Example:

The concrete beam shown below is subjected to a tensile load of

60

kN. Determine the

elongation of the member when the temperature increases 2

0

˚C.

Note that the beam is symmetrically

loaded and reinforced.

Given

I

nformation:

Concrete

⁄

Steel

R

einforcement

⁄

Solution:

Calculated Properties:

(

)

An a

lternate equation to determine tangential modulus of elasticity of concrete:

√

√

Note:

tangential modulus

is used since the concrete is subjected to

a

small load

and hence small

deformation. It is understood that u

nder small deformations

(i.e. prior to cracking)

the

tangential modulus is more accurate than the secant modulus.

√

√

Note: concrete tensile stress is determined from

direct tensile test

.

(

)

(

)

(

)

(

)

EQUILIBRIUM:

Assume concrete does

not crack

Assume reinforcement does not yield

COMPATIBILITY:

Assum

e

perfect bond

ing

(reasonable)

N

N

200

200

4

No. 15M

3000 mm

(No shrinkage or

creep)

(

)

(

)

(

)

(

)

SUBSTITUTION:

(

)

(

)

(

)

(

)

(

)

(

)

CHECK ASSUMPTIONS:

Concrete does not crack

Steel reinforcement does not yield

Note:

Thermal effects should not be included in strain checks since they do not produce any

internal stress

es

. They would

only be considered

if the member is restrained from movement

(fixed).

CHECK INITIAL LOAD:

(

)

(

)

(

)

(

)

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