1. Engr. Ayaz Waseem ( Lecturer/Lab Engr., CED) Columns
LECTURE # 5
CASE 4: DIVIDING POINT BETWEEN TRANSITION AND TENSION
CONTROLLED FAILURE:
In figure comparing ∆ a b c and ∆ c f g, we get,
cdc −
=
005.0003.0
ccd 005.0003.0003.0 =−
dc
8
3
=
= da
8
3
1β ………………….. (1)
Now, we know that in this case fs = fy. So, the only thing which is not known to us is fs′ .
′−
=′
a
da
s
1
003.0
β
ε
Now,
If εs′ < εy , then fs′ = Es. εs′
If εs′ ≥ εy , then fs′ = fy
So, using the values of fs (calculated from above step) and a (calculated from equation 1) we
can find out Pn and Mn using load and moment equations respectively.
CASE 5: Pn is given and Pn > Pnb:
If Pn > Pnb , then we are in compression failure region. For this case we know that
fs ≠ fy , but whether fs′ = fy or not, this we need to find out.
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