# Precast Bent System for High Seismic Regions: Laboratory Tests of Column-to-Footing Socket Connections

## CHAPTER 6. ANALYSIS OF MEASURED RESPONSE

This chapter documents a comparison between the measured responses obtained through laboratory testing and results obtained using analytical models. The response measured in the experiments is denoted with the subscript "u" (e.g., *M _{u}* – measured moment). The calculated quantities are denoted with subscripts as used in the AASHTO specifications (e.g.,

*V*– nominal shear strength and

_{n}*M*– nominal flexural strength).

_{n}^{(14,15)}

### Footing Overturning

To protect against overturning of a spread footing, the AASHTO Seismic Guide Specifications* *requires that the footing be able to resist the overstrength moment of the column. This requirement is manifested in two specific limitations:

- The centroid of the pressure block under the footing must lie within the middle two-thirds of the footing. If, as is common, the pressure block is assumed to be triangular, this means that the footing may lift off the soil over no more than half of its width.
- The peak stress under the footing may not exceed the nominal bearing capacity, which was 75 ksf for the soil at the site.

The prototype footings were designed at the limit of these requirements. The prototype bridge bent consisted of four columns. The maximum axial load (1,157 kips, including structural and footing weights plus influence of overturning), the maximum moment (41,428 kip-in., including overstrength), andthe maximum shear (345 kips) yielded an eccentricity of 4.3 ft. However, the minimum axial-load condition (*P _{min}*=737 kips,

*M*= 36,141 kip-in,

_{po}*V*= 301 kips) resulted in an eccentricity of 5.9 ft, which led to a minimum footing size of 18 ft.

_{po}To accommodate seismic loading from any direction, the footing was square. The resulting peak soil pressure under the critical combined loading was only 9.2 ksf, which was much less than the nominal capacity of 75 ksf, soil pressure. The support conditions are illustrated in figure 64.

To replicate this situation as closely as possible in the laboratory, the three specimens were supported along two lines, each situated (at lab scale) at the same eccentricity as the centroid of the limiting soil pressure block in the field. That distance was 42 percent of 5.9 feet, or 30 inches. However, to make it possible to conduct axial-load tests with support from all four edges of the footing, support was also provided, in all specimens, along the sides of the footing, as shown in figure 64. Doing so created a pressure distribution that consisted of a distributed load (along the sides) and two line loads (at the ends).

If the columns had been stronger than expected, the footing could have lifted off the supporting blocks and rocked about one of the line supports. This behavior would have limited the applied load and prevented the test from proceeding. To prevent this behavior, rods were placed on each side of the column to hold down the footing, and load cells were installed to detect any forces that might have restrained overturning. Each rod was located 31 inches from the column centerline in the direction of loading. A slack of 1/16 inch was provided at the start of the test between the load cell and the nut above it, so that in the absence of lift-off, the bolts and load cells would remain inactive but they would engage almost immediately after any lift-off started. In the tests, lift-off never occurred, and the load cells read zero at all times.

The test specimens were analyzed assuming that the support was provided by two line loads alone, ignoring any additional upwards pressure from the side strips. That arrangement was statically determinate, so the reactions could be computed from the measured loads and the resulting eccentricity could be computed and used as the measure of how close the footing was to violating the AASHTO Seismic Guide Specifications requirements.

Table 12 summarizes the maximum and minimum reactions and reports the resulting reaction force eccentricities.

Specimen | SF-1 | SF-2 | SF-3 | |||
---|---|---|---|---|---|---|

Direction | North | South | North | South | North | South |

Axial Load, P (kips)_{total} |
~174 | ~174 | ~167 | |||

Maximum Column Base Moment, M (kip-in.)_{u} |
-3,073 | 3,091 | -3,113 | 3,065 | -3,315 | 3,392 |

Drift Ratio at Maximum Column Base Moment (percent) | -2.61 | 1.95 | -1.45 | 1.38 | -2.69 | 2.64 |

Top Displacement at Maximum Column Moment (60 in above interface) (in.) | -1.57 | 1.17 | -0.87 | 0.83 | -1.61 | 1.58 |

Column shear at Maximum Moment, V (kips)_{u} |
-45.6 | 47.5 | -49 | 48.4 | -50.6 | 52 |

Eccentricity, e (in.) |
23.6 | 23.9 | 24.2 | 23.9 | 23.5 | 23.5 |

Maximum Reaction, R (kips)_{max} |
158.1 | 159.2 | 160.2 | 159.2 | 150.2 | 151.8 |

Minimum Reaction, R (kips)_{min} |
15.8 | 14.6 | 13.6 | 14.7 | 16.5 | 14.9 |

The eccentricities under load remained below the AASHTO Seismic Guide Specifications limits. They were calculated by dividing the moment at the base (due to column moment and shear) by the axial load acting on the specimens, including both the applied axial load and the weight of the column and footing (*P _{total}* = 173.8 kips for SF-1 and SF-2, and

*P*= 166.8 kips for SF-3). All specimens had the same 20-inch-diameter circular columns with a shear span ratio of 3. Specimens SF-1 and SF-2 shared the same footing geometry of 68 inches by 90 inches by 22.5 inches, but the depth of specimen SF-3 was shallower (10 inches). The heights of the four edges that supported the specimens were 3.75 inches, but their weight (about ~1 kip) was not included in this analysis.

_{total}The table shows that both reaction strips remained in compression during the tests, indicating that there was no lift-off. For specimens SF-1 and SF-2, the maximum estimated upward reaction at a support was about 160 kips, and the minimum was about 14 kips. The corresponding values for specimen SF-3 were 152 kips and 15 kips.

These reactions forces are used to estimate the demands on the footings.

