Assuming one entry per cell:
Is there only one letter at the end? If so, you can use:
=SUMPRODUCT(--LEFT(A1:A100,LEN(A1:A100)-1))
If there might be multiple letters at the end, a simple UDF would be simpler:
Option Explicit
Function AddStrings(rg As Range)
Dim L As Long
Dim I As Long
For I = 1 To rg.Count
L = L + Val(rg(I))
Next I
AddStrings = L
End Function
EDIT: If some of the cells might be blank, you can use either the UDF, or, if you prefer the formula, this array-entered formula:
=SUM(IFERROR(--LEFT(A1:A100,LEN(A1:A100)-1),0))
To array-enter a formula, after entering the formula into the cell or formula bar, hold down ctrl-shift while hitting enter. If you did this correctly, Excel will place braces {...} around the formula.