RIGIT FRAME FORMULAS/ A. KLEINLOGE

Organization of rigid frame formulas. 2. Arrangements of formulas. 3. The more important notations. 4. Sign conventions. 5. Assumptions made in deriving the formulas. 6. General loads on members, Frame 1: Single-leg, two-hinged rigid frame. Vertical leg. Horizontal girder. Frame 2: Single-leg, one-hinged rigid frame. Vertical leg, hinged at bottom. Horizontal girder. Frame 3: Single-leg, one-hinged rigid frame. Vertical leg. Horizontal girder, hinged at one end. Frame 4: Single-leg, hingless rigid frame. Vertical leg.Horizontal girder. Frame 5: Single-leg, rigid frame. Vertical leg. Horizontal girder with roller at one end. Frame 6: Single-leg, rigid frame. Vertical leg log on roller. Horizontal girder. Frame 7: Single-leg, two-hinged rigid frame. Vertical leg. Inclined girder. Frame 8: Single-leg, hingless rigid frame. Vertical leg. Inclined girder. Frame 9: Single-leg, two-hinged rigid frame. Inclined leg. Horizontal girder. Frame 10: Single-leg, hingless rigid frame. Inclined leg. Horizontal girder. Frame 11: Single-leg, two-hinged rigid frame. Inclined leg. Inclined girder. Frame 12: Single-leg, one-hinged rigid frame. Inclined leg. Inclined girder, hinged at one end. Frame 13: Single-leg, one-hinged rigid frame. Inclined leg, hinged at bottom. Inclined girder. Frame 14: Single-leg, hingless rigid frame. Inclined leg. Inclined girder. Frame 15: Symmetrical two-hinged, triangular rigid frame. Frame 16: Symmetrical triangular rigid frame with tie-rod. Externally simply supported. Frame 17: Symmetrical triangular two-hinged frame with hinged compression tie and with step-wise varying moments of inertia. Frame 18: Symmetrical triangular three-hinged frame with hinged tie-rod and variables moment of inertia. Frame 19: Fully fixed symmetrical triangular frame. Frame 20: Symmetrical triangular fixed frame with hinged tie-rod and variable moment inertia. Frame 21: Symmetrical triangular one-hinged frame with hinged tie-rod and variable moment inertia. Frame 22: Unsymmetrical two-hinged rigid frame. Hinges at same elevation. Frame 23: Unsymmetrical triangular rigid frame with horizontal tie-rod. Externally simply supported. Frame 24: Unsymmetrical triangular rigid frame. One support fixed, one support hinged: both supports at the same elevation. Frame 25: Unsymmetrical hingless, triangular rigid frame. Both supports at the same elevation. Frame 26: Unsymmetrical two-hinged triangular rigid frame. Supports at different elevation. Frame 27: Unsymmetrical triangular rigid frame. One support fixed, one support hinged: support at different elevations. Frame 28: Unsymmetrical hingless, triangular rigid frame. Supports at different elevation. Frame 29: : Unsymmetrical two-hinged triangular rigid frame. One leg vertical. Both supports at the same elevation. Frame 30: Triangular rigid frame with horizontal tie-rod. Externally simply supported. One leg vertical. Frame 31: Triangular hingless rigid frame. One leg vertical. Both supports at the same elevation. Frame 32: Triangular rigid frame. One leg vertical, hinged at bottom. Other support fixed. Both supports at the same elevation. Frame 33: Triangular rigid frame. One leg vertical, fixed at bottom. Other support hinged. Both supports at the same elevation. Frame 34: Single-leg, two-hinged rigid frame. Vertical leg. Horizontal girder. Skew corner. Frame 35: Single-leg, one-hinged rigid frame. Vertical leg. Horizontal girder, hinged at one end. Skew corner. Frame 36: Single-leg, one-hinged rigid frame. Vertical leg, hinged at bottom. Horizontal girder. Skew corner. Frame 37: Single-leg, two-hinged gable frame. Frame 38: Symmetrical fixed rectangular frame with hinged girder. Frame 39: Symmetrical rectangular two-hinged frame. Frame 40: Symmetrical rectangular frame with tie-rod, externally simply supported. Frame 41; Fully fixed symmetrical rectangular frame. Frame 42: Rectangular two-hinged frame with unequal moments of inertia of legs. Frame 43:Rectangular frame with tie-rod and unequal moments of the legs, externally simply supported. Frame 44: Fully fixed rectangular frame with unequal moments of inertia of the legs. Frame 45: Fixed rectangular frame with hinged kness and unequal-length legs. Frame 46: Two-hinged bent with legs of unequal length. Frame 47: Tied bent with inclined tie-rod. Externally simply supported. Frame 48: Hingeless bent with legs of unequal length. Frame 49: Bent with legs of unequal length. One support fixed, one support hinged. Frame 50: Symmetrical two-hinged bent with tie-rod at mid-height. Frame 51: Two-hinged bent with horizontal tie-rod at any elevation. Moments of inertia of legs change discontinuously at tie-rod elevation. Frame 52: Two-hinged rigid frame shed. Hinges at same elevation. Frame 53: Rigid frame shed with horizontal tie-rod. Externally simply supported. Frame 54: Two-hinged rigid frame shed. Hinges at different elevations. Frame 55: Rigid frame shed. One support fixed, one support hinged: supports at different elevations. Frame 56: Rigid frame shed. One support fixed, one support hinged: both supports at the same elevations. Frame 57: Rigid frame shed. One support fixed, one support hinged: supports at different elevations. Frame 58: Rigid frame shed. One support fixed, one support hinged: both supports at the same elevations. Frame 59: Rigid frame shed with fixed supports at different elevations. Frame 60: Rigid frame shed with fixed supports at the same elevation. Frame 61: Two-hinged bent with one skew corner. Hinges at different elevations. Frame 62: Tied bent with one skew corner and horizontal tie-rod. Externally simply supported. Frame 63: Two-hinged bent with one skew corner. Hinges at same elevation. Frame 64: Bent with one skew corner. One support fixed, one support hinged: supports at different elevations. Frame 65: Bent with one skew corner. One support fixed, one support hinged: supports at different elevations. Frame 66: Hingeless bent with one skew corner. Supports at different elevations. Frame 67: Hingeless bent with one skew corner. Both supports at the same elevation. Frame 68: Two-hinged shed. Frame 69 Externally simply supported shed with tie-rod. Frame 70: Two-hinged shed tie-rod at the eaves. Frame 71: Fully fixed shed. Frame 72: Fully fixed shed with tie-rod at the eaves. Frame 73: Symmetrical two-hinged, trapezoidal rigid frame. Symmetrical trapezoidal rigid frame with horizontal tie-rod. Externally simply supported. Frame 75: Symmetrical hingeless, trapezoidal rigid frame. Frame 76: Two-hinged trapezoidal rigid frame with legs of different slopes and lengths. Frame 77: Unsymmetrical trapezoidal rigid frame with horizontal tie-rod. Externally simply supported. Frame 78: Unsymmetrical two-hinged trapezoidal rigid frame. Hinges at same elevation. Frame 79: Trapezoidal rigid frame with legs of different slopes and lengths. One support fixed, one support hinged: supports at different elevations. Frame 80: Hingeless trapezoidal rigid frame with legs of different slopes and lengths. Supports at different elevations. Frame 81: Hingeless trapezoidal rigid frame with legs of different slopes and lengths. Supports at the same elevation. Frame 82: Two-hinged trapezoidal rigid frame with one vertical leg. Hinges at different elevations. Frame 83: Trapezoidal rigid frame with horizontal tie-rod and one vertical leg. Externally. Frame 84: Two-hinged trapezoidal rigid frame with one vertical leg. Hinges at same elevation. Frame 85: Trapezoidal rigid frame with one vertical leg, hinged at bottom. Other leg fixed. Supports at different elevations. Frame 86: Trapezoidal rigid frame with one vertical leg, fixed at bottom. Other leg hinged. Supports at different elevations. Frame 87: Hingeless trapezoidal rigid frame with one vertical leg. Supports at different elevations. Frame 88: Hingeless trapezoidal rigid frame with one vertical leg. Supports at same elevations. Frame 89: Symmetrical two-hinged, gable frame with vertical legs. Frame 90: Symmetrical gable frame with vertical legs and horizontal tie-rod. Externally simply supported. Frame 91: Symmetrical two-hinged gable frame with vertical legs and horizontal tie-rod at bottom of gable. Frame 92: Symmetrical hingeless gable frame with vertical legs. Frame 93: Symmetrical hingeless gable frame with vertical legs and horizontal tie-rod at bottom of gable. Frame 94: Symmetrical two-hinged gable frame with inclined legs.

