SELECT 
  RptID, 
  TimeCode,
  HrsDur,
  CASE WHEN LogSeq# = 1 THEN RptStartDttm
       ELSE 
         DO WHILE -- (? ? ?) -- 
           LogSeq# = 2 THEN RptStartDttm + LogSeq#1 HrsDur 
           LogSeq# = 3 THEN RptStartDttm + LogSeq#1 HrsDur + LogSeq#2 HrsDur
           LogSeq# = 4 THEN RptStartDttm + LogSeq#1 HrsDur + LogSeq#2 HrsDur + LogSeq#3 HrsDur
           etc.  until last LogSeq# for RptID
   --- (OR) ---
           LogSeq# = 2 THEN RptStartDttm + LogSeq#1 HrsDur
           LogSeq# = 3 THEN LogSeq#2 OpsStartDttm + LogSeq#2 HrsDur
           LogSeq# = 4 THEN LogSeq#3 OpsStartDttm + LogSeq#3 HrsDur
           etc. until last LogSeq# for RptID
        END LOOP
  END AS OpsStartDttm
FROM 
  DailyOps, 
  TimeLog
WHERE 
  DailyOps.RptID = TimeLog.RptID

Declare @DailyOps Table
(RptId Varchar(10),RptStartDttm datetime,RptEndDttm datetime)
Insert into @DailyOps
Select 'R1','01/13/2013 06:00:00:000','01/14/2013 06:00:00:000' union all
Select 'R2','01/14/2013 06:00:00:000','01/15/2013 06:00:00:000'

Declare @TimeLog Table
(LogId Varchar(10),RptID Varchar(10),HrsDue int,TimeCode Varchar(10),LogSeg int)

Insert into @TimeLog
Select 'L1A','R1',9,'MIRU',1 union all
Select 'L2B','R1',1,'BHA',2 union all
Select 'L3C','R1',4,'DR',3 union all 
Select 'L4D','R1',2,'SVY',4 union all 
Select 'L1AF','R2',5,'BHA',1 union all 
Select 'L21G','R2',6,'DR',2 union all 
Select 'L31D','R2',7,'RR',3


Select D.RptID,T.TimeCode,T.HrsDue,T.LogSeg,ISNULL(DateAdd(hh,P.HrsDue,D.RptStartDttm),D.RptStartDttm)RptStartDttm
from @DailyOps D
inner join @TimeLog T on T.RptID = D.RptID
OUTER APPLY
         (
         Select K.RptID,SUM(K.HrsDue)HrsDue from @TimeLog K
         left join @TimeLog S on S.RptID = K.RptID and S.LogSeg = K.LogSeg + 1
         Where K.RptID = T.RptID
         and S.LogSeg < = T.LogSeg
         Group by K.RptID
         )P

RptID	TimeCode	HrsDue	LogSeg	RptStartDttm
R1	MIRU	9	1	2013-01-13 06:00:00.000
R1	BHA	1	2	2013-01-13 15:00:00.000
R1	DR	4	3	2013-01-13 16:00:00.000
R1	SVY	2	4	2013-01-13 20:00:00.000
R2	BHA	5	1	2013-01-14 06:00:00.000
R2	DR	6	2	2013-01-14 11:00:00.000
R2	RR	7	3	2013-01-14 17:00:00.000

Create table DailyOps 
(
	RptID Varchar(2), 
	RptStartDttm DateTime, 
	RptEndDttm DateTime 
) 

Insert Into DailyOps 
Select 'R1', '2013/01/13 06:00', '2013/01/14 06:00'
Union ALL 
Select 'R2', '2013/01/14 06:00', '2013/01/15 06:00' 

Create Table TimeLog 
(
	LogID Varchar(5), 
	RptID Varchar(2), 
	HrsDur Int, 
	TimeCode Varchar(5), 
	LogSeqNo Int 
) 

Insert Into TimeLog 
Select 'L1A', 'R1', 9, 'MIRU', 1 
Union ALL	
Select 'L2B', 'R1', 1, 'BHA', 2	
Union ALL
Select 'L3C', 'R1', 4, 'DR', 3	
Union ALL
Select 'L4D', 'R1', 2, 'SVY', 4	
Union ALL
Select 'L1AF', 'R2', 5, 'BHA', 1	
Union ALL
Select 'L21G', 'R2', 6, 'DR', 2	
Union ALL
Select 'L31D', 'R2', 7, 'RR', 3 


;With CTE 
As 
(
	 Select a.*, p.LogID, p.HrsDur, p.TimeCode, p.LogSeqNo, p.hrsdur_new, ROW_NUMBER() Over (Partition By a.RptId Order By p.LogSeqNo) As rn
	 From DailyOps As a 
	 JOIN 
	 (
		  Select *, (Select SUM(HrsDur) From TimeLog Where RptID = a.RptID AND LogSeqNo <= a.LogSeqNo) As hrsdur_new 
		  From TimeLog As a 
	 ) As p ON a.RptID = p.RptID 
) 
Select a.RptID, a.TimeCode, a.HrsDur, (Case When b.rn IS NULL Then a.RptStartDttm Else DATEADD(HH,b.hrsdur_new,b.RptStartDttm) End) As OpsStartDttm 
From CTE as a LEFT JOIN CTE As b ON b.rn = (a.rn - 1) And a.RptID = b.RptID 

--Stats of my query--------------------------------

(7 row(s) affected)
Table 'Worktable'. Scan count 1, logical reads 27, physical reads 0, read-ahead reads 0, lob logical reads 0, lob physical reads 0, lob read-ahead reads 0.
Table 'DailyOps'. Scan count 2, logical reads 14, physical reads 0, read-ahead reads 0, lob logical reads 0, lob physical reads 0, lob read-ahead reads 0.
Table 'TimeLog'. Scan count 9, logical reads 9, physical reads 0, read-ahead reads 0, lob logical reads 0, lob physical reads 0, lob read-ahead reads 0.

 SQL Server Execution Times:
   CPU time = 0 ms,  elapsed time = 1 ms.
-------------------------------------------------------------

--Stats of the Outer Apply Query-----------------------------

(7 row(s) affected)
Table 'Worktable'. Scan count 14, logical reads 53, physical reads 0, read-ahead reads 0, lob logical reads 0, lob physical reads 0, lob read-ahead reads 0.
Table 'TimeLog'. Scan count 15, logical reads 15, physical reads 0, read-ahead reads 0, lob logical reads 0, lob physical reads 0, lob read-ahead reads 0.
Table 'DailyOps'. Scan count 1, logical reads 1, physical reads 0, read-ahead reads 0, lob logical reads 0, lob physical reads 0, lob read-ahead reads 0.

 SQL Server Execution Times:
   CPU time = 0 ms,  elapsed time = 4 ms.