Shelf Angle Design 31224p
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Shelf Angle Design Select Steel Angle Section:
Set Horizontal Leg:
37
2 4
Yield Strength of Steel Angle, Fy =
Weight/ft of Angle 23.6 lb/ft
36 ksi
Weight of Brick = 430 lb/ft Brick Thickness, t = 3.625 in Shelf Angle Spacing, S = 30 in 0.75 in Brick Overhang, c = Distance from bottom of angle to bolt centerline, d = 4 in
Strength Design: ASD Plate Bending of Horizontal Leg with the Critical Section at the Inside Face of the Vertical Eccentricity of the Load, Critical Moment in the Leg, Actual Bending Stress in the Leg, Allowable Bending Stress (0.6*Fy),
eb = 2.188 in Mb = 0.94 k*in/ft fb = 0.8 ksi Fb = 21.6 ksi
Plate Bending OK! Deflection Analysis: 0.0625 in Limit the total vertical deflection of the free end of the horizontal leg: Limit = The Total Vertical Deflection is the sum of two components: Cantilever Deflection and Torsional Rotation. The Cantilever Deflection is the vertical deflection of the tip of the leg, assuming the ed end is fixed. The Torsional Rotation component is the vertical deflection at the tip due to the rigid rotation of the section about its shear center due to the eccentricity of the load, calculated at midspan between s. Cantilever Deflection Dc =
a
P
0.0003 in
Dc=Pb2(3L-b)/6EI L
Rotational Deflection T= f= Dr =
Shear Center
0.067 k*in/in 0.00050 rad 0.0010 in
ft=uT(x)/JG dx
Total Deflection Dt =
0.0012 in
Design is OK Forces in the Bolt due to the Wall Load Shear: V = 1.08 kips Tension: Eccentricity from outside face of vertical leg to Wall Load = Total Gravity Moment per Bolt = Moment Arm (mid thickness of horizontal leg to centerline of bolt) = Pt=
2.9375 in 3.16 k*in 3.625 in 0.87 k
T(x) is the internal torque of the angle as a function of distance from the Integral is evaluated from x=0 to x=S/2 S = Distance between s
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
Shape L8x8x1.125 L8x8x1 L8x8x0.875 L8x8x0.75 L8x8x0.625 L8x8x0.5625 L8x8x0.5 L8x6x1 L8x6x0.875 L8x6x0.75 L8x6x0.625 L8x6x0.5625 L8x6x0.5 L8x6x0.4375 L8x4x1 L8x4x0.875 L8x4x0.75 L8x4x0.625 L8x4x0.5625 L8x4x0.5 L8x4x0.4375 L7x4x0.75 L7x4x0.625 L7x4x0.5 L7x4x0.4375 L7x4x0.375 L6x6x1 L6x6x0.875 L6x6x0.75 L6x6x0.625 L6x6x0.5625 L6x6x0.5 L6x6x0.4375 L6x6x0.375 L6x6x0.3125 L6x4x0.875 L6x4x0.75 L6x4x0.625 L6x4x0.5625 L6x4x0.5 L6x4x0.4375 L6x4x0.375 L6x4x0.3125 L6x3.5x0.5 L6x3.5x0.375 L6x3.5x0.3125 L5x5x0.875 L5x5x0.75 L5x5x0.625 L5x5x0.5
Designation L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L
Wgt (lbs/ft) 56.9 51 45 38.9 32.7 29.6 26.4 44.2 39.1 33.8 28.5 25.7 23 20.2 37.4 33.1 28.7 24.2 21.9 19.6 17.2 26.2 22.1 17.9 15.7 13.6 37.4 33.1 28.7 24.2 21.9 19.6 17.2 14.9 12.4 27.2 23.6 20 18.1 16.2 14.3 12.3 10.3 15.3 11.7 9.8 27.2 23.6 20 16.2
2
Area (in ) 16.7 15 13.2 11.4 9.61 8.68 7.75 13 11.5 9.94 8.36 7.56 6.75 5.93 11 9.73 8.44 7.11 6.43 5.75 5.06 7.69 6.48 5.25 4.62 3.98 11 9.73 8.44 7.11 6.43 5.75 5.06 4.36 3.65 7.98 6.94 5.86 5.31 4.75 4.18 3.61 3.03 4.5 3.42 2.87 7.98 6.94 5.86 4.75
Vert. Leg (in) 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 7 7 7 7 7 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 5 5 5 5
Thickness (in) 1.125 1 0.875 0.75 0.625 0.5625 0.5 1 0.875 0.75 0.625 0.5625 0.5 0.4375 1 0.875 0.75 0.625 0.5625 0.5 0.4375 0.75 0.625 0.5 0.4375 0.375 1 0.875 0.75 0.625 0.5625 0.5 0.4375 0.375 0.3125 0.875 0.75 0.625 0.5625 0.5 0.4375 0.375 0.3125 0.5 0.375 0.3125 0.875 0.75 0.625 0.5
51 L5x5x0.4375 52 L5x5x0.375 53 L5x5x0.3125 54 L5x3.5x0.75 55 L5x3.5x0.625 56 L5x3.5x0.5 57 L5x3.5x0.375 58 L5x3.5x0.3125 59 L5x3.5x0.25 60 L5x3x0.5 61 L5x3x0.4375 62 L5x3x0.375 63 L5x3x0.3125 64 L5x3x0.25 65 L4x4x0.75 66 L4x4x0.625 67 L4x4x0.5 68 L4x4x0.4375 69 L4x4x0.375 70 L4x4x0.3125 71 L4x4x0.25 72 L4x3.5x0.5 73 L4x3.5x0.375 74 L4x3.5x0.3125 75 L4x3.5x0.25 76 L4x3x0.625 77 L4x3x0.5 78 L4x3x0.4375 79 L4x3x0.375 80 L4x3x0.3125 81 L4x3x0.25 82 L3.5x3.5x0.5 83 L3.5x3.5x0.4375 84 L3.5x3.5x0.375 85 L3.5x3.5x0.3125 86 L3.5x3.5x0.25 87 L3.5x3x0.5 88 L3.5x3x0.375 89 L3.5x3x0.3125 90 L3.5x3x0.25 91 L3.5x2.5x0.5 92 L3.5x2.5x0.375 93 L3.5x2.5x0.25 94 L3x3x0.5 95 L3x3x0.4375 96 L3x3x0.375 97 L3x3x0.3125 98 L3x3x0.25 99 L3x3x0.1875 100 L3x2.5x0.5 101 L3x2.5x0.375 102 L3x2.5x0.3125
