Portal Rigid Plane Frame Analysis

Direct Stiffness Method — Fixed or Pinned Bases (Metric Units)

1  Joint Coordinates
Jointx (m)y (m)
1
2
3
4
Figure 1 — Portal frame geometry, loading & member numbering (interactive)
2  Support Constraints
JointCondition
1 (base left)
4 (base right)

Joints 2 and 3 are free (internal joints). Members: 1→2, 2→3, 3→4.

3  Member Properties
MbrE (MPa)A (cm²)I (cm⁴)L (m)
1—
2—
3—
4  Loading
4.1  Joint Loads
JointPx (kN)Py (kN)Mz (kN·m)
1
2
3
4
4.2  Distributed Loads on Members
MbrDirectionb/Lwb (kN/m)e/Lwe (kN/m)
1
2
3
5  Support Reactions
JointRx (kN)Ry (kN)Mz (kN·m)
1———
4———
6  Member End Forces
MbrJointAxial (kN)Shear (kN)Moment (kN·m)
11———
2———
22———
3———
34———
3———
7  Maximum Moments per Member
MbrTypeM (kN·m)Location (m)
1+M(max)——
−M(max)——
2+M(max)——
−M(max)——
3+M(max)——
−M(max)——
8  Joint Displacements
JointDx (mm)Dy (mm)θz (rad)θz (deg)
1————
2————
3————
4————
9  Bending Moment Diagram
Figure 2 — Bending moment diagram (kN·m) — drawn on tension side
Maximum Absolute Moment
— kN·m
Location
—
Reference: Matrix Structural Analysis — Direct Stiffness Method for 2D Rigid Frames