56392237 composites for construction structural design with frp materials

15.7 HEAVY-FRAME PULTRUDED CONNECTIONS 503

Figure 15.13 Out-of-plane forces in clip angle simple shear beam-to-column con-nections. (Courtesy of J. T. Mottram.)

15.7 HEAVY-FRAME PULTRUDED CONNECTIONS

In heavy-frame connections, the connection parts used to connect the mem-bers, which are usually at right angles, are eccentrically located with respectto the centroid of the members being connected. As a result, the connectionparts are subjected to loads that are offset from, or eccentric to, the line ofthe fasteners. This causes a localized bending moment to develop in the planeof the web, in addition to the in-plane loads that occur in lap joint connectionsseen in light trusses. For the in-plane component of the forces, the samediscussion and the guidance cited previously for lap joints is applicable to theparts of the heavy pultruded connection that carry in-plane loads.

The moment causes out-of-plane forces to develop at the face of the con-nected members which generate prying forces at the top and compressiveforces at the bottom of the connection. For example, a web clip subjected toa bending moment causes the top of the clip to pull away, or pry away, fromthe column flange, and the bottom part of the clip angle to be compressedinto the flange of the column (Fig. 15.13). This eventually leads to the failureof the clip angle, due to delamination due to tensile and flexural stresses atthe top of the angle, as shown in Fig. 15.14.

Failure may also occur at a webflange junction in the column behind thetop set of fasteners on the column flange. If the beam shown in Fig. 15.14were allowed to continue to rotate, the column could eventually fail in themode shown in Fig. 15.9.

504 PULTRUDED CONNECTIONS

Figure 15.14 Delamination of a web clip angle due to prying action. (Courtesy ofJ. T. Mottram.)

15.8 DESIGN OF BOLTED PULTRUDED CONNECTIONS

Guidance is given in this section for determining the critical stresses in pul-truded connections. The guidance is based on simplified mechanics consid-erations and assumes that only in-plane tension or out-of-plane tension orcompression loads are applied to an individual fastener or connection part (asin a shear clip connection). Combined in-plane tension and shear on boltgroups is not considered. Equations, however, are provided in the Eurocompdesign code for calculating stresses at the circumference of a hole in anorthotropic material under multiaxial stress states. It is not generally acceptedthat the level of complexity involved in performing such calculations is ap-propriate at this time, given the limited data available on pultruded materialsin bolted connections, especially beam-to-column connections. In what fol-lows, guidance is given only for the following connections:

1. In-plane lap-joint connections for in-plane tensile or compressive loadsfound in pultruded connections in light-frame overlapping joints and ingusset plates for bracing members (see Fig. 15.7) and in elements ofheavy-frame beam-to-column connections.

2. Out-of-plane beam-to-column connections for shear forces (and sec-ondary local moments) found in simple regular beam and columnframes. At this time this includes only (a) web clip angle connections(see Fig. 15.13) and (b) flexible seated connections. Guidance providedfor shear clips can also be used to design simple column base plates.These connections may be designed to account for the eccentricity ofthe shear load according to traditional elastic vector analysis that is usedfor steel bolted connection (Salmon and Johnson, 1996, p. 139). The

15.9 DETERMINATION OF STRESSES IN IN-PLANE LAP JOINTS 505

resulting load on each of the bolts due to a combination of direct shearand torsion on the fastener group (due to the eccentric shear load) isobtained using this traditional procedure. Using the resulting load, thecritical stresses at the individual bolt locations are determined.

In the absence of specific guidance for either in-plane or out-of-plane pul-truded connections, the basic principles used to design steel-bolted simpleshear connections can be followed for the design of bolted pultruded con-nections (Salmon and Johnson, 1996). However, the orthotropic properties ofthe pultruded based materials and FRP fasteners (if used) and geometric spac-ing recommendations for pultruded connections should be followed. In par-ticular, the orientation of the pultruded material in the connection shouldalways be considered (and indicated on detailing drawings of the connection).In the event that the connection capacity cannot be realized with an existingprofile wall thickness and pultruded plate thicknesses, the thickness of thepultruded material should be increased by adhesively bonding (during shopfabrication) a piece of pultruded plate material where required to strengthenthe existing part. In these situations it is recommended that a piece be bondedwith its major fiber orientation at 90 to the fiber orientation in the existingpart to create a material with more isotropic parts at the critical location.

15.9 DETERMINATION OF STRESSES IN IN-PLANE LAP JOINTS

In what follows, elementary one-dimensional mechanics-based equations arepresented for determining stresses in in-plane single- and multibolt lap joints.The equations for calculating the stresses on the connection parts are basedon assumptions of linear elastic material behavior and small deformations andgive design stresses that can be compared with coupon-level material testdata. However, these equations are used only as a guide to the strength of theconnection, since at the ultimate load the connection behavior is not linear,and large deformations can significantly alter the stress distributions andchange the failure modes.

15.9.1 Bearing Stress in the Base Pultruded Material

The average bearing stress at the hole in the base pultruded material is givenas

Pb (15.2)br d tb pl

where Pb is the load transferred at an individual bolt location, db the boltdiameter, and tpl the thickness of the base pultruded material.


