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calculations and theory and applications of bending moment variation
Typology: Lab Reports
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To calculate the bending moment and compare it to the experimental value.
Beam is symmetrical in the plane along which bending occurs. Only linear elasticity (up to proportionality limit) is analyzed. Initially there is no deformation and there is no varying cross section. Cross section of the beam is still plane after and during bending. Appropriate proportions make it impossible for the beam to fail in any other way than because of bending (no buckling and so on).
The Structure Test Frame (STR3) Hardware the bending moment in a beam, Beam, rolling pivot, Grooved hangers, cut position, support pivot, Moment arm, Supports, Force Sensor, “Set Zero” control. Figure 1 : Bending Moment Variation away from the P.O.L. (STR1012).
1. Set up the equipment as illustrated in Figure 1 such that the cut will be 140 mm from right support 2. Zero the force gauge before hanging any weights. 3. Measure the total distance between two supports (Total L)
The bending moment at A is: MA = -3.924×0.14 = -0.549 Nm And the bending moment at the cut is: BMTheoritical = RB × ( 0.14 )=−1.249 × 0. BMTheoritical =−0.175 Nm Drawing the bending moment diagram:
The reactions at the supports are calculated using equilibrium equations:
The bending moment at A is: MA = -3.924×0.14 = -0.549 Nm At the point of application of the second mass: M 2 =−0.549+(−3.924 +6.154 ) × 0. M 2 =−0.0584 Nm And the bending moment at the cut is: BMTheoritical = RB × ( 0.14 )=−0.268 × 0. BMTheoritical =−0.0375 Nm Drawing the bending moment at the cut is:
And the bending moment at the cut is: BMTheoritical = RB × 0.14=2.051 × 0. BMTheoritical =0.287 Nm Drawing the bending moment diagram:
