Stress & Safety Calculation for Girder w/ Temp Change

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In summary: E x coefficient of linear expansion x total strain + change in temp= 200x10 9 x 12x10-6 x 1.666x10-6 + 30 = 72 x 10 6In summary, the length of an unstressed girder is initially 1.2m at a temperature of 20 oC, but after a tensile load is applied, the temperature rises to 50 oC and the length becomes 1.202m. The calculated values are: (a) a tensile stress of 72 MN/m2 due to the applied load, (b) a factor of safety of 7.63 given a UTS of 550
  • #1
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Homework Statement


The length of a unstressed girder is found to be 1.2m at a temp of 20 oC. A tensile load is then applied and some time later the temp is 50 oC and the length of the girder 1.202m evaluate:
(a) the tensile stress due to the applied load in the girder.

(b) the factor of safety that is in operation if the UTS for the girder is 550MN/m2

(c) the strain and hence the change in length of the girder, if the temp remains at 20 oC

E = 200 GN/m2 coefficient of linear expansion = 12 x 10 - 6

Homework Equations



X = length x coefficient of linear expansion x change in temp

strain = coefficent of linear expansion x change in temp

stress = modulus of elasticity x coefficient of linear expansion x change in temp

stress = U.T.S/ F.S

The Attempt at a Solution


(a) stress = 200 x 10 9 x 12 x 10 - 6 x 30 oC ( this is from 50 oC- 20 oC = 30 oC)
= 72 MN/m2

(b) f.s = u.t.s/stress
550 x 10 6 / 72 x 10 6 = 7.63

(c) strain = coefficient of linear expansion x change in temp
12 x 10 -6 x 20 oC = 0.24 x 10 -3

if someone would be so kind to tell me if this correct it will be much appreciated.
 
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  • #2
This isn't quite right. The strain from the load and the strain from thermal expansion are additive. Try subtracting the thermal strain from the total strain to get the strain from the load only and using that to calculate the load.
 
  • #3
is this for part c or all of the question because i have taken away 50 oC - 20 oC = 30 oC
thanks for your reply.
 
  • #4
The problem is with part (a). What you have calculated is the stress that would exist in the girder if it were fixed at both ends and underwent a temperature increase of 30°C. But that's not what the question is looking for.
 
  • #5
This is what i did originally

stress/modulus of elasticity = coefficient of linear expansion x temp change - total strain
where modulus of elasticity = change in length / original length

= 0.02/1200 = 0.01666 x 10 -3 mm

therefore stress = E ( COEFFICIENT OF LINEAR EXPANSION X CHANGE IN TEMP - TOTAL STRAIN

200x10 9 x ( 12x10-6 x 30 - 0.01666 x 10 -3) = 68.668 x 10 6

i got told it was transposed wrong but don't no where just pulling my hair out now
 
  • #6
This is closer. The total strain is the thermal strain plus the strain from the load. You just need to express this correctly in equation form. Also, you've used a couple different length values (is the change in length 0.002m or 0.02mm?), so make sure to check that.
 
  • #7
so is this correct

stress = E ( coeffficient of linear expansion x change in temp + total strain

so stress = 200x10 9 x 12 x 10-6 x 30 + 1.666x10-6 = 72 x 10 6
 
  • #8
No. Read my posts again.
 
  • #9
try again

stress = E x coefficient of linear expansion x total strain + change in temp

transposition arhh
 

1. What is the purpose of stress and safety calculations for girders with temperature changes?

The purpose of these calculations is to ensure the structural integrity and safety of the girders under varying temperature conditions. It allows engineers to determine the maximum stress and strain that the girder can withstand without failure, and to ensure that safety factors are met.

2. How do temperature changes affect the stress and safety of girders?

Temperature changes can cause thermal expansion or contraction of the girder, leading to changes in stress and strain. This can potentially result in buckling, bending, or other forms of failure. Therefore, it is important to consider these effects in the design and construction of girders.

3. What factors are taken into account when calculating stress and safety for girders with temperature changes?

Some of the factors that are considered include the material properties of the girder, the magnitude and rate of temperature changes, the geometry and structural configuration of the girder, and the boundary conditions. Other factors such as the type of loading and environmental conditions may also be taken into account.

4. How are stress and safety calculations for girders with temperature changes performed?

These calculations are typically performed using structural analysis software or by hand using equations and formulas based on engineering principles. Finite element analysis may also be used to model the behavior of the girder under varying temperature conditions.

5. What are some common safety measures used to mitigate the effects of temperature changes on girders?

Some common safety measures include using materials with low thermal expansion coefficients, providing proper support and bracing to prevent buckling, and incorporating expansion joints to allow for movement without causing excessive stress. Regular inspections and maintenance can also help identify and address any potential issues related to temperature changes.

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