15.9.2 Net-Tension Stress in the Base Pultruded Material

The net-tension design stress at the location of the hole in the base pultrudedmaterial is given as

Pt (15.3)net Anet

where Pt is the tensile load transferred by the entire lap joint, consisting of anumber of columns of bolts, and the net area, Anet, is taken as

A t (W nd ) (15.4)net pl h

where n is the number of bolts in the row, and W the width of the plate atthe critical section, dh the hole diameter, and tpl the thickness of the basepultruded material. This assumes that the critical section will be through therow of holes and perpendicular to the longitudinal direction of the material.As in steel connections, the critical section may be staggered though multiplerows when holes are not in rows perpendicular to the load direction (Salmonand Johnson, 1996, p. 74). In orthotropic pultruded materials, the failure mayoccur in a staggered fashion even when the holes are in regular rows (Prab-hakaran et al., 1996). This may be considered to be a type of block shearfailure (discussed in what follows) in this case. At this time, the empiricalformula used for staggered rows for joints in steel members is recommendedas a first approximation for orthotropic pultruded materials:

2pA t W nd (15.5) net 4g

where the summation is over all diagonal distances in an assumed failurepath. This equation assumes that the strength of the material is the samealong all paths, which is not actually the case for orthotropic materials. Whereelements of profile sections are connected in tension (such as flanges of anglesand I-sections), it is recommended that only the width of the outstandingelement be considered to be effective (not the width of the entire section).The effective net area used in steel design should not be used for pultrudedmaterials. For multiple rows of bolts, the load distributions in Table 15.3should be used.

15.9.3 Shear-Out Stress in Base Pultruded Material

The shear-out stress at the bolt location at the material end edge in the di-rection of the load is given as

Pb (15.6)shear-out 2t epl

15.10 STRESSES IN OUT-OF-PLANE SHEAR CONNECTIONS 507

where Pb is the load transferred at an individual bolt location, e the enddistance, and tpl the thickness of the base pultruded material.

The shear-out stress at the bolt location in the material between two boltsin a column in the direction of the load is given as

Pb (15.7)shear-out 2t ppl

where Pb is the load transferred at an individual bolt location, p the pitchdistance, and tpl the thickness of the base pultruded material.

15.9.4 Shear Stress on a Bolt

The shear stress on a bolt is given as

Vb (15.8)b Ab

where Vb is the shear force on the bolt (accounting for single or double shearconfigurations) and Ab is the cross-sectional area of the bolt shank.

15.10 STRESSES IN OUT-OF-PLANE SHEAR CONNECTIONS

In simple shear beam-to-column connections, in addition to the stress staterelated to in-plane loading of lap-jointed parts noted above, additional stressesare determined in the profiles themselves and the connected parts. Thesestresses are developed due to the eccentricity of the shear load on the con-nection, which causes bending and shear stresses to develop in the connectionparts. For simple shear double clip angles connections, the following statesare considered.

15.10.1 Longitudinal Shear Stress at the Heel of an Angle

Shear stress in the heel of the connection angles is calculated as

V (15.9)pl 2Aheel

where V is the total design shear force (one-half to each clip angle) at thebeam end and Aheel tpl langle is the shear area of the heel, equal to thethickness of the angle multiplied by the length of the angle parallel to theshear force. If this stress exceeds the ultimate shear strength of the pultrudedmaterial, the connection will fail, due to shear failure of the clip angles.


R

bleg bleg

tpl tpl

S S

tw(beam)

tf(column)

Figure 15.15 Deformation and forces in back-to-back angles.

15.10.2 Flexural Stress in the Leg of an Angle Bolted to aColumn Member

Due to the prying action of an eccentric connection, the upper portion of theclip angle is subjected to a tensile force which causes the connected leg ofthe angle to bend and shear as shown in Fig. 15.15. Assuming that the doubleangle acts as a fixed beam loaded with a concentrated load (equal for theprying force), the bending and shear stress in the leg of the angle can becalculated. Assuming that the prying force, R, on a bolt a distance d from thecenter of rotation, determined using elastic vector analysis, is

MdR (15.10)2d

the moment at the connection, M Vev, is equal to the shear force multipliedby the eccentricity, ev, from the column face to the centroid of the bolts. Thelocal moment applied to the leg of each angle based on two back-to-backangles (assuming a fixedfixed beam with a central load equal to R) is

R(b t s)leg plm (15.11)leg 8

where bleg is the width of the angle leg and s is the side distance from thecenter of the bolt hole to the edge of the leg. The local shear force is, vleg R /2.

15.10 STRESSES IN OUT-OF-PLANE SHEAR CONNECTIONS 509

The flexural stress in the leg of the angle is then given as

m mleg leg (15.12)flex 2S (2e)t /6pl

where the effective length over which the angle bends is assumed to be twicethe distance from the top of the angle to the bolt (i.e., the edge distance, e).

