A two-span continuous beam ABC is shown in Figure 5. Using matrix analysis, calculate the member end forces for member AB. Note: The beam member stiffness matrix is given below. 100 kN 59 kN/m В E 5m 8 m 5 m E= 200 GPa I= 500x106 mm4 %3D [Q] = [k] {u}+{Qr} [Q] = member end force vector %3D [k] = member stiffness matrix {u} = member end displacement vector {Q} = member fixed-end force vector 12EI 6EI -12EI 6EI L' 6EI 4EI 6EI 2EI L [k] = -12EI 6EI 12EI 6EI L L' 6EI 2EI 6EI 4EI L' L L L TTT

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Loads and Reactive Forces

Loads are the external influences that a beam experiences under its working conditions. For instance, a beam may be subjected to shear loads, twisting loads, bending moment, and axial loads during its working conditions. Engineers primarily deal with beams and trusses in the civil engineering domain. Due to the influence of loads, it is very crucial to determine the induced stresses and deformation values. These values give an insight into the critical area of the beam that needs to be worked upon to make it fail-safe.