Problem 3 The plan and elevation of an earth retaining structure used for support excavation is shown in Figs. 2 and 3 respectively. The retaining structure is made of wood planks supported in the horizontal direction on vertical steel piles (HP sections). The HP piles shape of an H and are typically used for piles. The section properties of these sections (A, I, S, etc...) are given in Part 1 of the AISC steel manual. The spacing of the supporting HP piles is 20ft. The height of the piles is 15 from top of the pile to top of the footing. The height of the water table from the top of the footing is 9 ft as shown in the elevation in Fig. 3. The pile height and soil properties and the earth pressure distribution behind the retaining structure are shown in Fig. 3. Figs. 4 shows the equations for earth pressure. q is a live load surcharge that accounts for traffic on top of the embankment; q is typically assumed to be 250 psf (per AASHTO). Use Fy- 50 ksi Required 1. Determine the maximum horizontal force at the bottom of a typical interior HP pile due to lateral earth pressures and the live load on top of the embankment. 2. Determine the maximum moment at the bottom of a typical interior HP pile due to lateral earth pressures and the live load on top of the embankment. 3. If the maximum stress due to bending at the bottom of a typical interior HP pile cannot exceed 0.66Fy, what should be the minimum required section modulus Sx of the HP pile? What is the lightest HP pile that can be used? 4. If the maximum stress due to shear at the bottom of a typical interior HP pile cannot exceed 0.3Fy, what should be the minimum required web area (dx tw) of the HP pile? What will be the factored LRFD horizontal force and bending moment? (use the 5. values obtained from parts 1 and 2 and use load factor of 1.6 for earth pressure and 1.75 for live load). 6. If the section used was HP16x162, what would the deflection at top of pile? 20 L 1 typical HP interior pile Y=120 pf Kau32 Yet 140 pet Ka=0.82 K₂YH₂ Y = 120 paf (16/ft³) Ka 0.32 Ka 0,32 Fig 2-PLAN = 140 pcf Saturated soil pef}* Compressed Fig 3-3D View Yu H₂ ZZZZZZZZ Ka Oki Xu) H₂ F₁ 20 K₂9 Fig 4-Lateral earth pressure forces, live load surcharge forces wood plank 5. KYH, H, L F3 azka (Vst-√w) H₂ L F4- X H₂ L Fs. K.q (H₁+H₂) 1 H₁5 H₂ th F₁ is located at y = H₂ + H₂/3 from bottom Fo is located at yo Fs is located at y= H₂/₂ Fa is located at yo H₂/3 Fs is located at y = (H₁+ H₂)/₂ A F4 ********* 5 F KTH 9 K₂ (X-X) H₂ Fig 5- Equations for lateral earth pressure forces and live load surcharge forces