Respuesta :
The shear and moment throughout the beam as functions of x are V = ( 30 - 2x ) kip and M = ( - x² + 30 x - 216 ) kip ft for 0 ≤ x ≤ 6 ft and V = 8 kip and M = ( 8 x - 120 ) kip ft for 6 ≤ x ≤ 10 ft
What is meant by shear and moment?
The ability to construct shear force diagrams (SFD) and bending moment diagrams (BMD) is essential for any student studying statics, mechanics of materials, or structural engineering. Both a long and a short route can be used to complete them. The extended method is more thorough and yields formulas for the internal shear and internal bending moments in beams in terms of x: V(x) and M(x), respectively. In introductory statics classes, this is typically the approach required to demonstrate understanding of the situation. The rapid method eliminates the need for calculations in terms of x and instead employs a more visual method that you may use to highlight the crucial areas on the diagrams before simply connecting the dots.
How to solve?
For 0 ≤ x ≤ 6 ft,
∑ Fy = 0
30 - 2 x - V = 0
V = ( 30 - 2x ) kip
∑M = 0
M + 216 + 2 x ( x / 2 ) - 30 x = 0
M = ( - x² + 30 x - 216 ) kip ft
For 6 ≤ x ≤ 10 ft,
∑ Fy = 0
V - 8 = 0
V = 8 kip
∑ M = 0- M - 8 ( 10 - x ) - 40 = 0
M = ( 8 x - 120 ) kip ft
the shear and moment throughout the beam as functions of x are :
V = ( 30 - 2x ) kip and M = ( - x² + 30 x - 216 ) kip ft for 0 ≤ x ≤ 6 ft
V = 8 kip and M = ( 8 x - 120 ) kip ft for 6 ≤ x ≤ 10 ft
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