L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L
14.3 12.3 10.3 19.8 16.8 13.6 10.4 8.7 7 12.8 11.3 9.8 8.2 6.6 18.5 15.7 12.8 11.3 9.8 8.2 6.6 11.9 9.1 7.7 6.2 13.6 11.1 9.8 8.5 7.2 5.8 11.1 9.8 8.5 7.2 5.8 10.2 7.9 6.6 5.4 9.4 7.2 4.9 9.4 8.3 7.2 6.1 4.9 3.71 8.5 6.6 5.6
4.18 3.61 3.03 5.81 4.92 4 3.05 2.56 2.06 3.75 3.31 2.86 2.4 1.94 5.44 4.61 3.75 3.31 2.86 2.4 1.94 3.5 2.67 2.25 1.81 3.98 3.25 2.87 2.48 2.09 1.69 3.25 2.87 2.48 2.09 1.69 3 2.3 1.93 1.56 2.75 2.11 1.44 2.75 2.43 2.11 1.78 1.44 1.09 2.5 1.92 1.62
5 5 5 5 5 5 5 5 5 5 5 5 5 5 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3 3 3 3 3 3 3 3 3
0.4375 0.375 0.3125 0.75 0.625 0.5 0.375 0.3125 0.25 0.5 0.4375 0.375 0.3125 0.25 0.75 0.625 0.5 0.4375 0.375 0.3125 0.25 0.5 0.375 0.3125 0.25 0.625 0.5 0.4375 0.375 0.3125 0.25 0.5 0.4375 0.375 0.3125 0.25 0.5 0.375 0.3125 0.25 0.5 0.375 0.25 0.5 0.4375 0.375 0.3125 0.25 0.1875 0.5 0.375 0.3125
103 L3x2.5x0.25 104 L3x2.5x0.1875 105 L3x2x0.5 106 L3x2x0.375 107 L3x2x0.3125 108 L3x2x0.25 109 L3x2x0.1875 110 L2.5x2.5x0.5 111 L2.5x2.5x0.375 112 L2.5x2.5x0.3125 113 L2.5x2.5x0.25 114 L2.5x2.5x0.1875 115 L2.5x2x0.375 116 L2.5x2x0.3125 117 L2.5x2x0.25 118 L2.5x2x0.1875 119 L2x2x0.375 120 L2x2x0.3125 121 L2x2x0.25 122 L2x2x0.1875 123 L2x2x0.125 1 2 3
Long Leg Short Leg Equal Legs
L L L L L L L L L L L L L L L L L L L L L
4.5 3.39 7.7 5.9 5 4.1 3.07 7.7 5.9 5 4.1 3.07 5.3 4.5 3.62 2.75 4.7 3.92 3.19 2.44 1.65
1.31 0.996 2.25 1.73 1.46 1.19 0.902 2.25 1.73 1.46 1.19 0.902 1.55 1.31 1.06 0.809 1.36 1.15 0.938 0.715 0.484
3 3 3 3 3 3 3 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2 2 2 2 2
0.25 0.1875 0.5 0.375 0.3125 0.25 0.1875 0.5 0.375 0.3125 0.25 0.1875 0.375 0.3125 0.25 0.1875 0.375 0.3125 0.25 0.1875 0.125
Horz. Leg (in) 8 8 8 8 8 8 8 6 6 6 6 6 6 6 4 4 4 4 4 4 4 4 4 4 4 4 6 6 6 6 6 6 6 6 6 4 4 4 4 4 4 4 4 3.5 3.5 3.5 5 5 5 5
xb (in) 2.41 2.37 2.33 2.28 2.23 2.21 2.19 1.65 1.61 1.56 1.52 1.5 1.47 1.45 1.05 0.999 0.953 0.905 0.882 0.859 0.835 1.01 0.963 0.917 0.893 0.87 1.86 1.82 1.78 1.73 1.71 1.68 1.66 1.64 1.62 1.12 1.08 1.03 1.01 0.987 0.964 0.941 0.918 0.833 0.787 0.763 1.57 1.52 1.48 1.43
yb (in) 2.41 2.37 2.33 2.28 2.23 2.21 2.19 2.65 2.61 2.56 2.52 2.5 2.47 2.45 3.05 3 2.95 2.91 2.88 2.86 2.83 2.51 2.46 2.42 2.39 2.37 1.86 1.82 1.78 1.73 1.71 1.68 1.66 1.64 1.62 2.12 2.08 2.03 2.01 1.99 1.96 1.94 1.92 2.08 2.04 2.01 1.57 1.52 1.48 1.43
ry (2L-3/8) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ry (2L-3/4) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
rz (in) 1.56 1.56 1.57 1.58 1.58 1.59 1.59 1.28 1.28 1.29 1.29 1.3 1.3 1.31 0.846 0.848 0.852 0.857 0.861 0.865 0.869 0.86 0.865 0.872 0.875 0.88 1.17 1.17 1.17 1.18 1.18 1.18 1.19 1.19 1.2 0.857 0.86 0.864 0.866 0.87 0.873 0.877 0.882 0.759 0.767 0.772 0.973 0.975 0.978 0.983
5 5 5 3.5 3.5 3.5 3.5 3.5 3.5 3 3 3 3 3 4 4 4 4 4 4 4 3.5 3.5 3.5 3.5 3 3 3 3 3 3 3.5 3.5 3.5 3.5 3.5 3 3 3 3 2.5 2.5 2.5 3 3 3 3 3 3 2.5 2.5 2.5
1.41 1.39 1.37 0.996 0.951 0.906 0.861 0.838 0.814 0.75 0.727 0.704 0.681 0.657 1.27 1.23 1.18 1.16 1.14 1.12 1.09 1 0.955 0.932 0.909 0.871 0.827 0.804 0.782 0.759 0.736 1.06 1.04 1.01 0.99 0.968 0.875 0.83 0.808 0.785 0.705 0.66 0.614 0.932 0.91 0.888 0.865 0.842 0.82 0.75 0.706 0.683
1.41 1.39 1.37 1.75 1.7 1.66 1.61 1.59 1.56 1.75 1.73 1.7 1.68 1.66 1.27 1.23 1.18 1.16 1.14 1.12 1.09 1.25 1.21 1.18 1.16 1.37 1.33 1.3 1.28 1.26 1.24 1.06 1.04 1.01 0.99 0.968 1.13 1.08 1.06 1.04 1.2 1.16 1.11 0.932 0.91 0.888 0.865 0.842 0.82 1 0.956 0.933
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.986 0.99 0.994 0.748 0.751 0.755 0.762 0.766 0.77 0.648 0.651 0.654 0.658 0.663 0.778 0.779 0.782 0.785 0.788 0.791 0.795 0.722 0.727 0.73 0.734 0.637 0.639 0.641 0.644 0.647 0.651 0.683 0.684 0.687 0.69 0.694 0.621 0.625 0.627 0.631 0.534 0.537 0.544 0.584 0.585 0.587 0.589 0.592 0.596 0.52 0.522 0.525
2.5 2.5 2 2 2 2 2 2.5 2.5 2.5 2.5 2.5 2 2 2 2 2 2 2 2 2
0.661 0.638 0.583 0.539 0.516 0.493 0.47 0.806 0.762 0.74 0.717 0.694 0.581 0.559 0.537 0.514 0.636 0.614 0.592 0.569 0.546
0.911 0.888 1.08 1.04 1.02 0.993 0.97 0.806 0.762 0.74 0.717 0.694 0.831 0.809 0.787 0.764 0.636 0.614 0.592 0.569 0.546