The shear stress in the leg is given as

V R /2 (15.13)leg A t (2e)pl

where it is assumed that the shear stress is distributed over a length equal totwice the edge distance. This shear stress is the major cause of the delami-nation failure shown in Fig. 15.14. Failure will occur when this shear stressis equal to the interlaminar shear stress of the pultruded material.

15.10.3 Transverse Tensile Stress in a WebFlange Junctionof a Column

When the beam is connected to the flange of a column, the prying forceexerted by the top half of the back-to-back clip angles will subject the webflange junction of the column to a transverse tensile force that will tend topull the flange away from the web of the profile. This transverse tensile forceis assumed to act over an area equal to the thickness of the column web, tweb,multiplied by a length equal to half the angle height, langle /2. The transversetensile stress of the webflange junction is therefore given as

R (15.14)trans t (l /2)web angle

15.10.4 Block Shear in a Beam Web

Block shear failure, or cleavage failure (in Fig. 15.11) occurs in the basematerial over an area that fails due to a combination of net tension failureand shear failure. This type of failure can occur in the web of the beam whenthe top flange of the beam is coped for construction reasons. The failure ofthe pultruded material in the web depends on both the net tensile strength ofthe material and the shear strength of the material assuming that the axes oforthotropy of the pultruded material are aligned either parallel or perpendic-ular to the load direction. The tensile and shear stresses depend on the areaof the through-the-thickness surface that is subjected to tension and shear,and they cannot be calculated separately. An interaction equation, given be-low, is used to determine the capacity of the connection.


critical section in seat angle

xx

V

Note: Bolts notshown for clarity

Note: Always use a top clip angle inpultruded seat connection

Figure 15.16 Seated angle connection.

15.10.5 Flexural and Shear Stresses in Flexible Seated Connections

In beam-to-column connections in which a bottom seat is used to support thebeam at the column, critical shear and flexural stresses develop at the face ofthe outstanding leg, which acts as a cantilever, as shown in Fig. 15.16. Thelocal bending moment for the flexural stress calculation depends on the lo-cation of the shear force reaction on the seat. Generally, this is taken as halfthe distance between the beam end and the end of the angle leg. In seatedconnections a top clip must also be provided to stabilize the top flange of thebeam. Seated clip angles using pultruded angles are generally not used intypical designs, due to the low flexural stiffness of the pultruded angle in theclosing mode.

When both top and bottom clip angles (seats) and web clip angles areused, a pultruded connection (shown in Fig. 15.9) can develop a sufficientrotational stiffness to allow semirigid frame analysis and design. However, asdiscussed previously, the rotational stiffness can not be determined analyti-cally at this time and must be obtained by full-size experiments, if required.

15.11 CRITICAL CONNECTION LIMIT STATES

The critical strength when the pultruded base material fails due to bearing istaken as either the longitudinal or the transverse bearing strength of the pul-truded material. This is regarded as a basic material property and is obtainedfrom testing, which is generally reported by pultrusion manufacturers. If thebearing strength is not available from test data, it can be approximated as thematerial compressive strength for approximate calculations. Either the lon-gitudinal bearing strength or the transverse bearing strength is used, depend-ing on the direction of the member or element relative to the load:

15.11 CRITICAL CONNECTION LIMIT STATES 511

bear or (15.15)cr L,br T,br

Pultruded connections are currently designed only for the ultimate strengthlimit state. The bearing strength used for pultruded materials is the ultimatebearing strength (i.e., the load required to cause a shear-out failure behindthe hole), not the serviceability bearing strength (often defined as the loadcausing an axial deformation equal to 4% of the hole diameter according toASTM 953).

The critical strength for tensile failure of the pultruded material in the netsection6 either in the longitudinal or transverse direction is given as

net-tens 0.9 or 0.9 (15.16)cr L,t T,t

The critical strength for shear failure (and shear-out failure) of the parts ofthe connection is the in-plane shear strength of the pultruded material, givenas

(15.17)cr LT

When block shear is a possible failure mode, the net tension and the shearstrength of the pultruded material are used together in a combined stressinteraction equation. Since both net tension and shear failure in pultrudedmaterials are considered brittle failure modes, a linear interaction is used. Thenominal tensile capacity, Pn, of the connection is given as

net-tensP A A (15.18)n cr tens LT shear

where, Atens is the area along the tensile failure path and Ashear is the areaalong the shear failure path.

The critical flexural stress for flexural failure of the leg of the web clipangle due to prying action is

flex or (15.19)cr L,flex T,flex

where L,flex and T,flex are the longitudinal and transverse flexural strength ofthe pultruded material. Flexural strengths are typically reported by manufac-turers separately from tensile and compressive strengths. It is important tonote that in the web clip angle configuration, the transverse flexural stresswill control, due to the orientation of the angle relative to the bending, asshown in Fig. 15.15.

The critical shear stress for the interlaminar shear failure of the leg of theweb clip angle due to prying action is

6 See the important discussion in Chapter 14 related to the strength reduction factor used in thenet-section equations.


(15.20)cr TT

where TT is the interlaminar shear strength of the pultruded material in theleg of the angle. This value is typically reported by manufacturers.