Frame 95: Symmetrical gable frame with inclined legs and horizontal tie-rod. Externally simply supported. Frame 96: Symmetrical two-hinged gable frame with inclined legs horizontal tie-rod at bottom of gable. Frame 97: Symmetrical hingeless gable frame with inclined legs. Frame 98: Symmetrical hingeless gable frame with inclined legs and horizontal tie-rod at bottom of gable. Frame 99: Symmetrical two-hinged bent with skew corners. Frame 100: Symmetrical tied bent with skew corners. Externally simply. Frame 101 . Symmetrical tied bent with parabolic girder. Externally simply supported. Frame 102: Symmetrical two-hinged bent with parabolic girder and tie-rod under roof. Frame 103: Symmetrical hingeless bent with parabolic girder. Frame 104: Symmetrical vierendeel frame. Externally simply supported. Frame 105: Symmetrical square Vierendeel frame. Externally simply supported. All members having equal moments of inertia. Frame 106: Symmetrical Vierendeel frame on continuous elastic foundations. Frame 107: Symmetrical square Vierendeel frame on continuous elastic foundations. All members having equal moments of inertia. Frame 108: Unsymmetrical closed triangular rigid frame. Externally simply supported. Frame 109: Symmetrical closed triangular rigid frame. Externally simply supported. Frame 110: Equilateral closed triangular rigid frame. Externally simply supported. All members having equal moments of inertia. Frame 111: Vierendeel frames with two-axes of symmetry (cells), with or without non-yielding tie-rods and subject to uniform internal pressure only.

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