### Footing Response

#### Footing Flexural Strength

The footing flexural strength was evaluated following the recommendations of the AASHTO LRFD and the AASHTO Seismic Guide Specifications. ^{(14,15)} The test specimens were reinforced as shown in chapter 2. The nominal flexural capacity was calculated at the column face and wasbased on the bars within an effective width. For flexural strength and beam shear calculations, the effective width of the footing,*b _{eff}*, is defined as the sum of the column diameter and two times the spread footing depth (

*b*. Here,

_{eff }= D_{c}+2H_{f})*b*= 65 inches for specimens SF-1 and SF-2, and 40 inches for specimen SF-3.

_{eff}In contrast, AASHTO LRFD recommends that the cracking moment be calculated using the whole width of the footing (*b _{eff }*= 68 inches). This assumption implies that the moment distribution is constant across the width because, if it were not so, the stress would be higher than the average and cracking would initiate earlier at the point of peak moment. The AASHTO LRFD does not account for any differences between precast and cast-in-place behavior. In this study, the cracking moment of the test specimens was calculated using the whole width.

Table 13 summarizes the demands and computed capacities at the face of the columns. The moment demands in the footings at the column face were calculated using the computed reactions in table 12. The strengths reported in table 13 were calculated using both the specified and measured strengths of the materials.

Specimen | SF-1 | SF-2 | SF-3 | |||
---|---|---|---|---|---|---|

Capacity Values Input | Specified Properties | Measured Properties | Specified Properties | Measured Properties | Specified Properties | Measured Properties |

Measured M (kips-in)_{u} |
3,184 | 3,204 | 3,036 | |||

M (kips-in.)_{cr} |
2,754 | 3,512 | 2,754 | 3,581 | 544 | 765 |

M_{cr}/M_{u} |
0.86 | 1.10 | 0.86 | 1.12 | 0.18 | 0.25 |

Calculated M (kips-in.)_{n} |
5,254 | 5,569 | 5,254 | 5,622 | 3,419 | 4,033 |

M_{u}/M_{n} |
0.61 | 0.57 | 0.61 | 0.57 | 0.89 | 0.75 |

In the SF-1 and SF-2 specimens, the flexural demand at the column face slightly exceeded the cracking moment calculated based on the specified material properties. However, the concrete strength was higher than assumed in design, so the demand at the column face was slightly lower than the cracking moment calculated using measured material properties for SF-1 and SF-2. This calculation is consistent with the fact that footing cracking was not observed during the tests of specimens SF-1 and SF-2. For SF-3, the moment demand greatly exceeded the cracking capacity calculated using either the specified or measured materials properties.

The nominal moment capacity of the spread footings exceeded the moment induced in the footings by the columns. Using the measured properties, the moment demand-to-capacity ratios ranged from 0.57 to 0.75.

For specimens SF-1 and SF-2, the strains measured in the bottom mats show that the moment was not distributed evenly across the footing width; rather, the moment decreased with distance from the column. This general pattern is as expected, but some doubt exists about the exact values of the strains because of the need to correct the raw, measured strains for thermal affects. The thermal effects were potentially 2 to 3 times the mechanical strains. Furthermore, the footings in the tests were uncracked, whereas the AASHTO Seismic Guide Specifications equation for *b _{eff}* is based on the assumption that the footing is cracked, and cracking may affect

*b*. Because of these considerations, the data from specimens SF-1 and SF-2 do not provide a reliable basis for evaluating the AASHTO Seismic Guide Specifications definition of effective width.

_{eff}In the thin footing specimen (SF-3), the concrete was cracked, the mechanical strains were much larger, and there was no need to correct for thermal effects because temperature-compensated (three-wire) gauges were used. The data from specimen SF-3 should therefore have been useful for evaluating the AASHTO Seismic Guide Specifications b_{eff} model. However, the measured bar strains increased with distance from the column. This result was unexpected, and the reasons for it are unknown. For example, there was no indication that the gauges malfunctioned. These results suggest that the steel outside the effective width is the primary contributor to the flexural strength. This is both irrational and the opposite of what the AASHTO Seismic Guide Specifications model states, so the footing steel strain data from specimen SF-3 were ignored.

#### Footing One-Way Shear Strength

The AASHTO Seismic Guide Specifications require that the one-way shear strength to be calculated at the column face using the effective width, *b _{eff}*. The current WSDOT philosophy is to make the footing thick enough such that the concrete strength alone can resist all of the shear, and to place only the prescriptive transverse reinforcement recommended in the Caltrans SDC.

^{(16)}Specimens SF-1 and SF-2 were constructed with footings deep enough for the concrete alone to resist the shear (

*D*= 1.125).

_{c}/ h_{f }The current edition of the AASHTO Seismic Guide Specifications was based on the Caltrans SDC. However, the Caltrans SDC requirement for prescriptive ties was not included in the AASHTO Seismic Guide Specifications. The requirement for these prescriptive ties will be included in the next edition. Thus, to be in keeping with the intent of the AASHTO Seismic Guide Specifications, the full Caltrans SDC prescriptive ties were included in specimenSF-1. For the prototype, the requirement results in No. 5 ties at 12-inch spacing, which results in a nominal shear stress capacity, *v _{s}*, of 129 psi. For 4,000 psi concrete, this represents about

*2√f'*and is comparable in magnitude to the concrete contribution of

_{c}*v*= 2√f'

_{c}_{c}. In specimen SF-2, the stirrups were arbitrarily reduced by a factor of one-half (from the Caltrans SDC requirement), because placing stirrups in a spread footing on-site slows down construction, and they were believed to be unnecessary when the columns reinforcement is anchored with headed bars.

To force failure out of the column and into the connection region, the footing depth in specimen SF-3 was reduced to half of the column diameter ( *D _{c}/ h_{f }*= 0.5). Without transverse reinforcement, this thin footing would be susceptible to one-way shear failure, so ties were included in the footing. They were placed so that they would help to resist one-way ("beam") shear but would not affect two-way ("punching") shear.

Table 14 summarizes the computed one-way shear demands and strengths of the spread footings. Values are given for both the specified and measuredstrengths of the concrete and the steel (specified *f _{y }*= 70 ksi, since the smooth wire was used). The shear force demand,

*V*, was obtained from the measured loads and the known specimen weight.