The critical shear strength of a bolt is the ultimate shear strength of thebolt (either steel or FRP),

b b (5.21)cr ult

The critical tensile strength of an FRP bolt (or threaded rod) is determinedby the maximum (bolt) tensile load (see Table 15.1, line 2) based on threadshear failure, Tmax, given as

Tmaxb (15.22)cr Ab

15.12 DESIGN PROCEDURE FOR A PULTRUDED CONNECTION

The design procedure presented in what follows for pultruded connectionspermits design only by the allowable stress design (ASD) basis, as discussedin Chapter 12. Connection design at this time consists of dimensioning theconnection using the recommended geometric parameters and then checkingthe stresses in the connected members, fasteners, and connection parts usingsimple calculations described previously in order to determine gusset plate orangle thicknesses and bolt sizes. For beam simple shear connections, the loadtables presented in manufacturers design guides can be used to estimate thesize or the connection, or its load-carrying capacity, if necessary, for thepurposes of a preliminary design.

Step 1. Determine the design loads and ASD factors. The tensile load for anin-plane connection (or parts of an out-of-plane connection) or the shearload for an out-of-plane connection is determined from the structural ge-ometry and loading. A safety factor of 4 is used for all strengths in theconnection parts.

Step 2. Select the connection parts and fasteners and a trial geometry. Esti-mate the number of bolts based on the total tensile or shear force to betransferred. Determine the connection part thicknesses based on the bearingstrength of the pultruded material. Using the geometric parameters, dimen-sion the connection.

Step 3. Determine the maximum design stresses. Determine the designstresses on the connected members, fasteners, and connection parts usingthe trial geometric parameters.

15.12 DESIGN PROCEDURE FOR A PULTRUDED CONNECTION 513

Step 4. Determine critical stresses. Determine the critical stresses for theconnected members, fasteners, and connection parts. It is important to iden-tify the load direction in the connection and use the appropriate strengthvalues based on the orientation of the material relative to the load direction.

Step 5. Determine the factored critical stresses. Divide the critical stressesdetermined in step 4 by the appropriate safety factor.

Step 6. Check the ultimate strength of the trial connection. Check that thedesign stresses are less than the allowable stresses. Return to step 2 if thetrail connection does not work.

Step 7. Dimension the connection and call out all the parts. Dimension (ordesign if quantitative procedures are available) all the connection parts andgeometries. Provide a sketch of the connection showing all orientations ofpultruded materials used for gusset plates or doubler plates.

Design Example 15.1: Pultruded Beam-to-Column Clip Angle Connec-tion Design a simple shear web double clip-angle connection for the beam-to-column connection for the floor system presented previously in the designexamples for the beam in Chapter 13 and the column in Chapter 14. Thefloor plan is shown in Fig. 13.13. The beam size was determined previouslyto be a wide-flange W 10 10 profile with material properties given in12Table 13.7. The column size was determined previously to be a W 8 8

profile with material properties given in Table 14.1. Pultruded material from38the same manufacturer as the beam section and shown in Table 15.4 is to beused for the clip angles. Note that flexural and bearing strength values havebeen added to the properties provided for the beam in Chapter 13. Designthe connection using FRP bolts and nuts with the properties shown in Table15.1.

SOLUTION

Step 1. Determine the design loads and ASD factors. The beam is simplysupported and the maximum shear force at the end of the beam is

wl 372(15)V 2790 lbmax 2 2

Since only ASD design is to be performed, no load factors are used. A safetyfactor of 4 is used for all strengths in the connection parts.

Step 2. Select the connection parts and fasteners and a trial geometry. Forpreliminary sizing, consider the bearing capacity of the beam web, clip angles,and column flanges. Since the beam web carries the same end shear with halfthe number of holes as the clip angles and the column flanges, the beam web


TABLE 15.4 Pultruded Material Properties in the Clip Angles

Symbol Description Valuea

cEL Longitudinal compressive modulus 2.6 106 psitEL Longitudinal tensile modulus 2.6 106 psicET Transverse compressive modulus 1.0 106 psitET Transverse tensile modulus 0.8 106 psi

GLT In-plane shear modulus NRvL Major (longitudinal) Poisson ratio 0.33L,c Longitudinal compressive strength 30,000 psiL,t Longitudinal tensile strength 30,000 psiL,flex Longitudinal flexural strength 30,000 psiL,br Longitudinal bearing strength 30,000 psiT,c Transverse compressive strength 16,000 psiT,t Transverse tensile strength 7,000 psiT,flex Transverse flexural strength 10,000 psiL,br Transverse bearing strength NRTT Interlaminar shear strength 4,500 psiLT In-plane shear strength NREb Full-section flexural modulus 2.5 106 psiGb Full-section shear modulus 0.425 106 psi

a NR, not reported.

will be the controlling part in the connection (assuming that the clip angleand the column flange thicknesses are at least half the thickness of the beamweb). In addition, the beam web is loaded transverse to its primary fiberorientation, and its transverse bearing strength properties will be key. Thecolumn flanges and the clip angles will be loaded in bearing in their longi-tudinal directions and will therefore have higher bearing strengths.