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.528 0.533 0.428 0.43 0.432 0.435 0.439 0.487 0.487 0.489 0.491 0.495 0.42 0.422 0.424 0.427 0.389 0.39 0.391 0.394 0.398
Tensile Grp # 3 3 3 2 2 2 1 3 3 2 2 2 1 1 3 3 2 2 2 1 1 2 2 1 1 1 3 3 2 2 2 1 1 1 1 3 2 2 2 1 1 1 1 1 1 1 3 2 2 1
4
Ix (in ) 98 89 79.6 69.7 59.4 54.1 48.6 80.8 72.3 63.4 54.1 49.3 44.3 39.2 69.6 62.5 54.9 46.9 42.8 38.5 34.1 37.8 32.4 26.7 23.7 20.6 35.5 31.9 28.2 24.2 22.1 19.9 17.7 15.4 13 27.7 24.5 21.1 19.3 17.4 15.5 13.5 11.4 16.6 12.9 10.9 17.8 15.7 13.6 11.3
3
Sx (in ) 17.5 15.8 14 12.2 10.3 9.34 8.36 15.1 13.4 11.7 9.87 8.95 8.02 7.07 14.1 12.5 10.9 9.21 8.35 7.49 6.6 8.42 7.14 5.81 5.13 4.44 8.57 7.63 6.66 5.66 5.14 4.61 4.08 3.53 2.97 7.15 6.25 5.31 4.83 4.33 3.83 3.32 2.79 4.24 3.24 2.73 5.17 4.53 3.86 3.16
rx (in) 2.42 2.44 2.45 2.47 2.49 2.5 2.5 2.49 2.51 2.53 2.54 2.55 2.56 2.57 2.52 2.53 2.55 2.57 2.58 2.59 2.6 2.22 2.24 2.25 2.26 2.27 1.8 1.81 1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.86 1.88 1.9 1.9 1.91 1.92 1.93 1.94 1.92 1.94 1.95 1.49 1.51 1.52 1.54
4
Iy (in ) 98 89 79.6 69.7 59.4 54.1 48.6 38.8 34.9 30.7 26.3 24 21.7 19.3 11.6 10.5 9.36 8.1 7.43 6.74 6.02 9.05 7.84 6.53 5.83 5.1 35.5 31.9 28.2 24.2 22.1 19.9 17.7 15.4 13 9.75 8.68 7.52 6.91 6.27 5.6 4.9 4.18 4.25 3.34 2.85 17.8 15.7 13.6 11.3
3
Sy (in ) 17.5 15.8 14 12.2 10.3 9.34 8.36 8.92 7.94 6.92 5.88 5.34 4.79 4.23 3.94 3.51 3.07 2.62 2.38 2.15 1.9 3.03 2.58 2.12 1.88 1.63 8.57 7.63 6.66 5.66 5.14 4.61 4.08 3.53 2.97 3.39 2.97 2.54 2.31 2.08 1.85 1.6 1.35 1.59 1.23 1.04 5.17 4.53 3.86 3.16
1 1 1 2 2 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
10 8.74 7.42 13.9 12 9.99 7.78 6.6 5.39 9.45 8.43 7.37 6.26 5.11 7.67 6.66 5.56 4.97 4.36 3.71 3.04 5.32 4.18 3.56 2.91 6.03 5.05 4.52 3.96 3.38 2.77 3.64 3.26 2.87 2.45 2.01 3.45 2.72 2.33 1.91 3.24 2.56 1.8 2.22 1.99 1.76 1.51 1.24 0.962 2.08 1.66 1.42
2.79 2.42 2.04 4.28 3.65 2.99 2.29 1.94 1.57 2.91 2.58 2.24 1.89 1.53 2.81 2.4 1.97 1.75 1.52 1.29 1.05 1.94 1.49 1.26 1.03 2.3 1.89 1.68 1.46 1.23 1 1.49 1.32 1.15 0.976 0.794 1.45 1.13 0.954 0.776 1.41 1.09 0.755 1.07 0.954 0.833 0.707 0.577 0.441 1.04 0.81 0.688
1.55 1.56 1.57 1.55 1.56 1.58 1.6 1.61 1.62 1.59 1.6 1.61 1.61 1.62 1.19 1.2 1.22 1.23 1.23 1.24 1.25 1.23 1.25 1.26 1.27 1.23 1.25 1.25 1.26 1.27 1.28 1.06 1.07 1.07 1.08 1.09 1.07 1.09 1.1 1.11 1.09 1.1 1.12 0.898 0.905 0.913 0.922 0.93 0.939 0.913 0.928 0.937
10 8.74 7.42 5.55 4.83 4.05 3.18 2.72 2.23 2.58 2.32 2.04 1.75 1.44 7.67 6.66 5.56 4.97 4.36 3.71 3.04 3.79 2.95 2.55 2.09 2.87 2.42 2.18 1.92 1.65 1.36 3.64 3.26 2.87 2.45 2.01 2.33 1.85 1.58 1.3 1.36 1.09 0.777 2.22 1.99 1.76 1.51 1.24 0.962 1.3 1.04 0.898
2.79 2.42 2.04 2.22 1.9 1.56 1.21 1.02 0.83 1.15 1.02 0.888 0.753 0.614 2.81 2.4 1.97 1.75 1.52 1.29 1.05 1.52 1.16 0.994 0.808 1.35 1.12 0.992 0.866 0.734 0.599 1.49 1.32 1.15 0.976 0.794 1.1 0.851 0.722 0.589 0.76 0.592 0.412 1.07 0.954 0.833 0.707 0.577 0.441 0.744 0.581 0.494
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1.17 0.907 1.92 1.53 1.32 1.09 0.842 1.23 0.984 0.849 0.703 0.547 0.912 0.788 0.654 0.509 0.479 0.416 0.348 0.272 0.19
0.561 0.43 1 0.781 0.664 0.542 0.415 0.724 0.566 0.482 0.394 0.303 0.547 0.466 0.381 0.293 0.351 0.3 0.247 0.19 0.131
0.945 0.954 0.924 0.94 0.948 0.957 0.966 0.739 0.753 0.761 0.769 0.778 0.768 0.776 0.784 0.793 0.594 0.601 0.609 0.617 0.626
0.743 0.577 0.672 0.543 0.47 0.392 0.307 1.23 0.984 0.849 0.703 0.547 0.514 0.446 0.372 0.291 0.479 0.416 0.348 0.272 0.19
0.404 0.31 0.474 0.371 0.317 0.26 0.2 0.724 0.566 0.482 0.394 0.303 0.363 0.31 0.254 0.196 0.351 0.3 0.247 0.19 0.131
ry (in) 2.42 2.44 2.45 2.47 2.49 2.5 2.5 1.73 1.74 1.76 1.77 1.78 1.79 1.8 1.03 1.04 1.05 1.07 1.07 1.08 1.09 1.09 1.1 1.11 1.12 1.13 1.8 1.81 1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.17 0.972 0.988 0.996 1.49 1.51 1.52 1.54
3
Zx (in ) 31.6 28.5 25.3 22 18.6 16.8 15.1 27.3 24.2 21.1 17.9 16.2 14.5 12.8 24.3 21.6 18.9 16 14.5 13 11.5 14.8 12.6 10.3 9.09 7.87 15.5 13.8 12 10.2 9.26 8.31 7.34 6.35 5.35 12.7 11.2 9.51 8.66 7.78 6.88 5.97 5.03 7.5 5.76 4.85 9.33 8.16 6.95 5.68
3