_{u}Specimen | SF-1 | SF-2 | SF-3 | |||
---|---|---|---|---|---|---|

Capacity Values Input | Specified Properties | Measured Properties | Specified Properties | Measured Properties | Specified Properties | Measured Properties |

V(kips)_{c} |
153 | 195 | 153 | 198 | 37 | 52 |

V(kips)_{s} |
178 | 161 | 89 | 81 | 144 | 150 |

Calculated V(kips)_{n} |
331 | 356 | 242 | 279 | 181 | 202 |

Measured V_{u }(kips) |
154 | 155 | 151 | |||

Measured V_{u}/V_{n} |
0.47 | 0.43 | 0.64 | 0.56 | 0.83 | 0.75 |

The values presented show that failure in beam shear was improbable because the ratio

*V _{u}/V_{n}* (demand/capacity for measured material properties) was never greater than 0.75. That is consistent with the fact that there was no indication of one-way shear failure in any of the tests.

#### Combined Punching Shear and Moment Transfer

The transfer of moment from the column to the footing induces demands in the connection region that must be added to the two-way shear demands induced by the vertical load on the column. The AASHTO LRFD does not account for this moment transfer. Thus, the method from ACI 318-08, section 11.11.7, was used to estimate the combined shear stresses. Although punching shear failure is really manifested as a tension failure on a conical surface, the ACI procedure for both punching shear alone and for combined punching and moment transfer consists of computing shear stresses on a notional cylindricalfailure surface, assuming elastic behavior. Furthermore, the amount of moment being transferred by shear stresses is only a fraction, *g* _{v}, of the total moment. The remainder is assumed to be transferred by flexure; that is, by means of a couple consisting of a pair of horizontal forces. According to ACI 318-08, the combined shear stress is calculated using the equation in figure 65.

In this equation, *d* is the effective shear depth, is the fraction of the moment carried in shear, *J _{c}* is the moment of inertia of the critical perimeter line about the axis of bending, and

*c*is the distance from the centroid of the critical-shear perimeter to the edge where the stress is being calculated.

According to ACI 318-08, the calculated maximum shear stress should not exceed the limiting value of the equation shown in figure 66.

The concrete contribution is taken not to be higher than (*f' _{c}*is in psi) if shear reinforcement is used. Specimens SF-1 and SF-2 included stirrups within the critical perimeter, whereas specimen SF-3 did not. Table 15 summarizes the combined punching shear and moment transfer strengths and demands on the connection.

Specimen | SF-1 | SF-2 | SF-3 | |||
---|---|---|---|---|---|---|

Capacity Values Input | Specified Properties | Measured Properties | Specified Properties | Measured Properties | Specified Properties | Measured Properties |

v(ksi)_{c } |
0.126 | 0.161 | 0.126 | 0.164 | 0.253 | 0.356 |

v(ksi)_{s} |
0.147 | 0.133 | 0.084 | 0.076 | 0 | 0 |

Calculated v(ksi)_{n} |
0.274 | 0.295 | 0.211 | 0.241 | 0.253 | 0.356 |

Measured v(ksi)_{u } |
0.060 | 0.060 | 0.452 | |||

v_{u}/v_{n} |
0.22 | 0.20 | 0.28 | 0.25 | 1.79 | 1.27 |

Calculations were based on an equivalent square of a circular column. ACI-ASCE (American Society of Civil Engineers) Committee 426 recommends that combined punching shear and moment transfer for circular columns be calculated with an equivalent square. The base of the precast column was an octagon inscribed in a 20-inch-diameter circle. This approximation was considered sufficient since the perimeter of an inscribed octagon is only 2.6 percent less than that of a circle.

Table 15 shows that calculated capacities (for measured material properties) of specimens SF-1 and SF-2 exceeded the calculated demands by at least a factor of four. Consistent with this calculation, no sign of this failure mode was detected during testing of specimens SF-1 and SF-2. The depths of those specimens were roughly two times greater than the depth at which the combined punching shear and moment transfer would become a problem, according to the ACI 318 provisions.

In contrast, the demand was 27 percent larger than the calculated capacity for specimen SF-3. That results is consistent with what was observed during the test, in which the specimen ultimately failed (in the desired failure mode) in the combined punching shear and moment transfer during its last cycle (at a drift ratio exceeding 10 percent).

#### Footing Punching Shear Strength

The AASHTO LRFD recommends two equations to calculate the punching shear-strength capacity, one including and one excluding transverse steel. The equations were used to evaluate the performance in pure punching shear when the columns were loaded only with a large vertical load.

The prototype spread footing was originally designed to have the minimum transverse reinforcement according to the Caltrans SDC; the same was true for specimen SF-1. In specimen SF-2, the proportion of transverse reinforcement in the spread footing was reduced to half of the minimum required by Caltrans. Specimen SF-3 had stirrups, too, but they were placed so they would not increase the punching shear capacity.

Table 16 summarizes the punching shear capacities using the specified and measured strengths of the concrete and reinforcement.

Specimen | SF-1 | SF-2 | SF-3 | |||
---|---|---|---|---|---|---|

Capacity Values Input | Specified Properties | Measured Properties | Specified Properties | Measured Properties | Specified Properties | Measured Properties |

V, Eq. 6-3 (kips) _{c} |
292 | 372 | 292 | 380 | 133 | 188 |

V, Eq. 6-4 (kips)_{c} |
582 | 742 | 582 | 757 | N/A | N/A |

V(kips)_{s} |
441 | 399 | 253 | 229 | 0 | 0 |

Calculated V(kips)_{n} |
733 | 771 | 545 | 608 | 133 | 188 |

Maximum axial load V(kips)_{u} |
918 | 820 | 342 | |||

V_{u}/V_{n} |
1.25 | 1.19 | 1.50 | 1.35 | 2.57 | 1.82 |

Figure 67 (AASHTO LRFD equation 5.13.3.6.3-3), which takes into account that shear reinforcement is present in the footing, was used for specimens SF-1 and SF-2.

