A gas turbine engine arcuate segment includes arcuate flange with anti-chording means extending away from annular wall. Anti-chording means may include insert in or bonded to flange and made of different alpha material than the annular wall. Anti-chording means may be heating means for heating flange. Heating means includes hot air inlet to and an outlet from a circumferentially extending heating flow passage embedded in flange and may further include a cold air inlet to heating flow passage. Heating flow passage may be a serpentine heating flow passage with an undulating heating flowpath. A turbine nozzle segment includes one or more airfoils extending radially between inner and outer arcuate band segments and forward and aft outer flanges extending radially from the outer arcuate band segment include anti-chording means. An arcuate turbine shroud segment includes forward and aft shroud rail segments with anti-chording means.