Zy (in ) 31.6 28.5 25.3 22 18.6 16.8 15.1 16.2 14.4 12.5 10.5 9.52 8.51 7.5 7.72 6.77 5.81 4.86 4.38 3.9 3.42 5.65 4.74 3.83 3.37 2.9 15.5 13.8 12 10.2 9.26 8.31 7.34 6.35 5.35 6.31 5.47 4.62 4.19 3.75 3.3 2.85 2.4 2.91 2.2 1.85 9.33 8.16 6.95 5.68
4
J (in ) 7.13 5.08 3.46 2.21 1.3 0.96 0.682 4.35 2.96 1.9 1.12 0.822 0.584 0.396 3.68 2.48 1.61 0.933 0.704 0.501 0.328 1.47 0.873 0.459 0.3 0.2 3.68 2.51 1.61 0.954 0.704 0.501 0.34 0.218 0.129 2.07 1.33 0.792 0.585 0.417 0.284 0.183 0.108 0.396 0.174 0.103 2.07 1.33 0.792 0.417
Cw 32.5 23.4 16.1 10.4 6.16 4.55 3.23 16.3 11.3 7.28 4.33 3.2 2.28 1.55 12.9 8.89 5.75 3.42 2.53 1.8 1.22 3.97 2.37 1.25 0.85 0.54 9.24 6.41 4.17 2.5 1.85 1.32 0.9 0.58 0.34 4.04 2.64 1.59 1.18 0.84 0.58 0.37 0.22 0.78 0.34 0.2 3.53 2.32 1.4 0.74
ro (2L-3/8) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1.55 1.56 1.57 0.977 0.991 1.01 1.02 1.03 1.04 0.829 0.837 0.845 0.853 0.861 1.19 1.2 1.22 1.23 1.23 1.24 1.25 1.04 1.06 1.07 1.07 0.849 0.864 0.871 0.879 0.887 0.896 1.06 1.07 1.07 1.08 1.09 0.881 0.897 0.905 0.914 0.704 0.719 0.735 0.898 0.905 0.913 0.922 0.93 0.939 0.722 0.736 0.744
5.03 4.36 3.68 7.65 6.55 5.38 4.14 3.49 2.83 5.16 4.57 3.97 3.36 2.72 5.07 4.33 3.56 3.16 2.74 2.32 1.88 3.5 2.71 2.29 1.86 4.12 3.41 3.03 2.64 2.23 1.82 2.68 2.38 2.08 1.76 1.43 2.63 2.04 1.73 1.41 2.53 1.97 1.36 1.93 1.72 1.5 1.27 1.04 0.794 1.88 1.47 1.25
5.03 4.36 3.68 4.1 3.47 2.83 2.16 1.82 1.47 2.11 1.86 1.6 1.35 1.09 5.07 4.33 3.56 3.16 2.74 2.32 1.88 2.73 2.11 1.78 1.44 2.48 2.03 1.79 1.56 1.31 1.06 2.68 2.38 2.08 1.76 1.43 1.98 1.53 1.3 1.05 1.4 1.07 0.735 1.93 1.72 1.5 1.27 1.04 0.794 1.35 1.05 0.889
0.284 0.183 0.108 1.11 0.66 0.348 0.153 0.091 0.048 0.322 0.219 0.141 0.083 0.044 1.02 0.61 0.322 0.219 0.141 0.083 0.044 0.301 0.132 0.078 0.041 0.529 0.281 0.192 0.123 0.073 0.039 0.281 0.192 0.123 0.073 0.039 0.26 0.114 0.068 0.036 0.234 0.103 0.032 0.234 0.16 0.103 0.061 0.032 0.014 0.213 0.094 0.056
0.51 0.33 0.19 1.52 0.92 0.49 0.22 0.13 0.07 0.44 0.3 0.2 0.12 0.06 1.12 0.68 0.37 0.25 0.16 0.1 0.05 0.3 0.13 0.08 0.04 0.47 0.26 0.18 0.11 0.07 0.04 0.24 0.16 0.11 0.06 0.03 0.19 0.09 0.05 0.03 0.16 0.07 0.02 0.14 0.1 0.07 0.04 0.02 0.01 0.11 0.05 0.03
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.753 0.761 0.546 0.559 0.567 0.574 0.583 0.739 0.753 0.761 0.769 0.778 0.577 0.584 0.592 0.6 0.594 0.601 0.609 0.617 0.626
1.02 0.781 1.78 1.4 1.19 0.973 0.746 1.31 1.02 0.869 0.711 0.545 0.986 0.843 0.691 0.532 0.633 0.541 0.445 0.343 0.235
0.724 0.553 0.891 0.684 0.577 0.468 0.357 1.31 1.02 0.869 0.711 0.545 0.66 0.561 0.457 0.35 0.633 0.541 0.445 0.343 0.235
0.03 0.013 0.192 0.086 0.051 0.027 0.012 0.185 0.082 0.048 0.025 0.011 0.073 0.043 0.023 0.01 0.064 0.038 0.02 0.009 0.003
0.02 0.01 0.09 0.04 0.02 0.01 0.01 0.08 0.04 0.02 0.01 0.01 0.03 0.02 0.01 0 0.02 0.01 0.01 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
H (2L-3/8) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ro (2L-3/4) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
H (2L-3/4) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ro 4.31 4.35 4.37 4.41 4.45 4.47 4.48 3.89 3.93 3.96 3.99 4.01 4.02 4.04 3.77 3.79 3.82 3.85 3.86 3.88 3.89 3.33 3.36 3.38 3.4 3.42 3.19 3.22 3.26 3.29 3.31 3.32 3.34 3.36 3.38 2.83 2.86 2.89 2.9 2.92 2.94 2.96 2.97 2.88 2.92 2.93 2.65 2.68 2.71 2.74
H 0.632 0.63 0.629 0.627 0.627 0.627 0.624 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.637 0.632 0.629 0.628 0.627 0.627 0.627 0.626 0.625 0 0 0 0 0 0 0 0 0 0 0 0.634 0.634 0.63 0.63
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2.77 2.79 2.81 2.37 2.4 2.44 2.47 2.49 2.5 2.39 2.41 2.42 2.43 2.45 2.11 2.14 2.17 2.19 2.2 2.22 2.23 2.04 2.08 2.09 2.11 1.91 1.95 1.96 1.98 2 2.01 1.89 1.91 1.91 1.93 1.95 1.76 1.79 1.81 1.83 1.67 1.7 1.73 1.6 1.61 1.63 1.65 1.66 1.68 1.47 1.5 1.52
0.629 0.627 0.626 0 0 0 0 0 0 0 0 0 0 0 0.639 0.631 0.632 0.631 0.625 0.623 0.627 0 0 0 0 0 0 0 0 0 0 0.631 0.629 0.628 0.627 0.626 0 0 0 0 0 0 0 0.634 0.632 0.629 0.628 0.627 0.626 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1.54 1.55 1.4 1.43 1.45 1.46 1.48 1.31 1.34 1.36 1.37 1.39 1.22 1.24 1.25 1.27 1.05 1.07 1.09 1.1 1.12
0 0 0 0 0 0 0 0.639 0.632 0.63 0.628 0.627 0 0 0 0 0.637 0.633 0.63 0.628 0.626