In this equation, , and *V _{s}* =

*A*. Here,

_{v}f_{y}d_{v}/s*f'*is the unconfined concrete strength (in ksi),

_{c}*b*is the perimeter of the critical section,

_{0}*d*is the effective shear depth,

_{v}*A*is the area of ties crossing within

_{v}*d*from the column,

_{v}*f*is the yield strength of the ties, and

_{y}*s*is the spacing between ties.

Table 16 also shows the punching shear capacity calculated with AASHTO LRFD equation 5.13.3.6.3-1, which excludes any transverse steel.

In figure 68, *ß _{c}* is the ratio of long side to short side of the rectangle and other values are as defined for figure 67.

Because the stirrups did not cross the crack plane for specimen SF-3, only the equation in figure 68 was used for that specimen. For square critical sections, this equation increases the concrete contribution by approximately a factor of two, compared to the equation in figure 67.

After the cyclic tests were finished, specimens SF-1 and SF-2 were loaded axially until either the column punched through the footing or the (already damaged) column failed. The value measured for specimen SF-1 (842 kips) is not reported because it was loaded higher in the beginning to 918 kips. For reference, the maximum factored axial load on the prototype was *P _{u}* = 1.25DL+1.75LL = 1382 kips, which corresponded to 240 kips at laboratory scale. In both specimens, the axial load reached exceeded the nominal capacity and there was no indication of punching shear failure when the column failed in the previously damaged plastic hinge zone. By contrast, specimen SF-3 punched through the footing in combined punching shear and moment transfer so a pure axial test could not be conducted. However, the specimen was loaded successfully up to 342 kips prior to the lateral-load testing (see chapter 4), which was nearly twice the calculated capacity.

In all cases, even when the footing had been previously damaged by combined bending and axial load, the demand exceeded the nominal capacity, in some cases by a large margin. The implication is that the AASHTO procedure for computing punching shear strength is safe and may be quite conservative. The tests also show that, if the footing has already been damaged, the punching strength drops. For example, at zero drift (and approximately zero moment) after reaching a previous peak drift ratio of 9 percent, specimen SF-3 was unable to sustain an axial load of 159 kips, even though the nominal punching shear capacity was 188 kips, using measured material strengths. The drop in axial capacity that is caused by this level of damage is not surprising. AASHTO LRFD does not have a procedure for estimating strength under combined static axial load and moment, much less under cyclic moment. ACI 318-08 section 21.13.6 contains provisions for such cyclic loading, and the nominal strength is less than under static loading.

#### Footing Shear-Friction Strength

Loads were carried from the precast column to the cast-in-place spread footing by shear and normal stresses across the interface. The capacity of the "socket" was evaluated using the shear-friction calculation procedure in section 5.8.4 of the AASHTO LRFD. The nominal shear resistance was calculated using equation 5.8.4.1-3 in the AASHTO LRFD, shown here in figure 69.

In this equation, *V _{n}* ≤ min(

*K*). Here,

_{1}f'_{c}A_{cv},K_{2}A_{cv}*c*is the cohesive shear stress,

*A*is the area of concrete considered in an interface shear transfer, μ is the coefficient of friction,

_{cv}*f*is the yield stress of the reinforcement crossing the interface,

_{y}*P*is the net compressive force normal to the shear plane, P

_{c}_{c}was assumed to be zero in this case,

*K*is the fraction of concrete strength available to resist interface shear, and

_{1}*K*is the limiting interface shear resistant.

_{2}The precast test columns were roughened with the same roughness detail as required in the WSDOT BDM for the ends of prestressed girders.^{(17)} This roughness detail satisfied the AASHTO LRFD specifications in terms of minimum amplitude and minimum spacing between ridges. For a normal-weight concrete placed against an intentionally hardened concrete surface with an amplitude of 0.25 inches, the AASHTO LRFD proposes the following to be used in shear-friction design: *c* = 0.24 ksi, μ = 1.0, *K _{1}* = 0.25,

*K*= 1.5 ksi.

_{2}Figure 69 has two components that contribute to shear-friction: cohesion and friction. In the design of the prototype connection and for the test specimens, the cohesion component was ignored.

A question arises over the use of the main tension steel in the footing for resisting shear friction. The horizontal tension force is equilibrated by a horizontal compression force between the top of the footing and the column, which therefore provides friction capacity. While this argument is rational, and is based on equilibrium alone, the AASHTO specifications give no guidance on the use of flexural steel to also serve as shear friction steel. Therefore, in specimen SF-1 separate shear friction steel was designed to resist the entire vertical shear force.

The calculated amount of reinforcement needed to cross the interface (*A _{cv}*, 12 No. 4 bars) was stacked on the bottom mat around the column base to provide more confinement around the roughened base. These bars were placed diagonally and stacked in four layers for specimen SF-1. The amount was reduced by a factor of three, to four No. 4 bars for specimen SF-2, in an attempt to find out whether the main tension steel alone would provide sufficient shear friction capacity. However, one set (four bars) of diagonal steel was retained to act as trimming steel in the corners, since the column was octagonal but the opening in the mat of main steel was square. Discussions with WSDOT designers confirmed that they would require such trimming steel in the prototype.

For specimen SF-3, the required friction strength was the same as in specimen SF-1. However, when specimen SF-3 was designed, the results of the tests on specimens SF-1 and SF-2 were available, and in particular it was known that the diagonal steel had experienced low stresses and had contributed little to shear friction resistance. Thus, it was concluded that the main tension steel does indeed contribute towards shear friction resistance, and in specimen SF-3, which had a shallower footing and consequently less space for placing diagonal bars, the bottom mat flexural reinforcement was counted as part of the "shear friction" steel. The required total was made up by adding four No. 5 diagonal bars.

