DSVM42

Hydrostatic Pressure Applied on a Square Bar with Fully, Partially Submerged in a Fluid

Overview

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Reference:Any Basic Strength of Materials Book
Analysis Type(s):Static Structural Analysis
Element Type(s):Solid

Test Case

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Long bar 20m x 2m x 2m is immersed in a fluid and is fixed at one end. Fluid density is 1000 kg/m3 and Hydrostatic acceleration is 10 m/s2 in negative Z direction. Hydrostatic pressure is applied on a longitudinal face normal to X-axis at different locations as given in the scenarios below. Find normal stress in Z direction of square bar.

Scenario 1: Square bar is partially immersed in the fluid up to 15 m in Z direction from the fixed support.

Scenario 2: Square bar is fully immersed in the fluid up to 25 m in Z direction from the fixed support

Figure 42.1  Schematic

Material PropertiesGeometric PropertiesLoading
E = 2e11 Pa
γ = 0
ρ = 7850 kg/m3
Long bar = 20m x 2m x 2m
Hydrostatic Pressure Acceleration = -10 m/s2 (Z direction)
Surface Location:
Scenario 1: (2,1,5) m
Scenario 2: (2,1,-5) m

Analysis

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Scenario 1: Partialy Submerged (Pressure distribution in triangular form)

Pressure distribution on square bar in triangular form, one end is maximum and other end is zero

Pressure on square bar = P = ρ x g x h

Load per meter is w = P x L

Maximum bending moment =

Normal stress = Bending stress = Maximum bending moment / Sectional Modulus

Scenario 2: Fully Submerged (Pressure distribution in trapezoidal form)

Maximum bending moment =

where:

W1 = Maximum Load per meter (@ 25m)
W2 = Minimum Load per meter (@ 5m)
Normal stress = Bending stress = Maximum bending moment / Sectional Modulus

Results Comparison

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ResultsTargetDSError (%)
Normal Stress (Partially Submerged) (Pa)8.4375e68.4214e6-0.191
Normal Stress (Fully Submerged) (Pa)350e73.5241e70.689
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