Influence Lines for Determinate Structures - Examples & Applications

Construct the Influence Line for the vertical reaction at A ($R_A$) for a simply supported beam AB of length $L=10\text{ m}$.

Construct the Influence Line for Shear at point C (midspan, $x=5\text{ m}$).

Construct the Influence Line for the horizontal reaction at support B ($R_{Bx}$) of a simple gable frame using the quantitative method. The frame consists of two columns of height $h=4\text{ m}$ and two sloping roof members meeting at a central peak (total span $L=10\text{ m}$, peak height $6\text{ m}$). Support A is a pin and Support B is a pin. There is an internal hinge at the peak C.

Determine the absolute maximum shear ($V_{abs,max}$) in a simply supported beam of length $L=12\text{ m}$ subjected to a moving truck load consisting of three point loads: $P_1 = 40\text{ kN}$, $P_2 = 100\text{ kN}$ (spaced $3\text{ m}$ behind $P_1$), and $P_3 = 80\text{ kN}$ (spaced $4\text{ m}$ behind $P_2$).

Determine the absolute maximum bending moment ($M_{abs,max}$) in the same simply supported beam ($L=12\text{ m}$) subjected to the identical moving truck load ($P_1 = 40\text{ kN}$, $P_2 = 100\text{ kN}$, $P_3 = 80\text{ kN}$). The resultant is $R=220\text{ kN}$ located $3.91\text{ m}$ from $P_1$.