This argument could be further refined to show that not only the longitudinal bottom steel but also the transverse tension steel contributes to shear friction resistance. Consider a square footing subjected to north-south earthquake motion. Because the main bars are placed at the side of the column, rather than beneath it, a strut-and-tie model of the footing would contain struts that are oriented at a compound angle; that is, they would be diagonal when viewed in in both plan and section. The compressive force between the footing and column concrete would then be larger than the force from the north-south tension steel alone, and it is the normal force that determines the friction resistance. In this case the normal force is given by the vector sum of the tension strengths of the bottom tension steel in the two directions. Thus, even using the longitudinal tension steel to provide shear friction reinforcement is conservative.

It should be noted that AASHTO LRFD takes a different approach to shear friction than both ACI 318-08 and the Precast/Prestressed Concrete Institute (PCI) Design Handbook.^{(23)} The latter two specifications contain no contribution from cohesion, but the AASHTO LRFD does. During design, the cohesion component was ignored in the interest of safety and conservatism.

Table 17 lists the shear-friction capacities calculated using the equation in figure 69 for the socket connection. Note that the cohesive component has been included for the comparison with the maximum applied, post-lateral axial demand.

The table shows that AASHTO's cohesive component alone was enough the resist the maximum factored load of 240 kips for specimens SF-1 and SF-2. In contrast, the cohesive component in the thin footing in specimen SF-3 was not enough to resist the maximum axial load. There was no indication of sliding shear failure in any of the three test specimens at the interface between the column and the footing during the application of the maximum axial load.

Specimen | SF-1 | SF-2 | SF-3 | |||
---|---|---|---|---|---|---|

Capacity Values Input | Specified Properties | Measured Properties | Specified Properties | Measured Properties | Specified Properties | Measured Properties |

Calculated Cohesive Component (kip) | 330 | 330 | 330 | 330 | 147 | 147 |

Calculated Friction Component (kip) | 288^{1} |
306^{1} |
96^{1} |
102^{1} |
288^{2} |
318^{2} |

Calculated V(kip)_{n } |
618 | 636 | 426 | 432 | 435 | 465 |

Measured V (kip)_{u} |
918 | 820 | 342 | |||

V_{u}/V_{n} |
1.49 | 1.44 | 1.92 | 1.90 | 0.79 | 0.74 |

^{1} Including diagonal steel, which does not cross the interface between the precast and cast-in-place elements.^{2} Including diagonal steel and bottom mat of flexural reinforcement. |

#### Footing Joint Shear

The joint shear stress was evaluated by using a procedure recommended in section 6.4.5 in the AASHTO Seismic Guide Specifications.^{(15)} The column-to-footing joint principal stresses have to satisfy the equations shown in figures 70 and 71.

*f' _{c}* is in ksi, and

*p*and

_{c}*p*are calculated using the equations in figure 72 and 73.

_{t}In these equations, . Here, *T _{jv}* is the sum of the tensile forces in the column reinforcement, is the effective width of the footing,

*D*is the depth of the footing,

_{ftg}*P*is the axial force acting on the column and included overturning, and is the effective horizontal area at mid-depth of the footing assuming 45 degrees spread away from the boundary of the column.

_{col}The design overstrength moment (*M _{po}* =3,081 kip-in.,

*P*= 159 kips) and the total column tensile force associated with it (

*T*= 154 kips) were obtained from a moment-curvature program in OpenSees. Table 18 summarizes the results using specified and measured material properties. Demands in the connection of specimens SF-1 and SF-2 did not come close to the nominal stress limits given in the same table. The demands increased in specimen SF-3, which had a shallower foundation, as was expected, but did not exceed limits. There were no signs of joint shear failure of any kind in any of the tests.

Specimen | SF-1 | SF-2 | SF-3 | |||
---|---|---|---|---|---|---|

Capacity Values Input | Specified Properties | Measured Properties | Specified Properties | Measured Properties | Specified Properties | Measured Properties |

Compressive Limit Stress (ksi) |
1.00 | 1.25 | 1.00 | 1.37 | 1.00 | 1.98 |

Tensile Limit Stress (ksi) |
0.76 | 0.85 | 0.76 | 0.89 | 0.76 | 1.07 |

Compressive Demand Stress (ksi) |
0.29 | 0.29 | 0.64 | |||

Tensile Demand Stress (ksi) |
0.2 | 0.2 | 0.47 | |||

/ | 0.29 | 0.23 | 0.29 | 0.21 | 0.64 | 0.32 |

/ | 0.26 | 0.24 | 0.26 | 0.22 | 0.62 | 0.44 |

The applicability of these joint shear stress equations for socket connections, where the column longitudinal bars are terminated with anchors instead of being bent out into the foundation, is debatable. A strut-and-tie model of the joint, such as the one shown in figure 74, suggests that, after the joint cracks, the shear forces in it are carried by a diagonal strut. If the vertical column bars are bent outwards into the footing, the load transfer between strut and bar at the node has to be achieved by bond stress, because the direction of the force is parallel the bar axis. That load transfer mechanism has a low capacity, and the AASHTO limits on joint shear stress serve to keep the load in the strut down to a level at which the force can be transferred at the node without failure. However, if straight bars with anchor heads are used, the load transfer from the strut is achieved by bearing on the head, and not by bond. That mechanism has a high capacity, so much higher joint shear stresses should be permitted, in which case the need for ties is reduced or may be eliminated.

The test specimens all used headed bars, and the joint shear stresses were well below even the AASHTO limits, so it was not surprising that there were no signs of joint shear failure. Even in specimens SF-3, where the joint was smallest and the joint shear stress was highest, there were no signs of joint shear failure. As shown in figure 75, the base of the column, which constitutes the joint region, was still intact at the end of testing, and the concrete behind the anchor heads was still in place.

### Column Response

#### Column Axial-Load Capacity

The column needs to be able to resist the expected maximum axial load. The largest factored axial load for the prototype column was 1,382 kips, or 240 kips at specimen scale.

