ROBO240 Mechanics and Material, Assignment 1 Winter 2018 The above Engine Hoist
ID: 1767163 • Letter: R
Question
ROBO240 Mechanics and Material, Assignment 1 Winter 2018 The above Engine Hoist is designed by Strongway Hydraulic, the Hoist is made of steel and You are going to design different parts of the design based on what we have learnt to this point. For simplification you are assuming a 2D version of hoist as shown here: E Pin D-pin F-1000kg F-pin B (roller) A (roller) Figure "B" Part1-a: For the current setup shown in figure "A", is the structure: 1. Fully constrained 2. Partially constrained 3. UnconstrainedExplanation / Answer
Q1a. It is partially constrained
Q1b. It is statically indeterminate
In statics, a structure is statically indeterminate (or hyperstatic)[1] when the static equilibrium equations are insufficient for determining the internal forces and reactions on that structure.
Based on Newton's laws of motion, the equilibrium equations available for a two-dimensional body are
{displaystyle sum { ec {F}}=0} [sum { ec F}=0] : the vectorial sum of the forces acting on the body equals zero. This translates to
H = 0: the sum of the horizontal components of the forces equals zero;
V = 0: the sum of the vertical components of forces equals zero;
{displaystyle sum { ec {M}}=0} [sum { ec M}=0] : the sum of the moments (about an arbitrary point) of all forces equals zero.
Free body diagram of a statically indeterminate beam.
In the beam construction on the right, the four unknown reactions are VA, VB, VC and HA. The equilibrium equations are:
V = 0:
VA Fv + VB + VC = 0
H = 0:
HA = 0
MA = 0:
Fv · a VB · (a + b) - VC · (a + b + c) = 0.
Since there are four unknown forces (or variables) (VA, VB, VC and HA) but only three equilibrium equations, this system of simultaneous equations does not have a unique solution. The structure is therefore classified as statically indeterminate. Considerations in the material properties and compatibility in deformations are taken to solve statically indeterminate systems or structures.
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