Page 261 - Handbook of Structural Steel Connection Design and Details

Welded Joint Design and Production

246 Chapter Three

Four conditions are required for ductility:

1. There must be a shear stress ( ) component resulting from the
given load condition.
2. This shear stress must exceed its critical value by a reasonable
amount. The more it exceeds this value, the greater will be the
resulting ductility.
3. The plastic shear strain resulting from this shear stress must act
in the direction which will relieve the particular stress which can
cause cracking.
4. There must be sufficient unrestrained length of the member to
permit “necking down.”

If conditions (1) and (2) are not met, there will be no apparent duc-
tility and no yielding. The stress will simply build up to the ultimate
tensile strength with little or no plastic energy absorbed. This condi-
tion is called brittle failure.
Figure 3.27 shows two regions in question. Point A is at the weld
joining the beam flange to the face of the column flange. Here there is
restraint against strain (movement) across the width of the beam
flange (ε ) as well as through the thickness of the beam flange (ε ).
1 2
Point B is along the length of the beam flange away from the connect-
ing weld. There is no restraint across the width of the flange or
through its thickness.
In most strength of materials texts, the following equations can be
found:
ε = 1 ( σ − µσ − µσ )
3 3 2 1 (3.1a)
E
ε = 1 − ( µσ + σ − µσ ) (3.1b)
2 3 2 1
E
ε = 1 − ( µσ − µσ + σ ) (3.1c)
1 3 2 1
E
It can be shown that

E[ µε + µε + ( 1 − µ ε ) ]
σ = 3 2 1 (3.2a)
1
( 1 + )( − µ)
µ 1 2
E[ µε + ( 1 − µ ε + µε ]
)
σ = 3 2 1 (3.2b)
−
2
)
( 1 + µ 1 2 µ)
(
)
E[( 1 − µ ε + µε + µε ]
σ = 3 2 1 (3.2c)
−
3
(
( 1 + µ 1 2 µ)
)
Downloaded from Digital Engineering Library @ McGraw-Hill (www.accessengineeringlibrary.com)
Copyright © 2009 The McGraw-Hill Companies. All rights reserved.
Any use is subject to the Terms of Use as given at the website.