1. TENSION AND PRESSURE
TASK 1.
TASK:
The rigid beam shown in the figure is supported by three steel bars 1, 2 and 3 with the same cross-section of the same material. The vertical force applied to the structure is F = 170 kN. The material of the rods is steel S235. Permissible safety factor [S] = 1.5. Determine the required diameters of the rods. The rods are considered rigid. Do not take into account the weight of the rod and beam.
SOLUTION:
1. Determination of internal forces applied to the rods.
We compile a calculation scheme, which is a planar rod system.
The diagram shows which rods have tensile and which have compressive forces.
We construct equilibrium equations X = 0, Y = 0, MB = 0, MD = 0:
;
;
;
.
From the third equation we express MD = 0):
kN.
From the first equation X = 0) we express the relationship between the forces FN2 and FN3:
Take the fourth equation ( MB = 0) and replace (FN2 = 1.41FN3):
We publish:
kN.
Let’s take the found ratio (FN2 = 1.41FN3) and replace, we get:
kN.
CHECK: We enter the results obtained in the equation ( Y = 0):
2. Determination of required (essential) cross-sectional areas of rods.
The tensile and compressive strength conditions have the form σ = F / A ≤ [σ]. The actual voltage name must be equal to or slightly less than the allowable voltage. This is a control calculation formula. To obtain the design calculation formula, the actual stress is comparable to the allowable stress and the required (essential) cross-sectional areas of the published rods.
As the material is steel S235, the yield strength ReH = 235 MPa.
Permissible normal voltage [σ] = ReH / [S] = 235 / 1.5 = 157 MPa.
mm2;
mm2;
mm2.
3. Required dimensions of the rods.
Area of rod of circular cross-section:
Required dimensions of the rods:
mm;
mm;
mm.
ATTACHMENTS
esimene.jpg
teine.jpg
n__idis__lesanne_1.doc
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