Qualcosa del genere?
declare @t table (id int, tool varchar(10), on_hire date, off_hire date);
insert into @t values
(1,1,'2016-01-01','2016-01-10'),
(2,1,'2016-01-15','2016-01-20'),
(3,2,'2015-12-01','2016-01-10'),
(4,3,'2016-01-20','2016-02-10'),
(5,4,'2015-01-01','2017-01-10')
select tool, sum(datediff(d,on_hire,off_hire)) + 1 dayshired
from
(
select tool,
case
when on_hire < '2016-01-01' then '2016-01-01'
else on_hire
end as on_hire,
case
when off_hire > '2016-01-31' then '2016-01-31'
else off_hire
end as off_hire
from @t
) s
group by s.tool
