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analysis angle applied assumed axial bars bending calculate centre column complete plastiﬁcation compressive stress concrete beam couples cross-section dead load deﬂection diagonal tension direction displacement distance due to unit elastic equal external factor ﬁbres ﬁnd ﬁrst ﬁxed ﬁxed end ﬁxing ﬂange frame girder given in Fig horizontal Illustrative Problem inertia inﬂuence line left to right length live load maximum modulus negative neutral axis plane plastic hinge portal positive Pre-stressed Concrete principal stresses radians ratio reaction rectangular redundant reinforced concrete resultant right to left rotation shear stress shearing force simple beam slope span square inch statically indeterminate stirrups strain Strength of Materials stress diagram structure strut sway tensile stress theorem thrust tons per square tons-ft tons/sq uniformly distributed load unit load vertical wall yield stress zero