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A thread structure in accordance to one or more embodiments includes a thread extending helically along the cylindrical member in spaced thread turns, the thread having a crest extending between a first flank and a second flank and a root extending between the thread turns, the root having a curvatu

A thread structure in accordance to one or more embodiments includes a thread extending helically along the cylindrical member in spaced thread turns, the thread having a crest extending between a first flank and a second flank and a root extending between the thread turns, the root having a curvature defined by a portion of an ellipse tangentially adjoining the first and second flank at respective flank transition points, the ellipse having a major axis extending parallel to the axis and a minor axis extending perpendicular to the major axis and through a root bottom.

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1. A thread structure, comprising: a cylindrical member extending along an axis;a thread extending helically along the cylindrical member in spaced thread turns, the thread comprising: a crest extending between a first flank and a second flank;a root extending between the thread turns, the root havi

1. A thread structure, comprising: a cylindrical member extending along an axis;a thread extending helically along the cylindrical member in spaced thread turns, the thread comprising: a crest extending between a first flank and a second flank;a root extending between the thread turns, the root having a curvature defined by a portion of an ellipse tangentially adjoining the first and second flank at respective flank transition points, the ellipse having a major axis extending parallel to the axis and a minor axis extending perpendicular to the major axis and through a root bottom;a root semi-width at the flank transition points of about 0.050 to about 0.061 inches; andan equivalent root radius of about 0.057 to about 0.061 inches. 2. The thread structure of claim 1, further comprising: a root depth of about 0.012 to about 0.020 inches. 3. The thread structure of claim 2, wherein the root depth is about 0.013 to about 0.016 inches. 4. The thread structure of claim 1, further comprising: a root semi-width at the flank transition points of about 0.050 to about 0.055 inches;an equivalent root radius of about 0.057 to about 0.061 inches; anda root depth of about 0.012 to about 0.016 inches. 5. The thread structure of claim 4, wherein the root depth is about 0.014 to about 0.015 inches. 6. The thread structure of claim 1, further comprising: a root depth of about 0.012 to about 0.020 inches;a root semi-width at the flank transition points of about 0.050 to about 0.060 inches; anda pitch of about three threads per inch. 7. The thread structure of claim 1, further comprising: a root depth of about 0.013 to about 0.016 inches;a root semi-width at the flank transition points of about 0.050 to about 0.055 inches; anda pitch of about three threads per inch. 8. The thread structure of claim 1, further comprising: a root semi-width at the flank transition points of about 0.050 to about 0.061 inches;an equivalent root radius of about 0.057 to about 0.061 inches;a first flank angle relative to the minor axis of about 20 to about 30 degrees;a root depth of about 0.012 to about 0.020 inches;a pitch of about three threads per inch; anda taper of about 1.0 to about 1.5 tapers per foot. 9. The thread structure of claim 1, further comprising: a root semi-width at the flank transition points of about 0.052 inches to about 0.055 inches;an equivalent root radius of about 0.057 to about 0.059 inches;a first flank angle relative to the minor axis of about 24 to about 28.5 degrees;a root depth of about 0.013 to about 0.016 inches;a pitch of about three threads per inch; anda taper of about 1.0 to about 1.5 tapers per foot. 10. The thread structure of claim 1, further comprising: an equivalent root radius of about 0.057 to about 0.059 inches;a first flank angle relative to the minor axis of about 24 to about 28.5 degrees;a crest width of about 0.1 to about 0.2 inches; anda pitch of about three threads per inch. 11. A rotary shouldered connection (RSC), the RSC comprising: a first tubular having a longitudinal axis and a pin end carrying a thread structure;a second tubular having a box end carrying a thread structure, wherein the pin end and the box end are threadedly connected;the thread structure including a thread extending helically in spaced thread turns, the thread comprising: a crest extending between a first flank and a second flank;a root extending between the thread turns, the root having a curvature defined by a portion of an ellipse tangentially adjoining the first and second flank at respective flank transition points, the ellipse having a major axis extending parallel to the longitudinal axis and a minor axis extending perpendicular to the major axis and through a root bottom;a root semi-width at the flank transition points of about 0.050 to about 0.061 inches; andan equivalent root radius of about 0.057 to about 0.061 inches. 12. The RSC of claim 11, wherein the thread comprises: a root depth of about 0.012 to about 0.020 inches. 13. The RSC of claim 11, wherein the thread comprises: an equivalent root radius of about 0.057 to about 0.059 inches;a first flank angle relative to the minor axis of about 24 to about 28.5 degrees;a crest width of about 0.1 to about 0.2 inches; anda pitch of about three threads per inch. 14. The RSC of claim 11, wherein the thread comprises: a root semi-width at the flank transition points of about 0.050 to about 0.061 inches;an equivalent root radius of about 0.057 to about 0.061 inches;a first flank angle relative to the minor axis of about 20 to about 30 degrees;a root depth of about 0.012 to about 0.020 inches;a pitch of about three threads per inch; anda taper of about 1.0 to about 1.5 tapers per foot. 15. The RSC of claim 11, wherein the thread comprises: a root semi-width at the flank transition points of about 0.052 to about 0.055 inches;an equivalent root radius of about 0.057 to about 0.059 inches;a first flank angle relative to the minor axis of about 24 to about 28.5 degrees;a root depth of about 0.013 to ab about out 0.016 inches;a pitch of about three threads per inch; anda taper of about 1.0 to about 1.5 tapers per foot. 16. A drilling system, comprising: a drilling string comprising a rotary shouldered connection (RSC) having a thread structure on a tubular support member having a longitudinal axis, the thread structure including a thread extending helically in spaced thread turns, the thread comprising: a crest extending between a first flank and a second flank; anda root extending between the thread turns, the root having a curvature defined by a portion of an ellipse tangentially adjoining the first and second flank at respective flank transition points, the ellipse having a major axis extending parallel to the longitudinal axis and a minor axis extending perpendicular to the major axis and through a root bottom;a root semi-width at the flank transition points of about 0.050 to about 0.061 inches; andan equivalent root radius of about 0.057 to about 0.061 inches. 17. The drilling system of claim 16, wherein the thread comprises: a root depth of about 0.012 to about 0.020 inches. 18. The drilling system of claim 16, wherein the thread comprises: an equivalent root radius of about 0.057 to about 0.059 inches;a first flank angle relative to the minor axis of about 24 to about 28.5 degrees;a crest width of about 0.1 to about 0.2 inches; anda pitch of about three threads per inch. 19. The drilling system of claim 16, wherein the thread comprises: a root semi-width at the flank transition points of about 0.050 to about 0.061 inches;an equivalent root radius of about 0.057 to about 0.061 inches;a first flank angle relative to the minor axis of about 20 to about 30 degrees;a root depth of about 0.012 to about 0.020 inches;a pitch of about three threads per inch; anda taper of about 1.0 to about 1.5 tapers per foot. 20. The drilling system of claim 16, wherein the thread comprises: a root semi-width at the flank transition points of about 0.052 to about 0.055 inches;an equivalent root radius of about 0.057 to about 0.059 inches;a first flank angle relative to the minor axis of about 24 to about 28.5 degrees;a root depth of about 0.013 to about 0.016 inches;a pitch of about three threads per inch; anda taper of about 1.0 to about 1.5 tapers per foot.