The test program for all three specimens started with a pure axial load test to verify that the connection could resist at least the factored load. Once cyclic lateral loading was complete, the columns of SF-1 and SF-2 were again loaded axially until the column failed in the column hinge region,which had formed during the lateral-load tests. The axial-load capacity of the column was calculated using equation 5.7.4.4-2 in the AASHTO LRFD. ^{(14)} Figure 76 shows the AASHTO LRFD, excluding the prestressing terms.

Table 19 summarizes the nominal and measured axial capacities for the test columns. The capacities were calculated based on both the specified and measured material properties.

Specimen | SF-1 | SF-2 | SF-3 | |||
---|---|---|---|---|---|---|

Capacity Values Input | Specified Properties | Measured Properties | Specified Properties | Measured Properties | Specified Properties | Measured Properties |

Calculated P(kips)_{n} |
1077 | 1301 | 1077 | 1413 | 1077 | 1960 |

Measured P(kips)_{u} |
918 | 820 | 342 | |||

P_{u}/P_{n} |
0.85 | 0.71 | 0.76 | 0.58 | 0.32 | .17 |

During the lateral-load tests of specimens SF-1 and SF-2, there was no indication of loss of axial-load capacity in the columns. In the axial-load tests performed after completing those lateral load-tests, more than 58 percent of the nominal axial capacity of the column remained, even though the columns had hinged, and the spiral and some bars had fractured. The axial-load capacity of specimen SF-3 dropped when the column failed in combined moment transfer and punching shear under an axial load of 159 kips, which corresponded to 8 percent of the nominal column axial-load capacity calculated with the measured material properties.

#### Column Flexural Strength

The column flexural strength was computed following the recommendations given by the AASHTO LRFD and the AASHTO Seismic Guide Specifications. ^{(14,15)} The nominal capacity, *M _{n}*, of the column was calculated according to AASHTO LRFD specifications using the specified material properties.

In design, the overstrength demand on the spread footing comes mainly from the plastic capacity of the columns, computed for expected materials properties. The expected concrete compressive strength was 5.2 ksi for a specified strength of 4.0 ksi. This assumption was approximately correct for SF-1 and SF-2, but it underestimated the compressive strength of the concrete in SF-3 (8.0 ksi). The AASHTO expected tensile yield stress for the reinforcement was 68 ksi for a specified yield stress of 60 ksi. This assumption overestimated the yield stress in the actual reinforcement.

The AASHTO Seismic Guide Specifications recommends that the *M-φ* relationship be idealized as elastic perfectly plastic, in which the idealized curve passes through the point of first yield in the reinforcement (see figure 77). The idealized plastic moment capacity, *M _{p}*, was obtained by equating the areas between the idealized and the actual curves. The ultimate curvature,

*φ*, was determined as the smaller of:

_{u}- The ultimate confined concrete compressive strain,
*ε*_{cu}_{ }= 0.016, divided by the distance from the plastic neutral axis to the extreme fiber of the confined concrete. - The reduced ultimate tensile strain, = 0.09 (A706 No.6), of the steel divided by the distance from the plastic neutral axis to the extreme tension fiber of the longitudinal reinforcement.

The overstrength plastic moment capacity was obtained by multiplying *M _{p}* by an overstrength magnifier,

*λ*, which takes into account variations in material strengths. For ASTM A706 reinforcement, this magnifier is 1.2.

_{mo}To compute the flexural strengths according to the AASHTO Seismic Guide Specifications recommendations, moment-curvature analyses were performed usingthe software Xtract. That program uses Mander's confined concrete model and the AASHTO Seismic Guide Specification's strain-hardening steel model. ^{(15,19)} Table 20 summarizes the moment-curvature analysis performed for an axial force of 159 kips for the specified and measured material properties. For the analyses using the measured material properties, a factor of 1.2 was not applied to the calculated plastic moments.

The actual moment capacity exceeded the nominal moment capacity (using measured properties) according to AASHTO LRFD by about 20 percent. That discrepancy was expected, because the AASHTO nominal moment capacity does not account for strain-hardening in the reinforcement nor for differences between specified and actual material properties. The maximum moments measured in the tests were nearly identical to the overstrength plastic moment predicted with the AASHTO procedure for the specified material properties.

Specimen | SF-1 | SF-2 | SF-3 | |||
---|---|---|---|---|---|---|

Specified Properties | Measured Properties | Specified Properties | Measured Properties | Specified Properties | Measured Properties | |

Nominal Moment (kips-in.) | 2,711 | 2,576 | 2,711 | 2,613 | 2,711 | 2,774 |

Plastic Moment Capacity M_{p} (kips-in.) |
2,671 | 2,487 | 2,671 | 2,505 | 2,671 | 2,672 |

Overstrength Moment (kips-in.) | 3205 | 2,984 | 3205 | 3,006 | 3205 | 3,206 |

Largest Measured Moment M_{u} (kips-in.) |
3,091 | 3,113 | 3,392 | |||

M_{u}/ |
0.96 | 1.04 | 0.97 | 1.04 | 1.06 | 1.06 |

#### Column Shear Strength

The AASHTO Seismic Guide Specifications require that the shear demand, V_{po}, be calculated corresponding to the overstrength plastic moment, M_{po}. That demand was calculated using the equation shown in figure 78.

In this equation, *L* is the total height between the footing surface and the line of action of the lateral load. For specimens SF-1, SF-2, and SF-3, the actual shear demands were calculated to be 47.5, 49, and 52, respectively.

The nominal shear resistance was calculated according section 8.6.1 in the AASHTO Seismic Guide Specifications (see figure 79).

This procedure takes into account the contributions of both the concrete and the transverse reinforcement. The concrete contribution is calculated using the equations in figure 80 and 81.

Here, *f' _{c}* is in ksi;

*α'*(here, 3) was determined from an equation that takes into account volumetric transverse reinforcement ratio, yield stress of the spiral, and a ductility ratio; and

*P*is the ultimate compressive force acting on a section.

_{u}The reinforcement contribution was determined using the equation in figure 82.