Since the beam web is loaded transverse to its primary fiber direction, thetransverse bearing strength of the web is needed for the calculation. Since themanufacturer does not report this value, the transverse compressive strength(16,000 psi) of the pultruded material is used in its place as a conservativeestimate. With an ASD safety factor of 4.0, the allowable bearing stress inthe web is taken as 4000 psi. For the -in.-thick web material, the required12number of bolts, n, is determined based on an assumed bolt diameter of in.34

V 2790 3n 1.9 try two -in. bolts4d t 0.75(0.50)(4,000)b pl br,allow

Detail the connection using the recommended geometric parameters presentedin Table 15.2, assuming that equal leg angles of the 4 4 tpl series areused (where tpl is to be determined in what follows). The recommended andminimum values for the -in.-diameter bolt are shown in Table 15.1.34


TABLE 15.5 Geometric Parameters for Example Connection

Spacings for 34-in. Bolt

Recommended Minimum

34-in. Bolt

Actual Selected(Controlling Element)

Enda distance to boltdiameter, e /db

e 2.25 in. 1.50 in. 2.5 in. (angle leg)

Plate width to boltdiameter, w /db

w 3.75 in. 2.25 in. 4.0 in. (angle leg)

Side distance to boltdiameter, s /db

s 1.5 in. 1.13 in. 1.5 in. (column flange)

Longitudinal spacing(pitch) to boltdiameter, p /db

p 3.0 in. 2.25 in. 3.0 in. (angle leg)

Transverse spacing(gauge) to boltdiameter, g /db

g 3.0 in. 2.25 in. NA

Bolt diameter toplate thickness,db / tpl

db 0.5 in. 0.25 in. 2.0 (column flange)

Washer diameter tobolt diameter,dw /db

dw 1.5 in. 1.5 in. use 1.5 in.

Hole size clearance,dh db

tight fit (0.05db) 1 /16 in.b use 1/16 in.

a Also called edge distance.b Maximum clearance.

A -in. clearance between the end of the beam and the column face is12typically used in construction. Therefore, a -in. thickness of the clip angle12is preferred and 8-in.-long 4 4 equal leg angles are chosen for this12connection. The connection is detailed using the recommended spacing shownin Table 15.5 for the -in. bolts. In addition, the actual spacings chosen for34the connection are also shown. It can be seen that these fall within the geo-metric ranges recommended. Note that the minimum values are not violated.Side and plan views of the selected connection geometry are shown in Figs.15.17 and 15.18.

Step 3. Determine the maximum design stresses.Bearing Stresses Bearing stresses are calculated in the beam web, clip

angles, and column flange. To calculate bearing stresses at the top bolt holeon the beam web, the additional bearing force at the hole due to the eccen-


3.0

2.5

2.5 WF 10 x 10 x 1/2

WF 8 x 8 x 3/8

L 4 x 4 x 1/2

2.4 1.6

Figure 15.17 Beam-to-column connection with clip angles: side view.

1.5

1.5

Figure 15.18 Beam-to-column connection with clip angles: top view.

tricity of the shear force is calculated. The moment due to the total shearforce eccentricity relative to the face of the column is

M Ve 2790(2.4) 6696 in.-lbv

The horizontal force (in the plane of the web) at the top bolt due to themoment is

My 6696(1.5)R 2232 lbx 22 2(1.5)d

The vertical force at the bolt due to the vertical shear force is


V 2790R 1395 lbv 2 2

The resulting force on the bolt is

2 2 2 2R R R (2232) (1395) 2632 lbb x v

and the bearing stress on the bolt hole in the beam web is

R 2632b 7018 psibr d t 0.75(0.5)b pl

If only the vertical shear is considered (i.e., eccentricity is not considered),the bearing stress at the bolt hole is

V 2790/2b 3720 psibr d t 0.75(0.5)b pl

Note that the resultant force acts at an angle to the horizontal of

1395 arctan 32

2232

Therefore, the resultant force does not act either parallel or perpendicular tothe major fiber (roving) direction in the web.

The bearing stresses in the angle legs will be half of those in the beamweb since the two angles share the load. The maximum bearing stress, in-cluding the effects of the shear force eccentricity, is

R /2 2632/2b 3590 psibr d t 0.75(0.5)b pl

The bearing stress on the top bolts of the angles assuming only the horizontalcomponent due to the eccentricity is

R /2 2232/2x 2976 psibr d t 0.75(0.5)b pl

Note that in this case the bearing forces are applied at an orthogonal orien-tation to the pultruded material axes of orthotropy as compared with the beamweb (i.e., the horizontal component produces bearing stress in the weak di-rection of the pultruded material in the clip angle).

