## Semi-rigid joints in modeling of structures

The effects of the behaviour of the joints on the analysis of the structures should generally be taken into account. To identify whether the effects of joint behaviour on the analysis needs to be taken into account, three simplified joint models are distinguished:
• Simple (joint may be assumed not to transmit bending moments)
• continuous (joint may be assumed to have no effect on the analysis
• semi-continuous (joint needs to be taken into account in the analysis)
The joints should have sufficient strength to transmit the forces and moments acting at the joints resulting from the analysis. A joint may be classified as rigid, pinned or semi-rigid, according to its rotational stiffness, by comparing its initial rotational stiffness Sj,ini with the classification boundaries. A joint which does not meet the criteria for a rigid joint or a pinned joint, should be classified as a semi-rigid joint. Semi-rigid joints provides a predictable degree of interaction between members, based on the design moment-rotation characteristics of the joints.

In the case of a semi-rigid joint, the rotational stiffness Sj corresponding to the bending moment Mjed should generally be used in the analysis. If Mjed does not exceeds 2/3 of Mjrd, the initial rotational stiffness Sj,ini may be taken in the global analysis.

Rules for the determination of Sj,ini for joints connecting H or I sections are given in EC3-1-8 6.3.1.
Rules for the determination of Sj,ini for joints connecting hollow sections are not given in EC3.

Classification of joint stiffness

ConSteel and csJoint calculates the Sj,ini stiffness for semi-rigid joints with connecting H or I sections. The picture below shows the csJoint interface of a beam-to-beam end plate joint:
1. Value of initial stiffness is Sjini=26375 kNm/rad. This value is equal to 0,848Sb (the measure of         semi-rigidity is 77,5%) where Sb is the boundary value for rigid joint.

2. The moment resistance is Mjrd=33,7 kNm
The joint is loaded by Myed=40kNm
The resistance of the cross-section is Mcrd=86,2

3. The moment resistance (Mjrd) is greater than the design bending moment (Myed), but smaller than     the cross-section resistance. Consequently, the joint is partial strength.

Transfer of joint stiffness into the structural model

The stiffness of semi-rigid joints should be taken into consideration in the structural model. For elastic analysis, the stiffness of a joint can be approximated by a linear rotational spring with characteristic Sj,ini placed at the joint.

In ConSteel, spring characteristics can be defined at the end of the bar members.
The spring characteristic is associated with a release object at the end of a member. A release object contains seven spring characteristics (7 Dots Of Freedom). The spring characteristic of a semi-rigid joint corresponds to the qdegree of freedom (in our case, yy means the appropriate degree of freedom)kNm
(stiffness=Sj,ini/h=26375/3=8791kNm EC3-1-8 Table20.)

The spring characteristic can be built into the structural model by an "automatic" way. To do this, the created joint should be Placed at the node where the joint is situated.

The "automatic" procedure has the following steps:
1. Create the joint by csJoint
2. Save the joint model and close csJoint
3. "Place..." the joint model at the appropriate node of the structural model (picture above)
4. Run structural analysis
5. Open csJoint and select the joint model
6. Check the resistance of the joint

In step3 the spring characteristic is built into the structural model. In step 4 the analysis will include the effect of the joint stiffness (unless it was required in the "set analysis parameters" dialog). In step 5 the csJoint reads the design forces in order to check the joint.

Deflection of the beam without the stiffness of the joint:

Deflection of the beam with the effect of semi-rigidity:

More technical description can be found in ConSteels's user manual