Two Hinged Parabolic Arch

To compare the experimental values of horizontal reaction with the simplified theory.
To provide the influence line for this reaction.

APPARATUS

  • 1 HSC5m/f Dial Gauge Assembly
  • 1 HST501P Arch with Side Bracket*
  • 1 HST502 Track Plate Assembly with Dial Gauge
  • 1 HWH5 Reaction Load Hanger 2N
  •  7 HWH4 Load Hanger 1N
  • 1 HST405W Set of Weights

* Note

The parabolic arch has a uniform cross section 40 x 8mm and is made from mild steel. The span is 1m and the rise 0.2m. One hinged end is mounted on ball bearing rollers which run on a horizontal ground plate. Seven load hanger stirrups are attached to the arch at intervals of 0.125m (horizontally) across the span. A dial gauge indicates the horizontal displacement of the hinged end when load is applied to the arch. Provision is made for applying a horizontal thrust by adding loads to a hanger attached by a cord to the hinge. (Refer to Construction Appendix)

METHODOLOGY

PART 1: HORIZONTAL REACTION FOR POINT LOAD AT 3/8 SPAN

  1. With a load hanger on one of the stirrups near the middle of the arch, the dial gauge datum reading is noted at the moving hinge.
  2. 10N increments of vertical load are applied to the hanger up to a total not exceeding 50N.
  3. As each increment is added apply loads to the horizontal reaction hanger to restore the dial reading to the datum value, thus complying theoretical condition of zero displacement of the hinges.
  4. The horizontal reactions are recorded in Table 1.

PART 2: THEORETICAL REACTION FOR A UNIFORM LOAD

  1. With load hangers on all seven stirrups has been note the dial gauge datum.
  2. Placing 5N on each hanger has stimulated a uniform distributed load.
  3.  The horizontal reaction is found to give zero displacement of the moving hinge.
  4. The loading is increased to 10N per hanger and again the hinge is restored to its datum position.
  5. The results are recorded in Table 2.

PART 3: INFLUENCE LINE FOR H

  1. With all seven load hangers were still in the stirrups.
  2. The horizontal reaction is found for zero displacement as a 50N load is placed on each hanger in turn from left to right.
  3. The results are recorded in Table 3.
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