Initial Stress/Strain (Temperature, etc.)

Load Types > Initial stress/strain

Parent topic: RM Bridge - Load Types Library

Related concepts	Related reference
RM Bridge - Load Types Library	Load type > Primary Stress in Point Temperature loading (T) Structure > Elements > Time Action > TempVar Cable shortening by force (FX0)

Primary Stress in Point – load type TSTR0

Load Type	Description
TSTR0	Specification of primary longitudinal stresses for stress points. This load type is normally automatically created by the action TempVar and not for user input. However, user input is possible (e.g. for entering initial stresses due to welding, cooling of rolled shapes or hydration heat of thick concrete parts).

Temperature load – load type T

The temperature load creates a thermal strain in the beam element. The product of the material coefficient of thermal expansion and the temperature change gives this strain. In accordance with the beam theory without warping, the temperature strain may vary linearly over the cross-section. This variation is described by 3 components of the temperature change:

The temperature change part being constant over the cross-section (DT-G).
The temperature gradient in the local y-direction (TG_y).
The temperature gradient in the local z-direction (TG_z).

Note: The program does not offer the possibility to enter an initial temperature (i.e. the temperature characterizing the initial stress-less state). All temperature values such as DT-G or the temperatures assigned to cross-section Temperature Points are therefore not absolute values but differences with respect to the initial temperature of the structure. The average environment temperatures assigned to the elements in Element Time are not considered for the calculation of the temperature loading (only for creep and shrinkage).

The variation of the temperature load in longitudinal direction (over the element length) is always assumed constant over the whole element length. A suitable subdivision of the structure into small elements with constant temperature must be made to simulate essentially varying temperatures in beam longitudinal direction.

Input parameters:

Setting	Description
Alpha	Temperature expansion coefficient to be used. In the case of no input, the according values are taken from the material table. The value is approximately 1.0E-5 [1/°C] for all steel and concrete types, but some design codes require slightly different values to be used. Note: In the case of reinforced or pre-stressed concrete analyses it is always assumed, that steel and concrete have the same expansion coefficient and no internal primary stresses occur due to constant or linearly distributed temperature changes. The coefficient value assigned to the reinforcement or pre-stressing steel material is therefore never used, except for external sections of pre-stressing tendons treated like structural elements.
DT-G	DT-G Temperature change with respect to the stress-less or a previous state, which is constant over the cross section and produces only axial strains. Example: DT-G = +20°C and DT-Y = 0°C

Setting

Description

Alpha

Temperature expansion coefficient to be used. In the case of no input, the according values are taken from the material table. The value is approximately 1.0E-5 [1/°C] for all steel and concrete types, but some design codes require slightly different values to be used.

Note: In the case of reinforced or pre-stressed concrete analyses it is always assumed, that steel and concrete have the same expansion coefficient and no internal primary stresses occur due to constant or linearly distributed temperature changes. The coefficient value assigned to the reinforcement or pre-stressing steel material is therefore never used, except for external sections of pre-stressing tendons treated like structural elements.

DT-G

DT-G Temperature change with respect to the stress-less or a previous state, which is constant over the cross section and produces only axial strains.

Example: DT-G = +20°C and DT-Y = 0°C

The temperature gradients (TG_y, TG_z), and consequently the related strain gradients (κ_y) and (κ_z), are specified by value pairs of temperature difference and related length or width (DT-Y, H-Y and DT-Z, H-Z respectively).

Setting	Description
DT-Y, H-Y	Temperature difference DT-Y and related height H-Y, describing the temperature gradient TG_y= DT-Y/H-Y in the local y-direction, producing only bending strains in the X-Y plane.
DT-Z, H-Z	Temperature difference DT-Z and related height H-Z, describing the temperature gradient TG_z= DT-Z/H-Z in the local z-direction, producing only bending strains in the X-Z plane.

Note: Temperature gradients are specified as the change in temperature per unit length. The related temperature difference is positive if the temperature increases in the positive direction of the local axis. The related temperatures are assumed zero at the cross-section centroid.

Example 1

T_TOP=-35°C

T_BOTTOM=+20°C

H-Y=1.0

H-TOP=0.4

H-BOTTOM=0.6

DT-Y=T_TOP-T_BOTTOM=-35-(+20)=-55°C

D T - G = T_{B O T} + \frac{(T_{T O P} - T_{B O T})}{H - Y} \cdot H_{B O T}

=> DT-G=20 + (-35-20)*0.6/1.0 = -13°C

Example 2

T_TOP=+30°C

T_BOTTOM=+10°C

H-Y=1.0

H-TOP=0.3

H-BOTTOM=0.7

DT-Y=T_TOP-T_BOTTOM=+30-(+10)=+20°C

D T - G = T_{B O T} + \frac{(T_{T O P} - T_{B O T})}{H - Y} \cdot H_{B O T}

=> DT-G=+10+(+30-10)*0.7/1.0= 24°C

Some design codes require a non-linear variation of the temperature over the cross-section to be investigated (e.g. AASHTO). RM Bridge offers a possibility to take this demand into account by defining the temperature distribution in the cross-section very detailed and selecting the function TempVar to calculate the appropriate integrals characterizing the equivalent uniform temperature change and the gradients. This function is described in detail in section TempVar.

