What 29 CFR 1926.55 requires (plain English)
29 CFR 1926.55 is the construction industry's general air-contaminants standard: the counterpart to general industry's 1910.1000. It requires that a worker's exposure to gases, vapors, fumes, dusts, and mists be kept within the permissible exposure limits listed in Table 1 and Table 2 of the section, which are drawn largely from the 1970 threshold limit values and the Z-tables and have changed little since.
The operative rule is that exposure to any listed substance, measured from breathing-zone air samples, must not exceed the specified 8-hour time-weighted-average limit, and, where a limit is preceded by (C), must not exceed that ceiling value at any time. When a worker's exposure would exceed a limit, the employer must first apply feasible administrative or engineering controls (ventilation, substitution, process change), and use respiratory protection only to make up the difference while those controls are implemented or where they are not feasible.
1926.55 is the construction analog of 1910.1000, and many of its limits are the same decades-old figures; substances with their own comprehensive standards (lead, silica, asbestos, hexavalent chromium, and the rest) are governed by those specific standards instead. Because the general PELs are outdated, being 'under the PEL' does not guarantee safety, and OSHA encourages using more protective consensus limits where they exist.