You can add overflow behavior with scroll only in tbody and still do not have to set fixed sizes in pixels without having to separate the header of the columns with the body, as seen in the plugins that provide grids ?
css for overflow:
table.grid tbody {
overflow-y: scroll;
overflow-x: auto;
}
table:
<table class='grid'>
<thead> ... <thead>
<tbody>
...
</tbody>
<tfoot> ... </tfoot>
</table>
The intention is that even a table having records that go beyond the boundary of the area in which it is allocated, that it does not overlap that limit, but that the records are navigable through the scroll bar, as in systems grids desktop, and who knows how to try to adapt it to be responsible.
EDITION
Following is an example of how to just add css from overflow to tbody does not work:
As you can see in the image, the table is inserted in a div > Fixed 200px height . But table continues to exceed this limit.