b'h j= depth of the joint member b j= thickness of the joint member I = moment of inertia of the joint member (equal to moment of inertia of the main member) L j= length of the joint member Since knee braces are only loaded axially, and assuming pin-pin connection at each end, and ignoring the weight of the members, the b jand h jof the joint member can be calculated using Equation 9.This simplification is not applied to the joint members at the top of the post and at the bottom of the rafter as these joint members require member-specific flexural stiffness to resist internal shear and bending forces.h j,knee brace= b j,knee brace= A j, knee brace[9] THE OFFICIAL NFBA MAGAZINE Figure 2:Knee brace with slip at all joints (left) and with an equivalent slip at one joint (right) continued from page: 17Table 1:Member properties b m h m E m&j I m&j (P/) slip (P/) m (P/) j A j L j b j h jin in lb/in 2 in 4 lb/in lb/in lb/in in 2 in in inPost 5.5 5.5 1200000 76.26 6050000 76137 0.381 6.0 0.008 49.0377107Rafter 1.5 7.25 1600000 47.63 2900000 75110 0.282 6.0 0.006 45.05Knee Brace @ Rafter 1.5 5.5 1600000 20.80 77107 2200000 74496 0.279 6.0 0.009 29.89Knee Brace @ Post 1.5 5.5 1600000 20.80 77107 2200000 74496 0.279 6.0 0.009 29.89RESEARCH & TECHNOLOGYKnee Brace (Eq) 1.5 5.5 1600000 20.80 25702 2200000 25406 0.095 6.0 0.002 51.18where,b = member thickness, h = member depth, E = elastic modulus, I = moment of inertia, A = cross section area, L = length of the joint member, P/ = axial stiffness, subscript "m" is for "main member" (post, knee brace, rafter), subscript "j" is for joint memberThe results of this comparative analysis are summarized in Table 2.The difference in frame displacement between The results of this comparative analysis are summarized in Table 2.The difference in frame displacement between the two the two modeling methods is less than 1%, while the difference between the no slip model and one-slip model varies modeling methods is less than 1%, while the difference between the no slip model and one-slip model varies from 7.6 to from 7.6 to 16.8%.Based on the results, it can be concluded that the performance of the one-joint model is 16.8%.Based on the results, it can be concluded that the performance of the one-joint model is equivalent to the performance equivalent to the performance of the three-joint model. of the three-joint model.Table 2: Eave deflection and percent slippage for different assumptions Eave Deflection Modeling MethodRoof Pitch Load onNoThree SlipOne Slip Joint One Slip vsOne Slip vs Frame Slip Joints No Slip Three Slip(lb) (in) (in) (in)0:12 100 2.680 2.883 2.902 7.6% 0.7%3:12 100 2.462 2.676 2.684 8.7% 0.3%6:12 100 2.114 2.333 2.335 10.4% 0.1%12:12 100 2.277 2.659 2.636 16.8% 0.8% Knee Braces in Buildings with Diaphragm Action posts to increased bending stresses due to the vertical To understand the effects of knee braces on a post-framedeflection of the trusses under gravity loads (dead, snow, Knee Braces in Buildings with Diaphragm Actionlive).To consider this effect, Building #4 (60x80x16) and building with diaphragm action, three buildings are analyzed,Building #5 (80x160x16) are added to this study.Both and the results compared. The buildings are identified as To understand the effects of knee braces on a post-frame building with diaphragm action, three buildings are #1, #2 and #3.All three buildings have the same size ofbuildings are analyzed using a common diaphragm with analyzed, and the results compared. The buildings are identified as #1, #2 and #3.The size of all the buildings is: 40x80x16, but have diaphragms with different effectiveeffective shear modulus, G eff , of 2,210 lb/in. With these two 40x80x16, but have diaphragms with different effective shear modulus, G eff .Building #1 represents a building with shear modulus, G eff .Building #1 represents a buildingadditional buildings, 15 separate designs are analyzed. The a relatively flexible diaphragm (G eff= 1,260 lb/in).Building #2 represents an average diaphragm stiffness commonly with a relatively flexible diaphragm (G eff= 1,260 lb/in).analyses compare how knee braces affect the following:used in post-frame buildings today (G eff= 2,210 lb/in).Building #3 has a stiff diaphragm because of using stitch Building #2 represents an average diaphragm stiffness screws at the seams of overlapping panels (G eff= 6,200 lb/in).Each of these three buildings is designed as follows: commonly used in post-frame buildings today (G eff= 2,210Lateral displacement of the building at the eave line(1) without knee braces, (2) with knee braces but no slip at the joints, and (3) with knee braces with slip at the joints, lb/in).Building #3 has a stiff diaphragm because of usingLoad demand on end walls (maximum internal shear which amounts to 9 separate designs.load in end walls)stitch screws at the seams of overlapping panels (G eff= Knee braces are known to be problematic in post-frame buildings with long-span trusses because they subject the 6,200 lb/in).Each of these three buildings is designedLoad demand on diaphragm (maximum internal posts to increased bending stresses due to the vertical deflection of the trusses under gravity loads (dead, snow, as follows: (1) without knee braces, (2) with knee bracesshear load in diaphragm)live).To consider this effect, Building #4 (60x80x16) and Building #5 (80x160x16) are added to this study.Both but no slip at the joints, and (3) with knee braces withLoad demand on the foundation (shear and moment buildings are analyzed using a common diaphragm with effective shear modulus, G eff , of 2,210 lb/in. With these two slip at the joints, which amounts to 9 separate designs.post reactions at grade)additional buildings, 15 separate designs are analyzed. The analyses compare how knee braces affect the following: Knee braces are known to be problematic in post-frameStress unities in posts (ratio of load demand to allowableLateral displacement of the building at the eave line buildings with long-span trusses because they subject thecapacity, combined axial and flexural loading) Load demand on end walls (maximum internal shear load in end walls)Load demand on diaphragm (maximum internal shear load in diaphragm) 18 / FRAME BUILDER - MAY2023 Load demand on the foundation (shear and moment post reactions at grade)Stress unities in posts (ratio of load demand to allowable capacity, combined axial and flexural loading) Member sizes and properties are given in Table 3. Table 3: Member properties'