Some taiji practitioners believe that their art does not require any physical strength.
This belief probably arises from the view that pure softness can overcome pure hardness. Taking this view in their heart, the "soft" practitioners focus their training purely on the taijiquan forms and non-contentious pushhand exercises.
The "Pure Softness" approach originates from the Artisticalisation of the Martial Art - the art is practised as soft physical exercise. This aspect of the art lays importance on the spiritual and the will power. According to "On the Art of Taiji", artisticalisation of the art at its highest level may enable a practitioner to act more "skillfully" than a man with great physical strength.
Having said that, it should be noted that the "Soft" practitioners are only partially correct as "Artisticalisation" is only one of the Three Levels of Achievements in Taiji, In Martialisation of the art both "Chi" and "Lik" (i.e. physical strength) are important.
"On the Art of Taiji" stresses the importance of both "Chi" and "Lik" in the martialisation aspect. Physical strength is not downgraded. "Chi" and "Lik" are utilized to complement each other. Hence, there is nothing wrong in improving your physical strength if you know the basic principle of the art. In this aspect, the difference between external martial art and internal martial art is that in internal martial art, we use "Chi" to drive "Lik" and not the other way round .
To improve physical strength in the taiji way, you will need to learn the weapons (sabre, sword and pole) and other training tools, including but not limited to the taiji ball.