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1
Reference Formulas
∑ Fx=^0 C^ A B 2ABcos^ γ
2 2 2 = + − A
xA ˆx
∑ Fy=^0
α β sin γ
C
sin
B
sin
A = =
=
= =
n
i
Qy xA xiAi 1
∑ M^ =^0
a
b b ac
2
4 x
2 − ± − = A
yA yˆ
F x = Fcos θ p= 2 π r= πd ∑
=
= =
n
i
Q (^) x yA yiAi 1
F (^) y = Fsin θ A = W⋅l=t⋅d I =I+ Ad^2
2 2 F = Fx +F y 4
2 2 d A r
π =π =
x
y
F
F tan θ = M = Fd A
I r =
2 s
g = 9.81m F = mg c
I
S =
w dx
=−
dV y = mx+b 2
4 c J
V dx
=
dM
2 1
2 1
x x
y y m −
( )
4 4 co c i J
2 m
N Pa = (^2) s
kg m N
⋅ = π (radians)=^180 °
1 kPa = 1 , 000 Pa 2 in
psi = lb 2 in
kip ksi =
(^1 ) m
kN kPa = 1 kip = 1000 lb 12 in = 1 ft
MPa Pa
6 1 = 10 GPa Pa
9 1 = 10 1 m^ =^1000 mm
A
P f (^) c = allowable
ultimate F .S = L
δ ε =
A
P f (^) t = A
P f (^) v = A
P f (^) v 2
=
A
P f (^) p = J
T ρ τ = td
P
A
P f (^) p = =
I
My f (^) y = Ib
VQ f (^) v −ave= f^ =E^ ε
S
M
I
Mc f (^) b −max= = A
V
f (^) v max 2
− = for a rectangle^ AE
PL δ =
b
req F
M S ≥ t d
V
A
V
f
web w
v −max ≅ = for an^ I^ beam^ δ^ T =α(^ Δ T ) L
x I
V Q V
T longitudinal =^ Δ E
f (^) x y z
μ ε = ε =− ε T^ =α(^ Δ T )
2 I =∑Ic +∑ Ad
p I
VQ nF
connectedarea connector ≥^ ⋅ L
f (^) v G
ρφ = τ = ⋅ L
ρφ γ =
2 c 1 ab
T τ (^) max = c ab G
TL 3 2
φ = JG
TL φ =
2 3
(^1) ab
T τ (^) max = ab G
TL 3 3
1
φ = 3 3
1 ii
max max bt
Tt
τ =
t a
T max 2
= i (^) i
i
t
s
t
TL 2
4 a
φ 3 3
1 G bi ti
TL
φ =
EI R
M
ρ
Δ = dx EI
M ( x) 2 n= b+ 3
PU = PL γ L+PD γ D≤ φP n
AISC-LRFD:
PU : 1.4D
M (^) u ≤φbMn= 0. 9 FyZ
L Kl e = PU : 1.2D +1.6L+0.5(LrorSorR) M (^) ult =Mp=fyΣAiyi= fyZ
2
2
2
2
r
L
π EA
L
π EI P
e e
cr PU: 1.2D+ 1.6(LrorSorR)+
(0.5L or 0.8W) S
k = Z
y
p
f
M
Z =
PU: 1.2D+ 1.3W+0.5L +
0.5(Lr orSor R)
c c
P F A.
u cr g
2
2
r
L
E
f
e
cr
V ( 0. 6 F A ) 0. 9
u v yw w v
E
F
r
Kl (^) y c
Wood:
F =CD CMCF ×F tabulated
′ K λ^ c≤^1.^5
Fcr ( )F y
c
2
- 658
λ
c c p c D p
F ′ =F C = FC C
λc > 1. 5 y
c
cr
F F
2
λ
2
⎟ ⎠
d
l
K E
F
e
cE cE
K (^) cE = 0.3 sawn, 0.418 glulam
P
P
c n
u ≥ 02 φ
M
M
M
M
P
P
b ny
uy
b nx
ux
c n
u ≤ ⎟
φ φ φ
2
F
f F
f
F
f
cEx
c bx
bx
c
c ≤
P
P
c n
u < 02
M
M
M
M
P
P
b ny
uy
b nx
ux
c n
u ≤ ⎟
φ φ φ
I
Mc
A
P
f (^) max = + Pu^ ≤^ φt^ FyAg^ φt =^0.^9 Pu ≤φtFuAe φt= 0. 75
b
b
a
a
F
f
F
f
I
M z
I
M y
A
P
f
1 2 max =^ + +^1.^0 F
f
F
f
F
f
by
by
bx
bx
a
a
BOLTS, THREADED PARTS AND RIVETS
Allowable Shear in kips
-^ 25%
75%
75%
BOLTS, AND THREADED PARTS
Allowable Bearing load in kips