The bearing stresses in the column flanges do not include effects of ec-centricity and are due only to the vertical shear transferred to the column


flanges by the clip angles. The bearing in this case is aligned with the lon-gitudinal material axis of the flange and is

V 2790/4b 2480 psibr d t 0.75(0.375)b pl

Shear stresses in the clip angles Shear in the angles can result in as shear-out at the bolt holes and longitudinal shear failure at the heel of the angle:

V 2790/2b 558 psishear-out 2t e 2(0.5)(2.5)pl

V 2790 349 psipl 2A 2(0.5)(8)heel

Flexural and shear stresses in the angles due to prying action It isassumed that the prying force is equal to the horizontal component of the boltforce, Rx 2232 lb. The flexural stress and shear stress due to prying arecalculated as

R(b t s) 2232(4.0 0.5 1.6)leg plm 530 in.-lbleg 8 8

R 2232v 1116 lbleg 2 2

m m 530leg leg 2544 psiflex 2 2S 2et /6 2(2.5)(0.5) /6pl

v v 1116leg leg 446 psileg A t 2e 0.5(2)(2.5)pl

It can be seen that the end distance, e, plays a part in decreasing the localbending and shear stresses due to prying action. Decreasing the end distancewill increase these stresses. As noted in the text and shown in Fig. 15.14, thefailure of clip angle connection usually initiates due to delamination at thetop of the clip angle due to these local stresses.

Transverse tensile stress at the webflange junction in the column Thetransverse tensile stress at the webflange junction is calculated as

R 2232 1488 psitrans t (l /2) 0.375(8/2)web angle

Note that in the case of a top and bottom seated connection, the tensile pryingforce on the column flange will be exerted on the column at the location of


the top bolt row in the top seat. If the connection develops moment resistance,this prying force can be large and the webflange junction is susceptible totransverse tensile failure, as noted in the text. The calculation presented aboveis highly approximate, and full-scale testing should be conducted if the con-nection is intended to carry moment. This is required to determine the failuremodes of the connection in addition to its rotational stiffness for semirigidframe analysis.

Shear and tensile stresses on the bolts The bolts are subjected to singleshear at the column flanges and double shear at the column web,

V 2790/4 698y b 2A (0.75) /4 0.44b

1586 psi (column flange: single shear, no eccentricity)

R 2632/2 1316 b 2A (0.75) /4 0.44b

2991 psi (beam web: double shear, with eccentricity)

Tensile stress on bolt due to prying action Assume that the two top boltsat the column flange carry all the prying force.

R 2230x 2534 psib 2A 2(0.44)b

Steps 46. Determine the critical stresses and factored critical stresses, andcheck the ultimate strength of the trial connection. Critical limit states, criticalstresses, safety factors, allowable stresses, and stresses calculated for the ac-tual connection geometry and loads are shown in Table 15.6. Comments toexplain the results are provided in the last column of the table.

Based on the data provided in Table 15.6, the connection design is acceptedbut with a recommendation to strengthen the web of the section in the con-nection region by bonding (in the shop) two-sided or -in.-thick plates of1 1 8 4pultruded material with their longitudinal directions perpendicular to the web.Plates measuring the size of the leg of the web clip angle should be used.This is a highly conservative approach but is recommended since the trans-verse bearing strength of the pultruded material is not reported and the bearingload is at an inclined angle to the hole.

Note that the most critical elements of the design are the bearing stressesin the web and the local bending and shear stresses in the angles. Also, notethat the safety factor of 4.0 that is used for all pultruded connection designsat this time reflects the uncertainty in the calculations and the material prop-erties when multiaxial complex stress states exist in pultruded parts.

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PROBLEMS 521

TABLE P15.1 Fasteners for Bolted Pultruded Connections

FRP a. Strongwell Fibrebolt Studb. Creative Pultrusions Superstud

Hot-dipped galvanized steel a. SAE grade 5b. SAE grade 8c. A307 grade Bd. A325 type 1

Stainless steel a. Type 316 SSb. Type 18-8c. Type 304 SS

Pultrusion manufacturers provide load tables for clip angle connections(like the one discussed in this design example) which are based on only threepossible failure modes of the connection: bearing at the fasteners (not ac-counting for eccentricity or orthotropic bearing properties of the pultrudedmaterial parts), longitudinal shear failure at the heel of the angle, and boltshear failure. Testing by researchers has demonstrated that many of theseconnections can safely carry the design loads published (Lopez-Anido et al.,1999; Mottram and Zheng, 1999a,b), although the failure modes do not agreewith the modes described above. In actual applications of beam-to-columnclip angles, manufacturers always recommend using adhesive bonding to-gether with bolting. This is primarily for serviceability of the structure as -116in. hole clearances are also recommended. Full-scale testing of pultrudedconnections is recommended for all nonstandard connections to understandfailure modes and connection behavior in the service load range. Full-scaletests are recommended for efficient connection design of pultruded structures.

PROBLEMS

15.1 For - and 1-in.-diameter FRP and steel bolts (or studs) listed in Table12P15.1, obtain the following properties from the manufacturer or stan-dards organizations specifications: (a) ultimate tensile capacity (andyield strength for steel); (b) ultimate shear capacity; (c) maximumbolt torque; (d) dimensions of the standard nut; (e) cost (assume a2.5-in.-long bolt.)

