Beam Design

• Bending

–

– lateral stability

– unbalanced combination of laminations (gluelam)

• Shear

–

• Deflection

–

• Bearing

'

b b

Mf F

S= !

'1.5

v v

Vf F

A= ! (for rectangle beam)

max allow! " !

Lateral Stability

• Cause

• Result

– lateral instability

– decrease in allowable stress

compression

Consider this effect by CL

* CL is a similar adjustment factor with CP

* CP will be discussed in Ch. 7 (for column)

Lateral Stability

• full lateral support

– appropriate connection of a roof or diaphragm (sheathing)

– lu = 0

• Approximate method

– depth-to-thickness ratio (d/b) = 6

bridging or solid blocking required

at intervals of 8 ft max.

b

d

Lateral Stability

Solid blocking Bridging

Lateral Stability (using CL)

• Concept (Euler Buckling)

– Euler critical buckling stress

– Euler-based critical buckling stress

KbE = 0.439 for visually graded lumber

= 0.561 for MEL (machine evaluated lumber)

= 0.610 for MSR (machine stress rating) or gluelam

2

2( )Euler

EF

slenderness ratio FS

!=

"

'

2( )

bE y

bE

B

K EF

R=

Lateral Stability (using CL)

• Procedure of computing CL

Evaluating lu

Evaluating le

Calculating RB

Calculating FbE

Calculating CL

unbraced length of beam

slenderness ratio

b

d

2

e

B

l dR

b=

Lateral Stability (using CL)

• Effective unbraced length, le

Lateral Stability (using CL)

* * *21 / 1 / /

( )1.9 1.9 0.95

bE bx bE bx bE bx

L

F F F F F FC

+ += ! !

• Calculate CL

- Fbx* = tabulated bending stress for x axis multiplied by

adjustment factors (except Cfu, CV, and CL)

- Ey’ = modulus of elasticity about y axis multiplied by

adjustment factors

Lateral Stability (Example)

wTL = 1k / ft, D+S

48’

8 ftul =

6.75*37.5 24F-1.8E gluelam

962.56 7

37.5

ul

d= = < 2.06 198 in

e ul l= =

2

198*37.512.76

6.75

e

B

l dR

b= = =

'

2 2

0.610*16000005994 psi

( ) 12.76

bE y

bE

B

K EF

R= = =

* ( )( )( ) 2400*1.15*1.0*1.0 2760bx bx D M tF F C C C= = = psi

Lateral Stability (Example)

*

59942.172

2760

bE

bx

F

F= =

2* * *

1 / 1 / /

1.9 1.9 0.95

bE bx bE bx bE bx

L

F F F F F FC

! "+ += # #$ %

& '

*1 /

1.6691.9

bE bxF F+

=

0.962=

* Note

Allowable Bending Stress for Strong Axis: Choose the smaller

' ( )( )( )( )bx bx D M t LF F C C C C

+=

' ( )( )( )( )bx bx D M t VF F C C C C

+=

Bearing Stress

0.375b

b

b

lC

l

+=

' ( )( )( )( )c c M t i bF F C C C C

! !=c

Pf

A!= vs.

Unbalanced Combinations of

Laminations