Values of demand and capacity using both the specified and the measured material properties are given in table 21. There was no sign of shear failure in the columns during tests.

Specimen | SF-1 | SF-2 | SF-3 | |||
---|---|---|---|---|---|---|

Capacity Values Input | Specified Properties | Measured Properties | Specified Properties | Measured Properties | Specified Properties | Measured Properties |

(kips) | 55 | 62 | 55 | 65 | 55 | 78 |

(kips) | 70 | 59 | 70 | 59 | 70 | 59 |

(kips) | 125 | 121 | 125 | 124 | 125 | 137 |

Measured Shear Demand, V (kips)_{u} |
47.5 | 49 | 52 | |||

V/_{u} |
0.38 | 0.39 | 0.39 | 0.40 | 0.42 | 0.38 |

For specimen SF-1 and SF-2, the capacity decreased when calculated with measured material properties. That occurred because the yield strength of the 2-gauge spiral was lower than specified by ASTM A82, which is 70 ksi. A possible explanation for this discrepancy was that the spiral had to be straightened out for tensile testing. The increase in concrete strength for specimen SF-3 was large enough to counteract the loss of strength in the spiral. In all tests, column shear failure was improbable because the shear demands placed on the columns were well below the calculated shear capacity for all three specimens.

#### Column Splice in Specimens SF-1 and SF-2

Specimens SF-1 and SF-2 both had segmental columns with splices located 20 inches above the surface of the spread footings. Section 4.11.7 in the AASHTO Seismic Guide Specifications recommends that the plastic-hinge length, *L _{pr}*, be taken as the larger of 1.5 times the gross sectional diameter, the region where 75 percent of the overstrength moment occurs, or the analytical plastic-hinge length. L

_{pr}is calculated using the equation in figure 83.

To increase the demands on the splices, they were placed based on the moment diagram only, instead of placing the splice at the top of the plastic hinge region, as determined above. The base moment was assumed to have the computed overstrength value, and a straight-line diagram was constructed, dropping to zero at the level of the lateral load. The elevation at which the moment diagram corresponded to the first yield moment was approximately 18 inches above footing surface, and strain gauges were mounted on the column longitudinal bars at that location.

The bars yielded considerably, 2 inches below the splice. Potentiometers bridging the splice recorded crack opening displacements of about 0.045 inches. No grout damage was observed in spite of the initiation of yielding at the splice location. In both specimens, the splices performed well in flexure.

Each splice was built with a shear key at the center of the column, which was grouted. No shear slip was detected in either case. It is likely that the shear key was unnecessary. The peak shear force was approximately 53 kips, while the axial load was 159 kips. Thus, to prevent slip, and in the absence of additional forces from the bars, a coefficient of friction of 53/159 = 0.333 was needed. The effect of the bar forces on slip could also be taken into account. The total bar force is likely to be tensile because the distance from the neutral axis to the compression face is likely to be less than 0.5*D _{col}* as a result of the relatively low axial load. That implies that additional compression exists between the two concrete faces of the splice, so the normal force available for creating friction is greater than the 159 kip axial load and the friction coefficient needed to prevent slip is less than 0.333. Friction between precast elements and the adjacent grout layer has been measured at approximately 0.6. It is thus likely that slip would not have occurred even if the shear key had been omitted.

### Damage Progression Models

Berry and Eberhard proposed damage models to predict the onset of spalling, bar buckling, and bar fracture.^{(24,25)} The three relevant equations for spiral reinforced columns are shown in figures 84 through 86.

In these equations, *P* is the axial load applied, *L* is the distance to the point of contraflexure (here, 60 inches), *D* is the column depth (here, 20 inches), *A _{g}* is the column gross-sectional area,

*d*is the longitudinal reinforcement diameter,

_{b}*f'*is the concrete compressive strength, and

_{c}*ρ*=

_{eff}*ρ*, where

_{s}f_{ys}/f'_{c2}*ρ*is the transverse volumetric ratio and

_{s}*f*is the transverse reinforcement yield strength.

_{ys}Table 22 shows a comparison of the results from the models, using measured material properties, with the observed behaviors from the tests.

Specimen | Drift ratio at onset of spalling | Drift ratio at onset of bar buckling | Drift ratio at onset of bar fracture | ||||||
---|---|---|---|---|---|---|---|---|---|

Pred. | Obs. | Obs./Pred. | Pred. | Obs. | Obs./Pred. | Pred. | Obs. | Obs./Pred. | |

SF-1 | 1.87 | 1.07 | 0.57 | 6.03 | 7.09 | 1.18 | 6.50 | 10.61 | 1.63 |

SF-2 | 1.89 | 1.10 | 0.58 | 5.89 | 7.19 | 1.22 | 6.34 | 10.65 | 1.68 |

SF-3 | 1.94 | 1.41 | 0.73 | 5.50 | 7.15 | 1.30 | 5.92 | N/A | N/A |

Mean | 1.90 | 1.19 | 0.63 | 5.81 | 7.14 | 1.23 | 6.25 | 10.63 | 1.66 |

The onset of spalling occurred much earlier than predicted by the equation in figure 84. The drift ratio at the onset of bar buckling was predicted more accurately. Bar fracture occurred much later than predicted by the equation in figure 86.

### Effective Stiffness Model

The measured effective moduli of rigidity (*EI*) of the test specimens were compared with a model proposed by Elwood and Eberhard that takes into account for deformations due to flexure, shear and anchorage-slip.^{(26)} The effective modulus of rigidity is calculated using the equation in figure 87.

In this equation, *EI _{g}* is gross modulus of rigidity,

*P*is the axial load applied on the test specimen,

*A*is the gross-sectional area of the column,

_{g}*f'*is the unconfined concrete strength,

_{c}*d*is the longitudinal bar diameter, D is the column diameter, and

_{b}*a*is the cantilever length.

Table 23 summarizes the measured and the predicted values using the measured concrete strength. The measured and predicted effective modulus of rigidities compared well, with an average error of 10 percent.