15.2 Pultruded plate (also called pultruded flat sheet or pultruded sheet) isproduced in thicknesses from to 1 in. Pultruded plates are often18used as gusset plates, bearing plates, and stiffeners in pultruded con-nections. Obtain the mechanical properties listed in Tables 13.7 and14.1 for - and -in.-thick glasspolyester and glassvinylester pul-1 3 4 4truded plates produced by (a) Strongwell, (b) Creative Pultrusions,and (c) Bedford Reinforced Plastics. List the percentage difference


between the property of the pultruded material in a typical profile(Table 13.7 or Table 14.1) and the property of the pultruded materialin the plate.

15.3 For the recommended spacing requirements for lap joints shown inTable 15.2, determine the maximum number of -in.-diameter bolts12that can be used in one row in the elements of the pultruded profileslisted below. Assume that the bolt row is perpendicular to the loaddirection, which is along the axis of the profile and in the longitudinaldirection of the part. Sketch, to scale, the element of the part andshow the geometry of the bolt holes.(a) The flange of a 8 8 -in. I-shaped section38(b) The flange of a 12 12 -in. I-shaped section12(c) The web of a 8 8 -in. I-shaped section38(d) The web of a 12 12 -in. I-shaped section12(e) One leg of a 6 pultruded angle38(f) A wall of a 6 -in. square tube14(g) A 18-in.-wide pultruded plate(h) The web of a 24 3 -in. channel section14

15.4 For the lap-joint connections listed in Problem 15.3, determine thenominal, Pn, and the design, Pu, in-plane tensile load that can becarried out by the element under consideration [assume that only theelement (e.g., flange, web) is effective in carrying the tensile load].Consider the failure modes shown in Fig. 15.11. [Do not considersplitting failure; splitting failure can occur in highly orthotropic (typ-ically, unidirectional) composite materials where the transverse tensilestrength is much lower than longitudinal strength, shear strength, andbearing strength and is unlikely to occur in conventional pultrudedcomposites.]

15.5 Redesign the web clip angle simple shear connection in Design Ex-ample 15.1 assuming that the beam is a 12 6 -in. narrow-flange12I-shaped section. Consider the typical conventional pultruded materialproperties given in Table 15.4. Design the connection using -in.-12diameter type 306 stainless steel bolts. Size the clip angle such thatthree bolts can be used to attach the angles to the beam web andcolumn flange. Use the same loading as in Design Example 15.1.

15.6 Redesign the web clip angle simple shear connection in Design Ex-ample 15.1 assuming that the beam is a W 10 5 -in. beam and12that it is connected to the web of the column instead of the flange(see Mottram and Zheng, 1999a for examples of these minor-axisweb-cleated simple shear connections). Consider the typical conven-tional pultruded material properties given in Table 15.4. Design the

PROBLEMS 523

connection using galvanized steel grade 5 bolts. Use the same loadingas in Design Example 15.1.

15.7 U.S. manufacturers (Strongwell and Creative Pultrusions) publishload tables for beam clip angle simple beam-to-column connections.List (from manufacturers design guides) the clip angle connectiondetails (bolt size, angle length, angle thickness) that are recommendedby manufacturers for the connection loads in Design Example 15.1.

15.8 Two 4 4 in. in. long pultruded angles (glassvinylester1 1 84 4material properties from (a) Strongwell and (b) Creative Pultrusions)are used in a clip angle connection to connect a beam to a column.Determine the maximum shear force that can be transferred by thisclip angle connection assuming three -in. steel bolts are used in each12leg of the connection. Assume that the connection is designed foronly (1) shear through the heel of the angles and (2) bearing at thebolt holes. Do not consider eccentricity. Assume a bolted-only con-nection and that the geometric spacing parameters (Table 15.2) aresatisfied for this connection.

15.9 A stick-built frame is constructed using 3 3 in. pultruded tubes14as the vertical members and 4 in. channel sections as the1 1 18 4horizontal members (see a schematic of this type of construction inFig. 15.4). Both vertical members (columns) and horizontal members(girts) are continuous. Two channels are attached on the opposite sidesof each tube, creating a lattice-type frame that is stabilized with di-agonal braces. A single -in. stainless steel through-bolt is used at58each overlap location. Determine the vertical force that can be trans-ferred from the horizontal member to the vertical member at eachoverlapping joint. If the columns are 6 ft apart, what transverse loadcan one of the channels carry, assuming a concentrated load at itsmidspan (based on the connection capacity only)?

15.10 Consider the braced frame connection detail shown in Fig. 15.7. As-sume that the beam and the column are both 8 8 in. pultruded12sections. Dimension the remaining parts of this connection using stan-dard pultruded parts (angles, channels, I-shaped sections) and locateall holes. Use Table 15.2 to dimension the hole locations in the pul-truded parts. Assume that the braces can carry both tension and com-pression. Provide a sketch, to scale, showing all the connection parts.Draw an exploded sketch of the connection and show the forces tobe transferred between the various parts in the connection. List anddiscuss all the possible failure modes of this connection, especiallyconsidering the fiber orientations in the various pultruded parts in theconnection. No calculations are required for this problem; only a qual-itative analysis is expected.


