Charge-induced dimensional changes allow conducting polymers and single walled carbon nanotubes to function as electromechanical actuators. The unit cell of the prototypical conducting polymer, trans-polyacetylene, was calculated as a function of charge injection using density functional theory in combination with ultrasoft pseudopotentials using the solid-state Vienna ab initio simulation package. Test calculations on the charged pyridinium molecular ion give results in good agreement with the experimental geometry. Strain versus charge relationships are predicted from dimensional changes calculated using a uniform background charge ("jellium") for representing the counterions, which we show provides results consistent with experiment for doped polyacetylenes. These jellium calculations are consistent with further presented calculations that include specific counterions, showing that hybridization between the guest dopant ions and the host polyacetylene chains is unimportant. The lack of guest-host orbital hybridization allows a qualitative rigid band interpretation of the amount of charge transfer for both acceptor and donor doping. For polyacetylene, asymmetry of strain along the chain with respect to the sign of the charge is predicted: negative charge elongates and positive charge shortens the polymer. For charge less than 0.05e per carbon, an approximately linear dependence is obtained for the dependence of chain-direction strain on the amount of injected charge.