Specimen | Gross Section Modulus of Rigidity (kip-in^{2}) |
Normalized Effective Modulus of Rigidity (EI)_{eff}/EI_{g} |
||
---|---|---|---|---|

Pred. | Obs. | Obs./Pred. | ||

SF-1 | 31,639,709 | 0.30 | 0.26 | 0.87 |

SF-2 | 33,188,536 | 0.29 | 0.28 | 0.97 |

SF-3 | 39,878,444 | 0.26 | 0.22 | 0.85 |

Mean | 34,902,230 | 0.85 | 0.25 | 0.90 |

### Normalized Moment-Drift Response

The normalized moments for the three socket connection specimens are plotted versus drift ratio in figure 88. The measured moments were normalized with their corresponding values of *M _{n }*using measured properties. A typical cast-in-place column is shown for comparison. This reference specimen (DB5-RE) was also used for comparison with the "large-bar" column-to-cap beam connection tests, in research conducted by Pang et al. at the University of Washington.

^{(7)}In traditional cast-in-place construction, the construction procedure is similar for the column-to-cap beam connection and the column-to-footing connection. In the former, the longitudinal bars protrude up from the column to be cast with the cap-beam. In the latter, the procedure is the same, except that the bars protrude from the footing and are cast entirely within the column. In both connections, a horizontal cold joint is constructed between the elements.

The reference column shared the same geometry as specimens SF-, SF-2, and SF-3, but it had more longitudinal reinforcement (longitudinal ratio of 1.6 percent, 16 No. 5 bars, instead of 1 percent). The concrete specified strength differed as well (5,000 psi instead of 4,000 psi). The nominal moment strength of specimen DB5-RE was determined to be 3,815 kips-in.^{(7)}

The socket specimens behaved similar to the cast-in-place reference specimen. In all specimens, the overstrength moment exceeded the nominal moment strength, as expected. The difference was about 15 to 20 percent for all specimens. The peak strength was reached at 2 percent drift, and the moment was constant up to about 6 percent drift, with the exception of specimen SF-3, whose strength gradually decreased after 2.5 percent drift. As the specimens were cycled, the longitudinal bars buckled and later fractured. Specimen SF-3 failed in combined punching shear and moment transfer before any bar could fracture.

### Strength Degradation

Figure 89 compares the effective force versus drift ratio for the three specimens, which shows that the specimens performed similarly. The maximum effective force was approximately 51 kips for both specimens SF-1 and SF-2, whereas the peak was about 55 kips for specimen SF-3. The peak was reached at about 2 percent drift for all specimens. The load capacity remained almost constant up to 6 percent drift for specimens SF-1 and SF-2, after which both specimens lost strength at the same drift and degraded at the same rate. Specimen SF-3 proved to be about 7 to 10 percent stronger than specimens SF-1 and SF-2 and decayed more gradually, starting at 2.5 percent drift.

### Energy Dissipation

The energy dissipation is the area inside the force-displacement curve and is a measure of how much damping the system can provide during an earthquake. It was calculated in this research using the trapezoidal integration procedure shown in figure 90.

Figure 91 shows both the energy dissipated per cycle and the cumulative energy dissipation for the three specimens. To facilitate reading of the plots, the cycles are numbered continuously from the beginning. The tests consisted of sets of four cycles in which the peak amplitudes were 1.2A, 1.4A, 1.4A, and 0.33A, where A is the peak amplitude of the previous cycle set. The sets are visible as "humps" in the figure.

Figure 91 shows that the energy dissipation is almost the same in all specimens up to cycle 36 (cycle 9-4). However, in the last set of cycles there are slight differences between them, because buckling of the longitudinal reinforcement and first transverse reinforcement fracture were observed earlier in specimen SF-1 than in specimens SF-2 and SF-3. The transverse reinforcement in SF-1 fractured in cycle 34 (-6.88 percent drift), whereas the transverse reinforcement in SF-2 and SF-3 fractured in cycle 37 (-8.29 percent and +8.72 percent drift respectively). In cycle 38 (~10.6 percent drift), both specimen SF-1 and SF-2 fractured longitudinal bars for the first time. After the last cycle, SF-1 had fractured three bars and SF-2 had fractured four bars. Specimen SF-3 did not fracture any longitudinal bars.

Figure 92 shows the calculated equivalent viscous damping ratio versus every fourth cycle. Equivalent viscous damping was calculated using the equation in figure 93, where *A _{loop}* is the cycle energy and

*A*is the area of a rectangle circumscribing the loop.

_{rectangle}The same information is shown in figure 94, in which the equivalent viscous damping ratio is plotted against the average drift ratio for the same cycles.

Damping was similar but not identical for the three specimens. All tests showed higher damping in the beginning of tests. With increasing drift the systems were dissipating more energy. The responses of specimens SF-1 and SF-2 were almost identical, but specimen SF-3 was consistently lower after 1percent drift. Specimen SF-3 proved to be little bit stronger than the other two specimens, which resulted in lower damping values (*A _{rectangle}* is bigger in SF-3).

In all three specimens, the damping values at small drifts were quite large. This is believed to be a consequence of the process used to correct for the friction in the sliding channel in the Baldwin Universal Testing Machine. The friction was approximately constant throughout the test but, at low drifts, the amount of energy dissipated by the column was small. The result is that the relative error (caused by imperfect estimation of the true friction) was greatest at small drift ratios, and reliance should not be placed on those values.

Despite the fact that specimen SF-3 had a configuration that was very different from those of specimens SF-1 and DF-2, the energy dissipation behavior of all three was remarkably similar. Photographic evidence from the tests also shows extensive damage to the columns in all three specimens. Damage to the footing in specimen SF-3 only became visible starting at about 9 percent drift ratio. The observation suggests that specimen SF-3 was very close to being governed by column strength rather than footing connection strength. That, in turn, suggests that only a small increase in footing depth or connection reinforcement would be needed to make it behave like a conventional cast-in-place system.