Lab Report: Analysis of Symmetrical Portal Frame

The primary objectives of this experiment were:

• To experimentally determine the horizontal reaction component at a support of a two-pinned symmetrical portal frame under vertical load
• To demonstrate that horizontal sway force is distributed equally between the two columns
• To compare experimental results with theoretical calculations using the moment distribution method

• Symmetrical Portal Frame Apparatus
• Dial Gauge
• Weight Hangers
• Slotted Weights (Various denominations)
• Stabilizing Loads

A portal frame is a rigid frame structure, and when its supports are pinned, it becomes a statically indeterminate structure. This means the reactions at the supports cannot be determined using static equilibrium equations alone.

In this experiment, the Moment Distribution Method is used for theoretical analysis. This is an iterative method used to solve for the moments in indeterminate structures. The process involves:

• Calculating distribution factors
• Determining fixed-end moments
• Distributing moments at each joint until equilibrium is reached

The experiment investigates two conditions:

No Sway Condition: The frame is prevented from moving horizontally (swaying) at the beam level. The horizontal reaction is measured as a vertical load is applied.

Side Sway Condition: The frame is allowed to sway, and an additional horizontal load is applied. The analysis involves superimposing the effects of the vertical load (no sway) and the horizontal sway force.

1. Stabilizing loads of 10 N and 2 N were applied to the designated hangers
2. The initial reading on the dial gauge was recorded
3. For the “No Sway” condition:
   • A vertical load was applied at the center of the beam (10 N, 20 N, 30 N, 40 N)
   • An additional horizontal force was applied until the dial gauge returned to its initial reading
   • The magnitude of this horizontal force was recorded as the horizontal reaction
4. For the “Side Sway” condition:
   • A horizontal load of 10 N was applied to induce sway
   • A vertical load of 25 N was simultaneously applied
5. The experimental results were plotted and compared with theoretical values

Case A: No Sway Condition

Initial Dial Gauge Reading: 6.08 mm

Theoretical Calculation (No Sway):

Using the moment distribution method for a vertical load of 25 N:

• Fixed End Moments (FEMs) were calculated for the beam BC
• Distribution Factors (DFs) at joints B and C were determined to be 0.5 for each member
• After moment distribution, the horizontal reaction at each support was calculated to be H_A = H_D = 2.78 N

Case B: Side Sway Condition

A vertical load of 25 N and a horizontal sway force of 10 N were applied.

Experimental Result: The total horizontal reaction measured at support D was 8.3 N.

Theoretical Calculation (Side Sway):

The final reactions were determined by superposition:

• Effect of Vertical Load (No Sway): Horizontal reaction = 2.78 N (acting inwards)
• Effect of Horizontal Sway Force (10 N): Shared equally between columns (5 N each acting outwards)
• Total Theoretical Reaction at D: 2.78 N + 5 N = 7.78 N

• For 25 N vertical load (no sway):
  • Experimental horizontal reaction: 3.0 N
  • Theoretical value: 2.78 N
• For side sway condition (25 N vertical + 10 N horizontal):
  • Experimental total reaction: 8.3 N
  • Theoretical total reaction: 7.78 N
• Percentage error for side sway condition: 6.68%

The experiment successfully determined horizontal reactions for a symmetrical portal frame under both no sway and side sway conditions. The experimental values closely matched theoretical values from the moment distribution method, with 6.68% error for combined loading.

Results confirmed that horizontal sway force is shared equally between columns in symmetrical frames. Discrepancies may be attributed to:

• Instrumental limitations (joint friction, roller resistance)
• Measurement errors during load application
• Assumptions in theoretical calculations

The experiment provided practical validation of theoretical methods for analyzing indeterminate portal frames.