Cantilever Beam Analysis with Shear and Moment Diagrams

The image presents the step-by-step structural analysis of a cantilever beam. The key equations and values derived are:

$$ \sum X = 0 \implies H_A = 0 $$

$$ \sum Y = 0 \implies V_A = 94 \text{ ton} $$

$$ (30 + 14 + 50) - V_A = 0 $$

$$ \sum M_A = 0 \implies M_A = 100.71 $$

$$ (44 \times 0.7) + (50 \times 1.4) - M_A = 0 $$

Section 1:

$$ H_1 = 0, V_1 = 94 \text{ ton}, M_1 = -100.71 \text{ tm} $$

Section 2:

$$ H_2 = 0, V_2 = 57 \text{ ton}, M_2 = -37.45 \text{ tm} $$

Section 3:

$$ H_3 = 0, V_3 = 50 \text{ ton}, M_3 = 0 $$

Rules:

- Kesme kuvveti (V) dikdörtgen ise M üçgen.

- V üçgen ise M 1. dereceden parabol.

- 1. derece ise V, M 2. dereceden parabol.

Soruda görsel içerik var: The image contains hand-drawn sketches of a beam analysis. Top left: A fixed-end cantilever beam with a distributed load q=10 t/m, a point load of 30t, and a point load of 50t. Below this are the Shear (N/V) and Bending Moment (M) diagrams. Right side: Step-by-step hand-written calculations for reactions (HA, VA, MA) and section forces (V1, M1, V2, M2, V3, M3). Left bottom: A list of rules explaining the relationship between load distribution, shear force shape, and moment diagram curvature (degree of polynomials). Bottom: A schematic drawing showing the beam with labels for points 1, 2, 3 and reaction force vectors.