Set Horizontal Leg:
37
2 4
Yield Strength of Steel Angle, Fy =
Weight/ft of Angle 23.6 lb/ft
36 ksi
Weight of Brick = 430 lb/ft Brick Thickness, t = 3.625 in Shelf Angle Spacing, S = 30 in 0.75 in Brick Overhang, c = Distance from bottom of angle to bolt centerline, d = 4 in
Strength Design: ASD Plate Bending of Horizontal Leg with the Critical Section at the Inside Face of the Vertical Eccentricity of the Load, Critical Moment in the Leg, Actual Bending Stress in the Leg, Allowable Bending Stress (0.6*Fy),
eb = 2.188 in Mb = 0.94 k*in/ft fb = 0.8 ksi Fb = 21.6 ksi
Plate Bending OK! Deflection Analysis: 0.0625 in Limit the total vertical deflection of the free end of the horizontal leg: Limit = The Total Vertical Deflection is the sum of two components: Cantilever Deflection and Torsional Rotation. The Cantilever Deflection is the vertical deflection of the tip of the leg, assuming the ed end is fixed. The Torsional Rotation component is the vertical deflection at the tip due to the rigid rotation of the section about its shear center due to the eccentricity of the load, calculated at midspan between s. Cantilever Deflection Dc =
a
P
0.0003 in
Dc=Pb2(3L-b)/6EI L
Rotational Deflection T= f= Dr =
Shear Center
0.067 k*in/in 0.00050 rad 0.0010 in
ft=uT(x)/JG dx
Total Deflection Dt =
0.0012 in
Design is OK Forces in the Bolt due to the Wall Load Shear: V = 1.08 kips Tension: Eccentricity from outside face of vertical leg to Wall Load = Total Gravity Moment per Bolt = Moment Arm (mid thickness of horizontal leg to centerline of bolt) = Pt=
2.9375 in 3.16 k*in 3.625 in 0.87 k
T(x) is the internal torque of the angle as a function of distance from the Integral is evaluated from x=0 to x=S/2 S = Distance between s
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
Shape L8x8x1.125 L8x8x1 L8x8x0.875 L8x8x0.75 L8x8x0.625 L8x8x0.5625 L8x8x0.5 L8x6x1 L8x6x0.875 L8x6x0.75 L8x6x0.625 L8x6x0.5625 L8x6x0.5 L8x6x0.4375 L8x4x1 L8x4x0.875 L8x4x0.75 L8x4x0.625 L8x4x0.5625 L8x4x0.5 L8x4x0.4375 L7x4x0.75 L7x4x0.625 L7x4x0.5 L7x4x0.4375 L7x4x0.375 L6x6x1 L6x6x0.875 L6x6x0.75 L6x6x0.625 L6x6x0.5625 L6x6x0.5 L6x6x0.4375 L6x6x0.375 L6x6x0.3125 L6x4x0.875 L6x4x0.75 L6x4x0.625 L6x4x0.5625 L6x4x0.5 L6x4x0.4375 L6x4x0.375 L6x4x0.3125 L6x3.5x0.5 L6x3.5x0.375 L6x3.5x0.3125 L5x5x0.875 L5x5x0.75 L5x5x0.625 L5x5x0.5
Designation L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L
Wgt (lbs/ft) 56.9 51 45 38.9 32.7 29.6 26.4 44.2 39.1 33.8 28.5 25.7 23 20.2 37.4 33.1 28.7 24.2 21.9 19.6 17.2 26.2 22.1 17.9 15.7 13.6 37.4 33.1 28.7 24.2 21.9 19.6 17.2 14.9 12.4 27.2 23.6 20 18.1 16.2 14.3 12.3 10.3 15.3 11.7 9.8 27.2 23.6 20 16.2
2
Area (in ) 16.7 15 13.2 11.4 9.61 8.68 7.75 13 11.5 9.94 8.36 7.56 6.75 5.93 11 9.73 8.44 7.11 6.43 5.75 5.06 7.69 6.48 5.25 4.62 3.98 11 9.73 8.44 7.11 6.43 5.75 5.06 4.36 3.65 7.98 6.94 5.86 5.31 4.75 4.18 3.61 3.03 4.5 3.42 2.87 7.98 6.94 5.86 4.75
Vert. Leg (in) 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 7 7 7 7 7 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 5 5 5 5
Thickness (in) 1.125 1 0.875 0.75 0.625 0.5625 0.5 1 0.875 0.75 0.625 0.5625 0.5 0.4375 1 0.875 0.75 0.625 0.5625 0.5 0.4375 0.75 0.625 0.5 0.4375 0.375 1 0.875 0.75 0.625 0.5625 0.5 0.4375 0.375 0.3125 0.875 0.75 0.625 0.5625 0.5 0.4375 0.375 0.3125 0.5 0.375 0.3125 0.875 0.75 0.625 0.5
51 L5x5x0.4375 52 L5x5x0.375 53 L5x5x0.3125 54 L5x3.5x0.75 55 L5x3.5x0.625 56 L5x3.5x0.5 57 L5x3.5x0.375 58 L5x3.5x0.3125 59 L5x3.5x0.25 60 L5x3x0.5 61 L5x3x0.4375 62 L5x3x0.375 63 L5x3x0.3125 64 L5x3x0.25 65 L4x4x0.75 66 L4x4x0.625 67 L4x4x0.5 68 L4x4x0.4375 69 L4x4x0.375 70 L4x4x0.3125 71 L4x4x0.25 72 L4x3.5x0.5 73 L4x3.5x0.375 74 L4x3.5x0.3125 75 L4x3.5x0.25 76 L4x3x0.625 77 L4x3x0.5 78 L4x3x0.4375 79 L4x3x0.375 80 L4x3x0.3125 81 L4x3x0.25 82 L3.5x3.5x0.5 83 L3.5x3.5x0.4375 84 L3.5x3.5x0.375 85 L3.5x3.5x0.3125 86 L3.5x3.5x0.25 87 L3.5x3x0.5 88 L3.5x3x0.375 89 L3.5x3x0.3125 90 L3.5x3x0.25 91 L3.5x2.5x0.5 92 L3.5x2.5x0.375 93 L3.5x2.5x0.25 94 L3x3x0.5 95 L3x3x0.4375 96 L3x3x0.375 97 L3x3x0.3125 98 L3x3x0.25 99 L3x3x0.1875 100 L3x2.5x0.5 101 L3x2.5x0.375 102 L3x2.5x0.3125
L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L
