Statics and Stress: Calculate the stresses?

Watch this thread
lilminster
Badges: 8
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#1
Report Thread starter 5 years ago
#1
A 1.2m long concrete beam has a cross-sectional area of 0.05m2.

The beam is reinforced by 4 embedded steel bars, each 19mm in diameter, as shown in Figure Q5.

Calculate the stresses in the steel and concrete when a tensile load of 250kN
is applied to the beam.

For concrete E = 25GPa, steel E = 210GPa.

Please help!

Figure Q5:
https://www.dropbox.com/s/5buqh1chm1...pture.JPG?dl=0
0
reply
pleasedtobeatyou
Badges: 18
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#2
Report 5 years ago
#2
(Original post by lilminster)
A 1.2m long concrete beam has a cross-sectional area of 0.05m2.

The beam is reinforced by 4 embedded steel bars, each 19mm in diameter, as shown in Figure Q5.

Calculate the stresses in the steel and concrete when a tensile load of 250kN
is applied to the beam.

For concrete E = 25GPa, steel E = 210GPa.

Please help!

Figure Q5:
https://www.dropbox.com/s/5buqh1chm1...pture.JPG?dl=0
From equilibrium in the axial direction:

P = \int_A \sigma \ dA.

Discretise the integral in terms of the steel and concrete volume fractions:

P = \int_{\text{steel}} \sigma_s \ dA_s + \int_{\text{concrete}} \sigma_c \ dA_c.

The final two steps are trivial. Use the equation \sigma = E \epsilon and the fact that the strain must be identical in both constituents and you should get very close to your answer.
1
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest

How confident are you that you'll achieve the grades you need to get into your firm uni?

I think I've exceeded the grades for my university offer (20)
16.95%
I think I've met the grades for my university offer (31)
26.27%
I think I've missed the grades for my university offer (63)
53.39%
Something else (tell us in the thread) (4)
3.39%

Watched Threads

View All