Electric water heater if fully repairable by homeowner:
A] First of all, we know your upper element is working because you have some hot water:http://waterheatertimer.org/How-it-works.html
That says tank is not overheating.
It says tank is getting 240Volts.
It we know water heater is 240Volts because you have 2 elements.
And it says reset button is not tripped.B] That leaves 4 suspects
Suspect 1) Bad Upper thermostat or Bad Lower thermostat: solution replace both thermostats for about 25$. Steps shown in link below.http://waterheatertimer.org/How-to-replace-thermostat-on-electric-water-heater.html
Suspect 2) Burned out Lower element: solution take out element, clean sediment out of tank, put in new element. Steps shown in link belowhttp://waterheatertimer.org/How-to-clean-sediment-out-of-electric-water-heater.html
Suspect 3) Loose wire or connection: solution open covers and remove insulation and look for signs of burning and high heat. Tighten all screws very tight. Replace burned part. Put insulation and covers back over thermostat so thermostat not exposed to cool air which will cause thermostat to misread tank temperature.
C] Before replacing anything, you can test water heater parts and determine exact
cause of problem. Testing requires $5 multimeter from Lowes or Home Depot:
Install battery in multimeter.
When test calls for testing voltage, rotate multimeter dial to 240 or 250 or 277 Volts.
When test calls for testing continuity, rotate multimeter dial to ohms (upside down horseshoe symbol is ohms)http://waterheatertimer.org/How-to-troubleshoot-electric-water-heater.html
After doing 30 minutes of testing, you will be expert in water heaters.
D] You replaced elements for a reason
Did you test elements before replacing?
Was tank producing some hot water before you replaced elements?
If tank producing some hot water, then lower element was bad, and upper element was good.
And when you replaced lower element, did you also clean sediment out of tank?
If sediment builds up inside tank, it will reach lower element and burn out the element.
That could have been original problem, and it could be same problem again.
Restore full efficiency to tank by cleaning out sediment and replacing lower element.http://waterheatertimer.org/Clean-sediment-out-of-water-heater.html
E} More reading to preserve tank and save money long termhttp://waterheatertimer.org/Replace-anode-rod.htmlhttp://waterheatertimer.org/9-ways-to-save-with-water-heater.html