14.3 12.3 10.3 19.8 16.8 13.6 10.4 8.7 7 12.8 11.3 9.8 8.2 6.6 18.5 15.7 12.8 11.3 9.8 8.2 6.6 11.9 9.1 7.7 6.2 13.6 11.1 9.8 8.5 7.2 5.8 11.1 9.8 8.5 7.2 5.8 10.2 7.9 6.6 5.4 9.4 7.2 4.9 9.4 8.3 7.2 6.1 4.9 3.71 8.5 6.6 5.6
4.18 3.61 3.03 5.81 4.92 4 3.05 2.56 2.06 3.75 3.31 2.86 2.4 1.94 5.44 4.61 3.75 3.31 2.86 2.4 1.94 3.5 2.67 2.25 1.81 3.98 3.25 2.87 2.48 2.09 1.69 3.25 2.87 2.48 2.09 1.69 3 2.3 1.93 1.56 2.75 2.11 1.44 2.75 2.43 2.11 1.78 1.44 1.09 2.5 1.92 1.62
5 5 5 5 5 5 5 5 5 5 5 5 5 5 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3 3 3 3 3 3 3 3 3
0.4375 0.375 0.3125 0.75 0.625 0.5 0.375 0.3125 0.25 0.5 0.4375 0.375 0.3125 0.25 0.75 0.625 0.5 0.4375 0.375 0.3125 0.25 0.5 0.375 0.3125 0.25 0.625 0.5 0.4375 0.375 0.3125 0.25 0.5 0.4375 0.375 0.3125 0.25 0.5 0.375 0.3125 0.25 0.5 0.375 0.25 0.5 0.4375 0.375 0.3125 0.25 0.1875 0.5 0.375 0.3125
103 L3x2.5x0.25 104 L3x2.5x0.1875 105 L3x2x0.5 106 L3x2x0.375 107 L3x2x0.3125 108 L3x2x0.25 109 L3x2x0.1875 110 L2.5x2.5x0.5 111 L2.5x2.5x0.375 112 L2.5x2.5x0.3125 113 L2.5x2.5x0.25 114 L2.5x2.5x0.1875 115 L2.5x2x0.375 116 L2.5x2x0.3125 117 L2.5x2x0.25 118 L2.5x2x0.1875 119 L2x2x0.375 120 L2x2x0.3125 121 L2x2x0.25 122 L2x2x0.1875 123 L2x2x0.125 1 2 3
Long Leg Short Leg Equal Legs
L L L L L L L L L L L L L L L L L L L L L
4.5 3.39 7.7 5.9 5 4.1 3.07 7.7 5.9 5 4.1 3.07 5.3 4.5 3.62 2.75 4.7 3.92 3.19 2.44 1.65
1.31 0.996 2.25 1.73 1.46 1.19 0.902 2.25 1.73 1.46 1.19 0.902 1.55 1.31 1.06 0.809 1.36 1.15 0.938 0.715 0.484
3 3 3 3 3 3 3 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2 2 2 2 2
0.25 0.1875 0.5 0.375 0.3125 0.25 0.1875 0.5 0.375 0.3125 0.25 0.1875 0.375 0.3125 0.25 0.1875 0.375 0.3125 0.25 0.1875 0.125
Horz. Leg (in) 8 8 8 8 8 8 8 6 6 6 6 6 6 6 4 4 4 4 4 4 4 4 4 4 4 4 6 6 6 6 6 6 6 6 6 4 4 4 4 4 4 4 4 3.5 3.5 3.5 5 5 5 5
xb (in) 2.41 2.37 2.33 2.28 2.23 2.21 2.19 1.65 1.61 1.56 1.52 1.5 1.47 1.45 1.05 0.999 0.953 0.905 0.882 0.859 0.835 1.01 0.963 0.917 0.893 0.87 1.86 1.82 1.78 1.73 1.71 1.68 1.66 1.64 1.62 1.12 1.08 1.03 1.01 0.987 0.964 0.941 0.918 0.833 0.787 0.763 1.57 1.52 1.48 1.43
yb (in) 2.41 2.37 2.33 2.28 2.23 2.21 2.19 2.65 2.61 2.56 2.52 2.5 2.47 2.45 3.05 3 2.95 2.91 2.88 2.86 2.83 2.51 2.46 2.42 2.39 2.37 1.86 1.82 1.78 1.73 1.71 1.68 1.66 1.64 1.62 2.12 2.08 2.03 2.01 1.99 1.96 1.94 1.92 2.08 2.04 2.01 1.57 1.52 1.48 1.43
ry (2L-3/8) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ry (2L-3/4) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
rz (in) 1.56 1.56 1.57 1.58 1.58 1.59 1.59 1.28 1.28 1.29 1.29 1.3 1.3 1.31 0.846 0.848 0.852 0.857 0.861 0.865 0.869 0.86 0.865 0.872 0.875 0.88 1.17 1.17 1.17 1.18 1.18 1.18 1.19 1.19 1.2 0.857 0.86 0.864 0.866 0.87 0.873 0.877 0.882 0.759 0.767 0.772 0.973 0.975 0.978 0.983
5 5 5 3.5 3.5 3.5 3.5 3.5 3.5 3 3 3 3 3 4 4 4 4 4 4 4 3.5 3.5 3.5 3.5 3 3 3 3 3 3 3.5 3.5 3.5 3.5 3.5 3 3 3 3 2.5 2.5 2.5 3 3 3 3 3 3 2.5 2.5 2.5
1.41 1.39 1.37 0.996 0.951 0.906 0.861 0.838 0.814 0.75 0.727 0.704 0.681 0.657 1.27 1.23 1.18 1.16 1.14 1.12 1.09 1 0.955 0.932 0.909 0.871 0.827 0.804 0.782 0.759 0.736 1.06 1.04 1.01 0.99 0.968 0.875 0.83 0.808 0.785 0.705 0.66 0.614 0.932 0.91 0.888 0.865 0.842 0.82 0.75 0.706 0.683
1.41 1.39 1.37 1.75 1.7 1.66 1.61 1.59 1.56 1.75 1.73 1.7 1.68 1.66 1.27 1.23 1.18 1.16 1.14 1.12 1.09 1.25 1.21 1.18 1.16 1.37 1.33 1.3 1.28 1.26 1.24 1.06 1.04 1.01 0.99 0.968 1.13 1.08 1.06 1.04 1.2 1.16 1.11 0.932 0.91 0.888 0.865 0.842 0.82 1 0.956 0.933
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.986 0.99 0.994 0.748 0.751 0.755 0.762 0.766 0.77 0.648 0.651 0.654 0.658 0.663 0.778 0.779 0.782 0.785 0.788 0.791 0.795 0.722 0.727 0.73 0.734 0.637 0.639 0.641 0.644 0.647 0.651 0.683 0.684 0.687 0.69 0.694 0.621 0.625 0.627 0.631 0.534 0.537 0.544 0.584 0.585 0.587 0.589 0.592 0.596 0.52 0.522 0.525
2.5 2.5 2 2 2 2 2 2.5 2.5 2.5 2.5 2.5 2 2 2 2 2 2 2 2 2
0.661 0.638 0.583 0.539 0.516 0.493 0.47 0.806 0.762 0.74 0.717 0.694 0.581 0.559 0.537 0.514 0.636 0.614 0.592 0.569 0.546
0.911 0.888 1.08 1.04 1.02 0.993 0.97 0.806 0.762 0.74 0.717 0.694 0.831 0.809 0.787 0.764 0.636 0.614 0.592 0.569 0.546
