I assume that you have plotted a beam, which is supposed to bend as you change the slider value. Since you are able to plot the new position into the axes, I assume that you know how to write callbacks. I further assume that there are parts of the plot that should stay the same, and parts that should change.
To change the parts that need changing, the easiest method is just to delete them and then to redraw. In order to delete specific items from a plot, it's best to tag them. Thus, your plotting would go like this
%# remove the old position
%# find the handle to the old position by searching among all the handles of
%# the graphics objects that have been plotted into the axes
oldPosHandle = findall(handles.axes1,'Tag','position');
delete(oldPosHandle);
%# plot new position
PL1Draw = line([zpl1 zpl1],[SH/2 PL1*10]);
%# add the tag so that you can find it if you want to delete it
set(PL1Draw,'Tag','position');
Note 1
To make the GUI respond faster (if needed), do not delete and re-plot, but change the 'XData' and 'YData' property of the old position object.
Note 2
If you aren't already doing so, put the plotting function (the one that updates everything in the plot, not just the position of the load) in a separate function, not into the callback of the slider, and have instead the slider callback call the plot function. This way, you can call the same plotting function from several buttons and sliders, which makes the code a lot easier to maintain.
EDIT
I have updated the commands. Note that there is no special 'tagging' function. 'Tag' is a property of every graphics object, like 'Units', or 'Color'. It simply helps you to label the graphics objects so that you don't need to remember the handles.