Cable shortening defined by an equivalent force – load type FX0

Load Type	Description
FX0	Equivalent normal force in the element; a stress-free element length differing from the system length is assigned to the element by specifying the equivalent normal force Fx required for yielding this length difference. The effect of this load type is identical to LX0. At first, the stress-free length LX0 = LX / (1+Fx/(E×A) is internally computed by using the specified normal force Fx. Then the program proceeds in the same manner than for load type LX0.

Load Type

Description

FX0

Equivalent normal force in the element; a stress-free element length differing from the system length is assigned to the element by specifying the equivalent normal force Fx required for yielding this length difference. The effect of this load type is identical to LX0. At first, the stress-free length LX0 = LX / (1+Fx/(E×A) is internally computed by using the specified normal force Fx. Then the program proceeds in the same manner than for load type LX0.

Secondary component – bending part – load type TB

Load Type	Description
TB	This and the ensuing 3 Load Types define strain states linearly distributed over the element length. These strain states are defined by specifying equivalent internal force states. The total strain state is separated in a bending part (TB) and a shear part (TS). A "primary" part can in addition be specified (TB0, TS0).

The input parameters related to the bending part are the normal force and the 2 bending moments at the start and end points of the elements. The represent the longitudinal strain ε_s in the center of gravity and the bending strains χ_y and χ_Z (gradients of longitudinal strains in y and z directions).

The shear part is specified by the torsional moment and the 2 shear forces, representing the respective shear strain components.

Both, bending and shear part may be separated in a "secondary part", which causes reactions of the structural system, and a "primary part", which characterizes the non-linearity of the strain distribution over the cross-section. The related internal forces (stress integrals over the cross-section) are internally in equilibrium on the cross-section level.

The load type TB describes the secondary part of the bending strain. Loading definitions of this type with the respective parameters are automatically generated in the schedule action TempVar in case of calculating the effects of a non-linear temperature loading. They are written into the corresponding load sets and can be viewed in the GUI after this schedule action has been successfully performed.

Using the load types TB, TB0, TS, TS0 for directly defining equivalent strain states requires a deeper insight and is not recommended in practical applications.

Secondary component – shear part – load type TS

Load Type	Description
TS	Secondary shear-part of the strain state; this part occurs theoretically in the case of temperature loading varying in the longitudinal direction. For modeling the effects of non-linear temperature in TempVar it is seldom generated (only if the cross-sections at the start and end of the element are different). Shear forces only arise due to equilibrium conditions if the end moments related to the temperature gradient are different on both ends of the element.

Load Type

Description

Secondary shear-part of the strain state; this part occurs theoretically in the case of temperature loading varying in the longitudinal direction. For modeling the effects of non-linear temperature in TempVar it is seldom generated (only if the cross-sections at the start and end of the element are different). Shear forces only arise due to equilibrium conditions if the end moments related to the temperature gradient are different on both ends of the element.

Primary component – bending part – load type TB0

Load Type	Description
TB	The primary part is also defined in terms of internal forces, although it characterises an internal equilibrium state. The fictitious internal force characterising this state is defined to be the force producing the correct stress in 2 points of the cross-section (the upper and lower edge). This part is generated in the case of non-linear temperature calculation, if the option Include Primary TempVar effects has been selected in the Recalc pad.

Load Type

Description

The primary part is also defined in terms of internal forces, although it characterises an internal equilibrium state. The fictitious internal force characterising this state is defined to be the force producing the correct stress in 2 points of the cross-section (the upper and lower edge). This part is generated in the case of non-linear temperature calculation, if the option Include Primary TempVar effects has been selected in the Recalc pad.

Primary component – shear part – load type TS0

Normally not existent

Stress-free element lenght - load type LX0

Load Type	Description
LX0	Stress-free "fitting"-length; a stress free element length LX0 other than the system length is assigned to the element. The initial strain required for yielding the elongation, characterised by the difference between the specified length and the system length, is calculated. This strain is applied in the same manner than a temperature change DT-G. The stress-free length LX0 is used as well for determining the initial strain (ε₀ = (LX0-LX)/LX0) and the related end force FX0 = E×A× ε₀ , as for calculating the linear normal force stiffness (E×A / LX0).

Load Type

Description

LX0

Stress-free "fitting"-length; a stress free element length LX0 other than the system length is assigned to the element.

The initial strain required for yielding the elongation, characterised by the difference between the specified length and the system length, is calculated. This strain is applied in the same manner than a temperature change DT-G. The stress-free length LX0 is used as well for determining the initial strain (ε₀ = (LX0-LX)/LX0) and the related end force FX0 = E×A× ε₀ , as for calculating the linear normal force stiffness (E×A / LX0).

Both load types LX0 and FX0 correspond physically to the installation process of a pre-stressed cable stressed in a pre-stressing bed (not against the system). (The load type FCAB simulates stressing against the system). This pre-stressed element is installed in the actual system. The actual distance between the connection points characterises the length in the fully (with Fx) pre-stressed state. LX0 is the length arising in the case that the connection to the system is dropped. The calculation process simulates removing the pre-stressing bed. The pre-stressing forces are then acting on the system at both connection points. The system will give way and the resulting force in the cable will be (more or less, depending on the system stiffness) smaller than the specified fixed end value Fx.