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.528 0.533 0.428 0.43 0.432 0.435 0.439 0.487 0.487 0.489 0.491 0.495 0.42 0.422 0.424 0.427 0.389 0.39 0.391 0.394 0.398
Tensile Grp # 3 3 3 2 2 2 1 3 3 2 2 2 1 1 3 3 2 2 2 1 1 2 2 1 1 1 3 3 2 2 2 1 1 1 1 3 2 2 2 1 1 1 1 1 1 1 3 2 2 1
4
Ix (in ) 98 89 79.6 69.7 59.4 54.1 48.6 80.8 72.3 63.4 54.1 49.3 44.3 39.2 69.6 62.5 54.9 46.9 42.8 38.5 34.1 37.8 32.4 26.7 23.7 20.6 35.5 31.9 28.2 24.2 22.1 19.9 17.7 15.4 13 27.7 24.5 21.1 19.3 17.4 15.5 13.5 11.4 16.6 12.9 10.9 17.8 15.7 13.6 11.3
3
Sx (in ) 17.5 15.8 14 12.2 10.3 9.34 8.36 15.1 13.4 11.7 9.87 8.95 8.02 7.07 14.1 12.5 10.9 9.21 8.35 7.49 6.6 8.42 7.14 5.81 5.13 4.44 8.57 7.63 6.66 5.66 5.14 4.61 4.08 3.53 2.97 7.15 6.25 5.31 4.83 4.33 3.83 3.32 2.79 4.24 3.24 2.73 5.17 4.53 3.86 3.16
rx (in) 2.42 2.44 2.45 2.47 2.49 2.5 2.5 2.49 2.51 2.53 2.54 2.55 2.56 2.57 2.52 2.53 2.55 2.57 2.58 2.59 2.6 2.22 2.24 2.25 2.26 2.27 1.8 1.81 1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.86 1.88 1.9 1.9 1.91 1.92 1.93 1.94 1.92 1.94 1.95 1.49 1.51 1.52 1.54
4
Iy (in ) 98 89 79.6 69.7 59.4 54.1 48.6 38.8 34.9 30.7 26.3 24 21.7 19.3 11.6 10.5 9.36 8.1 7.43 6.74 6.02 9.05 7.84 6.53 5.83 5.1 35.5 31.9 28.2 24.2 22.1 19.9 17.7 15.4 13 9.75 8.68 7.52 6.91 6.27 5.6 4.9 4.18 4.25 3.34 2.85 17.8 15.7 13.6 11.3
3
Sy (in ) 17.5 15.8 14 12.2 10.3 9.34 8.36 8.92 7.94 6.92 5.88 5.34 4.79 4.23 3.94 3.51 3.07 2.62 2.38 2.15 1.9 3.03 2.58 2.12 1.88 1.63 8.57 7.63 6.66 5.66 5.14 4.61 4.08 3.53 2.97 3.39 2.97 2.54 2.31 2.08 1.85 1.6 1.35 1.59 1.23 1.04 5.17 4.53 3.86 3.16
1 1 1 2 2 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
10 8.74 7.42 13.9 12 9.99 7.78 6.6 5.39 9.45 8.43 7.37 6.26 5.11 7.67 6.66 5.56 4.97 4.36 3.71 3.04 5.32 4.18 3.56 2.91 6.03 5.05 4.52 3.96 3.38 2.77 3.64 3.26 2.87 2.45 2.01 3.45 2.72 2.33 1.91 3.24 2.56 1.8 2.22 1.99 1.76 1.51 1.24 0.962 2.08 1.66 1.42
2.79 2.42 2.04 4.28 3.65 2.99 2.29 1.94 1.57 2.91 2.58 2.24 1.89 1.53 2.81 2.4 1.97 1.75 1.52 1.29 1.05 1.94 1.49 1.26 1.03 2.3 1.89 1.68 1.46 1.23 1 1.49 1.32 1.15 0.976 0.794 1.45 1.13 0.954 0.776 1.41 1.09 0.755 1.07 0.954 0.833 0.707 0.577 0.441 1.04 0.81 0.688
1.55 1.56 1.57 1.55 1.56 1.58 1.6 1.61 1.62 1.59 1.6 1.61 1.61 1.62 1.19 1.2 1.22 1.23 1.23 1.24 1.25 1.23 1.25 1.26 1.27 1.23 1.25 1.25 1.26 1.27 1.28 1.06 1.07 1.07 1.08 1.09 1.07 1.09 1.1 1.11 1.09 1.1 1.12 0.898 0.905 0.913 0.922 0.93 0.939 0.913 0.928 0.937
10 8.74 7.42 5.55 4.83 4.05 3.18 2.72 2.23 2.58 2.32 2.04 1.75 1.44 7.67 6.66 5.56 4.97 4.36 3.71 3.04 3.79 2.95 2.55 2.09 2.87 2.42 2.18 1.92 1.65 1.36 3.64 3.26 2.87 2.45 2.01 2.33 1.85 1.58 1.3 1.36 1.09 0.777 2.22 1.99 1.76 1.51 1.24 0.962 1.3 1.04 0.898
2.79 2.42 2.04 2.22 1.9 1.56 1.21 1.02 0.83 1.15 1.02 0.888 0.753 0.614 2.81 2.4 1.97 1.75 1.52 1.29 1.05 1.52 1.16 0.994 0.808 1.35 1.12 0.992 0.866 0.734 0.599 1.49 1.32 1.15 0.976 0.794 1.1 0.851 0.722 0.589 0.76 0.592 0.412 1.07 0.954 0.833 0.707 0.577 0.441 0.744 0.581 0.494
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1.17 0.907 1.92 1.53 1.32 1.09 0.842 1.23 0.984 0.849 0.703 0.547 0.912 0.788 0.654 0.509 0.479 0.416 0.348 0.272 0.19
0.561 0.43 1 0.781 0.664 0.542 0.415 0.724 0.566 0.482 0.394 0.303 0.547 0.466 0.381 0.293 0.351 0.3 0.247 0.19 0.131
0.945 0.954 0.924 0.94 0.948 0.957 0.966 0.739 0.753 0.761 0.769 0.778 0.768 0.776 0.784 0.793 0.594 0.601 0.609 0.617 0.626
0.743 0.577 0.672 0.543 0.47 0.392 0.307 1.23 0.984 0.849 0.703 0.547 0.514 0.446 0.372 0.291 0.479 0.416 0.348 0.272 0.19
0.404 0.31 0.474 0.371 0.317 0.26 0.2 0.724 0.566 0.482 0.394 0.303 0.363 0.31 0.254 0.196 0.351 0.3 0.247 0.19 0.131
ry (in) 2.42 2.44 2.45 2.47 2.49 2.5 2.5 1.73 1.74 1.76 1.77 1.78 1.79 1.8 1.03 1.04 1.05 1.07 1.07 1.08 1.09 1.09 1.1 1.11 1.12 1.13 1.8 1.81 1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.17 0.972 0.988 0.996 1.49 1.51 1.52 1.54
3
Zx (in ) 31.6 28.5 25.3 22 18.6 16.8 15.1 27.3 24.2 21.1 17.9 16.2 14.5 12.8 24.3 21.6 18.9 16 14.5 13 11.5 14.8 12.6 10.3 9.09 7.87 15.5 13.8 12 10.2 9.26 8.31 7.34 6.35 5.35 12.7 11.2 9.51 8.66 7.78 6.88 5.97 5.03 7.5 5.76 4.85 9.33 8.16 6.95 5.68
3
