CalcHandbook

Fixed-Base Portal Frame — Horizontal Point Load at Eave

Frames · Fixed-Base Rectangular Portal · Horizontal Point Load at Eave (B) · Slope-deflection closed-form (sway)
1

Geometry, load and stiffness

Span, column height, horizontal point load at B, and section moments of inertia
m
m
kN
Define separate section inertia / elastic modulus for column and beam
Model: Supports A and D are FIXED (transmit both rotation and translation); joints B and C are rigid. P is applied horizontally exactly at B (left column-beam joint, eave level). This load case is NOT SYMMETRIC (unlike Type 3) — the frame SWAYS sideways; solved with slope-deflection. The two columns are assumed IDENTICAL, which gives H = P/2 (at each support, independent of kr), but Mbase, Mcorner and Rv do depend on kr.
2

Reactions and horizontal thrust

H, Rv
krbeam/column relative stiffness ratio (E·I) = EbIb·hEcIc·ℓ = — = —
Hat each support, opposing P — independent of kr = P2 = — = —kN
Rvat each support, vertical (force couple) = 3kr·Phℓ(1+6kr) = — = —kN
Why H is independent of kr but Rv is not: since the beam is axially rigid and the columns are identical, H = P/2 always holds (same mechanism as in Type 2). But because the fixed bases develop base moments, overturning equilibrium is now shared (partly) between Rv and the base moments — which makes Rv depend on kr. Uplift (tension) on the A side, compression on the D side.
3

Bending moments

Base (Mt) and corner (Mk) moments
Mtbase (A, D) — same magnitude at both = (1+3kr)·Ph2(1+6kr) = — = —kN·m
Mkcorner (B, C) — equal to Rv·ℓ/2 = 3kr·Ph2(1+6kr) = — = —kN·m
The column moment varies LINEARLY from Mt at the base to −Mk at the corner, and typically CHANGES SIGN within the column (inflection point) — a characteristic of swaying frames, unlike the non-sway behavior of Type 1 / Type 3. The beam moment varies linearly between −Mk at B and +Mk at C (same pattern as Type 2), passing through zero at midspan.
Bending Moment Diagram (M) — on the frame
4

Shear and axial force

V, N in the columns and beam — on the frame
Vcolumn (both, constant) · beam (constant, no distributed load) = H · Rv
Ncolumn AB (B side): Rv, tension · column CD (C side): Rv, compression · beam: H, compression = Rv · H
Shear Force Diagram (V) — on the frame
Axial Force Diagram (N) — on the frame