The frame supports the distributed load shown. Determine the state of stress acting at point E. Show the results on a differential element at this point. The section is composed of two materials where E₁ = 200 GPa, and E₂ = 150 GPa AC xxx E. 4 kN/m -1.5 m 1.5 m -3 m 3 m BA 20 mm 60 mm 20 mm 5 m E 50 mm E₁ = 200 GPa E₂ = 150 GPa

The frame supports the distributed load shown. Determine the state of stress acting at point E. Show the results on a differential element at this point. The section is composed of two materials where E₁ = 200 GPa, and E₂ = 150 GPa AC xxx E. 4 kN/m -1.5 m 1.5 m -3 m 3 m BA 20 mm 60 mm 20 mm 5 m E 50 mm E₁ = 200 GPa E₂ = 150 GPa

Materials Science And Engineering Properties

1st Edition

ISBN:9781111988609

Author:Charles Gilmore

Publisher:Charles Gilmore

Chapter9: Time, Temperature, And Mechanical Properties

Section: Chapter Questions

Problem 9.3P

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Concept explainers

Methods to Determine Vertical Stress

The load applied to the soil is transferred to the underground. The presence of water at soil pores and solid grains above the soil are the primary components that are responsible for the effective load transfer. Due to the load acting, the internal component of the soil or the underground formations undergoes deformations or a tectonic shift. The amount of deformation depends upon the amount of load acting on the soil surface, which indeed, depends on the weight of everything present above the soil. Due to this, the underground soil element develops internal stresses which try to resist the tectonic changes.

Question

The frame supports the distributed load shown. Determine the state of stress
acting at point E. Show the results on a differential element at this point. The
section is composed of two materials where E₁ = 200 GPa, and E₂ = 150 GPa
AC
xxxx
E.
4 kN/m
-1.5 m 1.5 m---
-3 m
3 m
BA
20 mm
60 mm
20 mm
5 m
E
50 mm
E₁
= 200 GPa
E₂ = 150 GPa

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Step 1: Draw the free body diagram

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Step 2: Equilibrium of vertical forces

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Step 3: Draw the free body diagram of section AE.

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Step 4: Equilibrium of horizontal forces

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Step 5: Calculation of moment of inertia

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Step 6: Calculation of normal stress

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Step 7: Calculation of shear stress

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Step 8: State of stress at point E

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