**Problem Statement**Use the area moment method for this problem: Separate M/EI diagram for the point load, and the uniformly distributed load. Then superimpose.**Figure Analysis:**- **Task**: Determine the slope and deflection at point A of the cantilevered beam.- **Material Properties**: - Modulus of Elasticity, \( E = 29(10^3) \) ksi - Moment of Inertia, \( I = 245 \, \text{in}^4 \)**Beam Description:**- **Supports**: Cantilevered at point B- **Loads**: - Uniformly distributed load of \( 2 \, \text{kip/ft} \) over a length of 3 feet from point B. - Point load of 3 kips at point A.- **Dimensions**: - Total length of 6 feet, with sections from B to the midpoint and midpoint to A each measuring 3 feet.**Diagram**- The beam is shown with arrows indicating the distributed and point loads.- The diagram is labeled from B to A, demonstrating the placement of the loads and the dimensions along the beam.

Given data: E=29×103 ksi I=245 in4Determining slope and deflection at A. Moment area method: M/EI diagram for point load and UDL. Centroid distances: for diagram 1:x1=23×6=4 ftfor diagram 2:x2=3+34×3=5.25 ft Slope at A: θA-θB=area of M/EI diagram between A&B.θA-θB=-12×18EI×6-13×9EI×3θA-θB=-63EIAs we know slope at fixed support is zero. θB=0θA=-63EI EI=29×103×245 k.in2EI=49340.278 k.ft2θA=-6349340.278 θA=1.2768×10-3 rad (clock-wise) Deflection at A. δA-δB=moment of area of M/EI diagram between A&B, about AδA-δB=-12×18EI×6×23×6-13×9EI×3×5.25δA-δB=-263.25EIAs we know deflection at fixed support is zero. δB=0δA=-263.25EIEI=29×103×245 k.in2δA=-263.25×12×12×1229×103×245δA=0.064 in down ward

Engineering

Civil Engineering

Use area moment method for this problem: Separate M/El diagram for the point load, and the uniformly distributed load. Then superimposed. F12-10. Determine the slope and deflection at A of the cantilevered beam. E 29(10°) ksi, / = 245 in". 3 kip 2 kip/ft B 3 ft 3 ft-

Use area moment method for this problem: Separate M/El diagram for the point load, and the uniformly distributed load. Then superimposed. F12-10. Determine the slope and deflection at A of the cantilevered beam. E 29(10°) ksi, / = 245 in". 3 kip 2 kip/ft B 3 ft 3 ft-

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Beams

In structural engineering, a beam is a component made of a variety of materials (including steel alloys, and wood) that can resist loads applied laterally to the beam axis. Members, elements, rafters, shafts, and purlins are all terms used to describe beams.

Question

**Problem Statement**

Use the area moment method for this problem: Separate M/EI diagram for the point load, and the uniformly distributed load. Then superimpose.

**Figure Analysis:**

- **Task**: Determine the slope and deflection at point A of the cantilevered beam.
- **Material Properties**:
- Modulus of Elasticity, \( E = 29(10^3) \) ksi
- Moment of Inertia, \( I = 245 \, \text{in}^4 \)

**Beam Description:**

- **Supports**: Cantilevered at point B
- **Loads**:
- Uniformly distributed load of \( 2 \, \text{kip/ft} \) over a length of 3 feet from point B.
- Point load of 3 kips at point A.
- **Dimensions**:
- Total length of 6 feet, with sections from B to the midpoint and midpoint to A each measuring 3 feet.

**Diagram**

- The beam is shown with arrows indicating the distributed and point loads.
- The diagram is labeled from B to A, demonstrating the placement of the loads and the dimensions along the beam.

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