Zy (in ) 31.6 28.5 25.3 22 18.6 16.8 15.1 16.2 14.4 12.5 10.5 9.52 8.51 7.5 7.72 6.77 5.81 4.86 4.38 3.9 3.42 5.65 4.74 3.83 3.37 2.9 15.5 13.8 12 10.2 9.26 8.31 7.34 6.35 5.35 6.31 5.47 4.62 4.19 3.75 3.3 2.85 2.4 2.91 2.2 1.85 9.33 8.16 6.95 5.68
4
J (in ) 7.13 5.08 3.46 2.21 1.3 0.96 0.682 4.35 2.96 1.9 1.12 0.822 0.584 0.396 3.68 2.48 1.61 0.933 0.704 0.501 0.328 1.47 0.873 0.459 0.3 0.2 3.68 2.51 1.61 0.954 0.704 0.501 0.34 0.218 0.129 2.07 1.33 0.792 0.585 0.417 0.284 0.183 0.108 0.396 0.174 0.103 2.07 1.33 0.792 0.417
Cw 32.5 23.4 16.1 10.4 6.16 4.55 3.23 16.3 11.3 7.28 4.33 3.2 2.28 1.55 12.9 8.89 5.75 3.42 2.53 1.8 1.22 3.97 2.37 1.25 0.85 0.54 9.24 6.41 4.17 2.5 1.85 1.32 0.9 0.58 0.34 4.04 2.64 1.59 1.18 0.84 0.58 0.37 0.22 0.78 0.34 0.2 3.53 2.32 1.4 0.74
ro (2L-3/8) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1.55 1.56 1.57 0.977 0.991 1.01 1.02 1.03 1.04 0.829 0.837 0.845 0.853 0.861 1.19 1.2 1.22 1.23 1.23 1.24 1.25 1.04 1.06 1.07 1.07 0.849 0.864 0.871 0.879 0.887 0.896 1.06 1.07 1.07 1.08 1.09 0.881 0.897 0.905 0.914 0.704 0.719 0.735 0.898 0.905 0.913 0.922 0.93 0.939 0.722 0.736 0.744
5.03 4.36 3.68 7.65 6.55 5.38 4.14 3.49 2.83 5.16 4.57 3.97 3.36 2.72 5.07 4.33 3.56 3.16 2.74 2.32 1.88 3.5 2.71 2.29 1.86 4.12 3.41 3.03 2.64 2.23 1.82 2.68 2.38 2.08 1.76 1.43 2.63 2.04 1.73 1.41 2.53 1.97 1.36 1.93 1.72 1.5 1.27 1.04 0.794 1.88 1.47 1.25
5.03 4.36 3.68 4.1 3.47 2.83 2.16 1.82 1.47 2.11 1.86 1.6 1.35 1.09 5.07 4.33 3.56 3.16 2.74 2.32 1.88 2.73 2.11 1.78 1.44 2.48 2.03 1.79 1.56 1.31 1.06 2.68 2.38 2.08 1.76 1.43 1.98 1.53 1.3 1.05 1.4 1.07 0.735 1.93 1.72 1.5 1.27 1.04 0.794 1.35 1.05 0.889
0.284 0.183 0.108 1.11 0.66 0.348 0.153 0.091 0.048 0.322 0.219 0.141 0.083 0.044 1.02 0.61 0.322 0.219 0.141 0.083 0.044 0.301 0.132 0.078 0.041 0.529 0.281 0.192 0.123 0.073 0.039 0.281 0.192 0.123 0.073 0.039 0.26 0.114 0.068 0.036 0.234 0.103 0.032 0.234 0.16 0.103 0.061 0.032 0.014 0.213 0.094 0.056
0.51 0.33 0.19 1.52 0.92 0.49 0.22 0.13 0.07 0.44 0.3 0.2 0.12 0.06 1.12 0.68 0.37 0.25 0.16 0.1 0.05 0.3 0.13 0.08 0.04 0.47 0.26 0.18 0.11 0.07 0.04 0.24 0.16 0.11 0.06 0.03 0.19 0.09 0.05 0.03 0.16 0.07 0.02 0.14 0.1 0.07 0.04 0.02 0.01 0.11 0.05 0.03
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.753 0.761 0.546 0.559 0.567 0.574 0.583 0.739 0.753 0.761 0.769 0.778 0.577 0.584 0.592 0.6 0.594 0.601 0.609 0.617 0.626
1.02 0.781 1.78 1.4 1.19 0.973 0.746 1.31 1.02 0.869 0.711 0.545 0.986 0.843 0.691 0.532 0.633 0.541 0.445 0.343 0.235
0.724 0.553 0.891 0.684 0.577 0.468 0.357 1.31 1.02 0.869 0.711 0.545 0.66 0.561 0.457 0.35 0.633 0.541 0.445 0.343 0.235
0.03 0.013 0.192 0.086 0.051 0.027 0.012 0.185 0.082 0.048 0.025 0.011 0.073 0.043 0.023 0.01 0.064 0.038 0.02 0.009 0.003
0.02 0.01 0.09 0.04 0.02 0.01 0.01 0.08 0.04 0.02 0.01 0.01 0.03 0.02 0.01 0 0.02 0.01 0.01 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
H (2L-3/8) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ro (2L-3/4) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
H (2L-3/4) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
ro 4.31 4.35 4.37 4.41 4.45 4.47 4.48 3.89 3.93 3.96 3.99 4.01 4.02 4.04 3.77 3.79 3.82 3.85 3.86 3.88 3.89 3.33 3.36 3.38 3.4 3.42 3.19 3.22 3.26 3.29 3.31 3.32 3.34 3.36 3.38 2.83 2.86 2.89 2.9 2.92 2.94 2.96 2.97 2.88 2.92 2.93 2.65 2.68 2.71 2.74
H 0.632 0.63 0.629 0.627 0.627 0.627 0.624 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.637 0.632 0.629 0.628 0.627 0.627 0.627 0.626 0.625 0 0 0 0 0 0 0 0 0 0 0 0.634 0.634 0.63 0.63
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2.77 2.79 2.81 2.37 2.4 2.44 2.47 2.49 2.5 2.39 2.41 2.42 2.43 2.45 2.11 2.14 2.17 2.19 2.2 2.22 2.23 2.04 2.08 2.09 2.11 1.91 1.95 1.96 1.98 2 2.01 1.89 1.91 1.91 1.93 1.95 1.76 1.79 1.81 1.83 1.67 1.7 1.73 1.6 1.61 1.63 1.65 1.66 1.68 1.47 1.5 1.52
0.629 0.627 0.626 0 0 0 0 0 0 0 0 0 0 0 0.639 0.631 0.632 0.631 0.625 0.623 0.627 0 0 0 0 0 0 0 0 0 0 0.631 0.629 0.628 0.627 0.626 0 0 0 0 0 0 0 0.634 0.632 0.629 0.628 0.627 0.626 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1.54 1.55 1.4 1.43 1.45 1.46 1.48 1.31 1.34 1.36 1.37 1.39 1.22 1.24 1.25 1.27 1.05 1.07 1.09 1.1 1.12
0 0 0 0 0 0 0 0.639 0.632 0.63 0.628 0.627 0 0 0 0 0.637 0.633 0.63 0.628 0.626
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