1. ENGINEERING EVALUATION
Evaluator: Kevin Wilson – Structural Engineer Date: 9/7/11
Unit: All Building: All Elevation: All
Location: All
References:
None
Problem Description:
Design a hanger bracket for scaffold storage to be fabricated out of 3/8” thick x 2” wide bar.
Evaluation Summary:
The bracket can be fabricated from 3/8” thick x 2” wide bar as shown on Sketch 1 on the following page.
The rated capacity of this hanger bracket is 450 lbs.
1 of 6
3. Evaluation of Hanger Bracket load rated at
450 lbs.
Engineering Evaluation
Bellefonte Nuclear Plant
Evaluation of Hanger Bracket for Material Storage:
kip 1000 lb⋅:= ksi 1000
lb
in
2
⋅:= psi 1
lb
in
2
⋅:=
Calculate Section Properties for 3/8" thick x 2" wide Bar:
W 2.0in:= H 0.375in:=
A W H⋅:= Area A:= AY
2
3
⎛
⎜
⎝
⎞
⎟
⎠
A⋅:= AX AY:=
Moment of Inertia Calculation:
Ix
W H
3
⋅
12
:= Iy
H W
3
⋅
12
:=
Radius of Gyration Calculation:
rx
H
12
:= ry
W
12
:=
Section Modulus Calculation:
Sx
W H
2
⋅
6
:= Sy
H W
2
⋅
6
:=
Properties:
Area 0.75 in
2
=
X-Axis Y-Axis
AX 0.5in
2
= AY 0.5in
2
=
rx 0.108 in=Ix 0.009 in
4
= ry 0.577 in=Iy 0.25 in
4
=
Sx 0.047 in
3
= Sy 0.25 in
3
=
rx 0.108 in= ry 0.577 in=
3 of 6
4. Evaluation of Hanger Bracket load rated at
450 lbs.
Engineering Evaluation
Bellefonte Nuclear Plant
E 29000000psi:=
Fy 36ksi:=
w 32.2
lb
in
:= l 14in:=
R
w l⋅
2
:=
R 225.4 lb⋅=
V R:=
Shear Stress Check:
Fv 0.52 Fy⋅:= V 0.225 kip⋅= Av A
2
3
⋅:=
fv
V
Av
:= fv 0.451 ksi⋅= < Fv 18.72 ksi⋅= OK
Bending Stress Check:
M_max
w l
2
⋅
8
:=
M_max 0.789 in kip⋅⋅= Fb 0.66 Fy⋅:=
fb
M_max
Sx
:= fb 16.8299 ksi⋅= < Fb 23.76 ksi⋅= OK
Deflection Check:
Δmax
5w l
4
⋅
384 E⋅ Ix⋅
⎛
⎜
⎝
⎞
⎟
⎠
:= Δmax 0.06319 in⋅= < 0.125in OK
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5. Evaluation of Hanger Bracket load rated at
450 lbs.
Engineering Evaluation
Bellefonte Nuclear Plant
Calculations for loading on angle brace as a Column subjected to compression (formulas are from AISC Steel
Manual, Section 1.5 & 1.6:
Properties of the beam section:
E 29000000psi:= Fy 36ksi:=
Cmx 1.0:= Cmy 1.0:=
PC 0.320kip:= PBX 0kip:= PBY 0kip:=
l 1.5ft:= K 1.2:=
General Calculations:
r min rx ry,( ):= Fex
12 π
2
⋅ E⋅
23
K l⋅
rx
⎛
⎜
⎝
⎞
⎟
⎠
2
⋅
:= Fey
12 π
2
⋅ E⋅
23
K l⋅
ry
⎛
⎜
⎝
⎞
⎟
⎠
2
⋅
:= Fbx 0.66 Fy⋅:=
Fby 0.66Fy:=
Calculate Allowable Compression Stress:
CC
2π
2
E⋅
Fy
:= Sr
K l⋅
r
:= Sr 199.532=
CC 126.099=
Fa
12π
2
E
23 Sr
2
⋅
Sr CC≥if
1
Sr
2
2 CC
2
⋅
−
⎛
⎜
⎜
⎝
⎞
⎟
⎟
⎠
Fy⋅
5
3
⎛
⎜
⎝
⎞
⎟
⎠
3Sr
8 CC⋅
⎛
⎜
⎝
⎞
⎟
⎠
+
Sr
3
8 CC
3
⋅
⎛
⎜
⎜
⎝
⎞
⎟
⎟
⎠
−
Sr CC<if
:=
Fa 3.751 ksi⋅=
__________________________________________________________________________________________________
Maximum Compressive Load Calculation:
Pcr 1.7 Area⋅ Fa⋅:= Pcr 4.782 kip⋅= Pallow Pcr
2
3
⎛
⎜
⎝
⎞
⎟
⎠
⋅:= Pallow 3.188 kip⋅= > PC 0.32 kip⋅=
OK
Calculate Axial Stress:
fa
PC
Area
:= fa 0.427 ksi⋅= fa
Fa
0.114= < 1.0 OK
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6. Evaluation of Hanger Bracket load rated at
450 lbs.
Engineering Evaluation
Bellefonte Nuclear Plant
1
1 3
3
2
2
d
c2
kip 1000 lb⋅:= ksi 1000
lb
in
2
⋅:=
d 2 in⋅:=
Fu 70 ksi⋅:= Weld electrode minimum
tensile strength for E70XX.
Fy 21.3 ksi⋅:= Base metal yield strength for
ASTM A36 @ 100° F.
Forces and Moments on weld group:
F1 0.450 kip⋅:= F2 0 kip⋅:= F3 0 kip⋅:=
M1 0 kip⋅ in⋅:= M2 0 kip⋅ in⋅:= M3 0 kip⋅ in⋅:=
Weld group section properties:
AW1 d:= AW2 AW1:= AW3 AW1:= c2
d
2
:= c3 0 in⋅:=
AW1 2 in⋅= AW2 2 in⋅= AW3 2 in⋅= c2 1 in⋅= c3 0 in⋅=
SW3
d
2
6
:= JW
d
3
12
:=
SW3 0.667 in
2
⋅= JW 0.667 in
3
⋅=
Forces on weld:
f1
F1
AW1
M3
SW3
+:= f2
F2
AW2
M1 c3⋅
JW
+:= f3
F3
AW3
M1 c2⋅
JW
+:=
f1 0.225
kip
in
⋅= f2 0
kip
in
⋅= f3 0
kip
in
⋅=
fr f1
2
f2
2
+ f3
2
+:= fr 0.225
kip
in
⋅=
Weld size required:
wbase_metal
fr
0.4 Fy⋅
:= wbase_metal 0.026 in⋅= wweld_metal
fr
0.707 0.3⋅ Fu⋅
:= wweld_metal 0.015 in⋅=
wprovided .1875in:= IR
max wbase_metal wweld_metal,( )
wprovided
:= IR 0.141= < 1.0 ∴ OK
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