Braces overlap and are NOTconnected

8 8 in. columns (continuous at floors)

6 6 in. beams

Connection A

12

38

Figure P15.12

15.11 Design a double-clip-angle coped-beam shear connection for a 6 6 in. stringer that is connected to a 10 in. girder such that3 1 108 2the top surfaces of the top flanges are at the same elevation. Designthe connection for a 1200-lb shear force at the stringer end. Makesure to consider the block-shear failure mode in the web of thestringer. Use profiles with homogeneous glassvinylester pultrudedproperties (Table 13.7).

15.12 Consider the pultruded heavy-frame structure used in the design ex-amples in Chapters 13 and 14 with the floor plan shown in Fig. 13.13.In the direction of the 6-ft-wide bays, the lateral load in the three-story pultruded structure is carried by braced frames (9-ft-high storyheight) 6 ft wide by 27 ft high as shown in Fig. P15.12. At each floorlevel 6 6 in. stringers are used to frame between the columns.38(Note that the beams frame into the weak axis direction of the col-umns, as shown in Fig. 13.13.) Assume that columns are pinned attheir bases and that the vertical braced frame is subjected to a lateralload at each floor of 2000 lb. The lateral drift is limited to L /500.Design the braces assuming a lateral load from either direction. Usedouble angles for the braces (see Fig. 15.7 for a strong axis beamcolumn connection for this type of connection, and consult manufac-turer design guides for other possible configurations). Design thebolted connection between the bracing member and the columnbeamconnection area (connection A). Use recommended geometric con-nection limits to detail the brace connections. Account for the gravityloads on the columns, but do not redesign the columns for the addi-tional axial load that develops due to the lateral loads (however, this

SUGGESTED PULTRUDED STRUCTURE DESIGN PROJECTS 525

would need to be done in an actual design). Use the design basis ofyour choice.

SUGGESTED PULTRUDED STRUCTURE DESIGN PROJECTS

The following pultruded design projects are suggested for the students in acomposites for construction design class. The design project should preferablybe done in groups of two or three students. Students should be given 4 to 6weeks to compete the design project (which therefore needs to be assignedearly in the semester). The final deliverable should be a design proposal7 thatincludes the problem statement, scope, codes and specifications, loads, ma-terials, design calculations, design drawings, and a cost analysis. A presen-tation of the design proposal should be given in class. Invite owners anddesigners to form part of the project jury to obtain feedback from industryon the designs presented.

15.1 Pultruded light-truss pedestrian bridge. Design a truss bridge to re-place an existing pedestrian bridge using FRP pultruded materials. Stu-dents should scout the local area (campus, downtown, etc.) to find apedestrian bridge with a 30- to 70-ft span and use this bridge as thebasis for the design. Pay attention to details of connections and at-tachments to the foundation or abutment. Use the AASHTO GuideSpecification for Design of Pedestrian Bridges (1997) for loads anddynamic requirements.

15.2 Pultruded heavy-girder pedestrain bridge. Design a girder and stringerbridge to replace an existing pedestrian bridge using FRP pultrudedmaterials. Students should scout the local area (campus, downtown,etc.) to find a pedestrian bridge with a 20- to 40-ft span and use thisbridge as the basis for the design. Pay attention to details of connec-tions and attachments to the foundation or abutment. Consider usingbuilt-up beam members if conventional shapes do not work. Use theAASHTO Guide Specification for Design of Pedestrian Bridges (1997)for loads and dynamic requirements.

15.3 Pultruded highway sign bridge. Design a cantilever or a frame highwaysign bridge to replace an existing sign bridge using FRP pultrudedmaterials. Students should scout the local area (campus, downtown,etc.) and find either a cantilever sign bridge (typical arm of 20 ft) orframe sign bridge (typical span of 60 to 100 ft) and use this actualsign bridge as the basis for the design. Pay attention to details ofconnections and attachments to the foundation. Consider using built-

7 Items listed are at the discretion of the instructor.


up or latticed members if conventional shapes do not work. Considera truss bridge. Use the AASHTO Standard Specifications for StructuralSupports for Highway Signs, Luminaires and Traffic Signals (2001 andinterims) for loads and other design requirements.

15.4 Pultruded light-frame structure. Do a schematic design of a pultrudedlight frame structure to house a cooling tower system consisting of two18-ft-diameter fan units (see Fig. 1.16 for an example of this type ofstructure and visit the Cooling Tower Institute website (www.cti.org)for more information and links to company literature with more detailson these types of structures). The external dimensions of the structureare: 30 ft wide (5 bays at 6 ft), 48 ft long (8 bays at 6 ft), and the fandeck is 32 ft above the concrete mat foundation. The operating weightof each fan unit is 80,000 lb. Assume that the tower is to be constructedin an industrial park in rural Kansas. Design for a wind pressure of 30psf.

527

References

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(2002), Standard Specification for Highway Bridges, 17th ed., American As-sociation of State Highway and Transportation Officials, Washington, DC.

(2005), LRFD Bridge Design Specifications, 3rd ed., American Association ofState Highway and Transportation Officials, Washington, DC.

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