of the diaphragm at the podium roof level was examined in a three- dimensional computer model of the structure and found to be insignificant i.

Thus, it was deemed acceptable to model all diaphragms as rigid for subsequent analyses. The rigid diaphragm assumption is especially helpful in the context of nonlinear response history analysis, where the additional degrees of freedom needed to model diaphragm stiffness explicitly can render analysis times prohibitive. Another reasonable approach to the primary model would be to include the level 3 diaphragm explicitly and model all other diaphragms as rigid. The floor diaphragms are modeled as rigid.

However, the ELF analysis of the three-dimensional model is still useful in assessing whether torsional irregularities are present. The ELF seismic forces derived in Table 6. The maximum and average story drifts along an edge transverse to the direction of loading for the critical direction of eccentricity at each level are then compared. For this torsionally regular structure, the accidental torsion amplification factor, Ax, is equal to 1.

A three-dimensional modal response spectrum analysis is performed per Standard Section The design response spectrum is based on Standard Section Twelve modes provide more than enough participation to capture 90 percent of the actual mass in each direction of response as required by Standard Section The complete quadratic combination CQC modal combination rule was selected for this task to account for coupling of closely-spaced modes that are likely present in symmetrical structures.

Five percent modal damping in all modes is specified for the response spectrum analysis to match the assumption used in deriving the design response spectrum of Figure 6.

If the design value for modal base shear is less than 85 percent of the ELF base shear calculated using a period of CuTa see Sec. However, lateral displacements are still examined in the elastic analysis to ensure they remain reasonably close to the limits derived in Section 6. This check is illustrated in Section 6.

Seismic drift is examined in accordance with Standard Section The design story drift in each translational direction was extracted from the three- dimensional ETABS model corresponding to the response spectrum case, including 5 percent accidental torsion, exciting that same direction.

Although only strictly required for structures possessing torsional irregularities as defined by Standard Table However, the response spectrum used in the analysis has already been scaled twice.

The second scaling was by a factor in each direction to ensure that the design base shear forces in each direction to meet the minimum 85 percent of ELF base shear. This latter scaling does not apply to drifts, per Standard Section Thus, the 1. The resulting scale factors applied to the results of the scaled spectra are 3. It would also be possible to simply perform an additional response spectrum analysis with the design spectrum multiplied by 0.

Story drifts in all ten stories of the hospital building are within the allowable story drift limit of 0. Although story drifts calculated using MRSA reach a maximum value at the roof level that is just 89 percent of the 0.

A comparison of story drift ratios also confirms that no story drift ratio is more than percent of that for the story above, as required to prove certain vertical irregularities are not present in the structure via the exception to Standard Section Tensa Fab.

A short summary of this paper. E1 Try the arrangement shown in Fig. Assume that the flange splices carry all of the moment and that the web splice carries only the shear.

The splice is near a point of lateral restraint. The ends are not prepared for full contact in bearing. ISHB E3 To account for it the section modulus is taken as 1. The connection has to transfer a factored shear of kN. Use bolts of diameter 20 mm and grade 4. E5 1 The recommended gauge distance for column flange is mm. Therefore required angle back mark is 50 mm. E5 with vertical pitch of 75 mm 4 Check bolt force Similar to the previous case, the shear transfer between the beam web and the angle cleats can be assumed to take place on the face of the beam web.