The first visible parts of the new city hall building appeared on the downtown construction site this week, with stairwells and elevator shafts rising from the ground and the foundations taking shape.

The $23.4-million project is on budget and about a week ahead of schedule, even though wet weather has somewhat hindered progress, city Capital Programs and Buildings Director Gerry Jones said Friday.

“It has been a challenge, but the contractor shuffled quite a few things around to keep things moving,” Jones said. “They have rain dates built in, but we’ve had an abnormal amount of rain.”

The construction is taking place at the corner of West Washington Street and Henley Place, behind the current city hall building. City Council decided to replace the aging building with new construction.

Jones said nearby residents and workers will begin seeing a lot of activity soon.

Work on the main slab is set to begin July 22, Jones said, and the metal frame of the building will take shape in mid-August.

Jones said upcoming work would cause some noise and traffic changes. Nearby residents will be notified, he said.

“We’re going to do our best to keep those kind of things to a minimum,” he said.

The project is on track to meet the move-in date of late August 2014, he added.

The $23.4-million price tag does not include furniture or other equipment, which is expected to be a hefty amount by itself, because the project includes a new 911 call center with updated equipment. The city’s current equipment is being phased out and will be unusable by 2015, officials have said.